├── .gitignore
├── LICENSE
├── Makefile
├── README.md
└── src
├── base32.c
├── base32.h
├── crypto_hash_sha512.c
├── crypto_hash_sha512.h
├── crypto_int32.h
├── crypto_int64.h
├── crypto_sign.h
├── crypto_uint32.h
├── crypto_uint64.h
├── crypto_verify_32.c
├── crypto_verify_32.h
├── horse25519.c
└── ref10
├── api.h
├── base.h
├── base2.h
├── d.h
├── d2.h
├── fe.h
├── fe_0.c
├── fe_1.c
├── fe_add.c
├── fe_cmov.c
├── fe_copy.c
├── fe_frombytes.c
├── fe_invert.c
├── fe_isnegative.c
├── fe_isnonzero.c
├── fe_mul.c
├── fe_neg.c
├── fe_pow22523.c
├── fe_sq.c
├── fe_sq2.c
├── fe_sub.c
├── fe_tobytes.c
├── ge.h
├── ge_add.c
├── ge_add.h
├── ge_double_scalarmult.c
├── ge_frombytes.c
├── ge_madd.c
├── ge_madd.h
├── ge_msub.c
├── ge_msub.h
├── ge_p1p1_to_p2.c
├── ge_p1p1_to_p3.c
├── ge_p2_0.c
├── ge_p2_dbl.c
├── ge_p2_dbl.h
├── ge_p3_0.c
├── ge_p3_dbl.c
├── ge_p3_to_cached.c
├── ge_p3_to_p2.c
├── ge_p3_tobytes.c
├── ge_precomp_0.c
├── ge_scalarmult_base.c
├── ge_sub.c
├── ge_sub.h
├── ge_tobytes.c
├── keypair.c
├── open.c
├── pow22523.h
├── pow225521.h
├── sc.h
├── sc_muladd.c
├── sc_reduce.c
├── sign.c
└── sqrtm1.h
/.gitignore:
--------------------------------------------------------------------------------
1 | *.swp
2 | *~
3 | *.o
4 | /horse25519
5 |
--------------------------------------------------------------------------------
/LICENSE:
--------------------------------------------------------------------------------
1 | This is free and unencumbered software released into the public domain.
2 |
3 | Anyone is free to copy, modify, publish, use, compile, sell, or
4 | distribute this software, either in source code form or as a compiled
5 | binary, for any purpose, commercial or non-commercial, and by any
6 | means.
7 |
8 | In jurisdictions that recognize copyright laws, the author or authors
9 | of this software dedicate any and all copyright interest in the
10 | software to the public domain. We make this dedication for the benefit
11 | of the public at large and to the detriment of our heirs and
12 | successors. We intend this dedication to be an overt act of
13 | relinquishment in perpetuity of all present and future rights to this
14 | software under copyright law.
15 |
16 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
17 | EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
18 | MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
19 | IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR ANY CLAIM, DAMAGES OR
20 | OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE,
21 | ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
22 | OTHER DEALINGS IN THE SOFTWARE.
23 |
24 | For more information, please refer to
25 |
--------------------------------------------------------------------------------
/Makefile:
--------------------------------------------------------------------------------
1 | CFLAGS := -O2 -g -Wall -Werror -Wno-error=deprecated-declarations -Wextra -I./src -DNDEBUG
2 | LDFLAGS := -lcrypto -lpthread
3 |
4 | SRCS = src/ref10/fe_0.c \
5 | src/ref10/fe_1.c \
6 | src/ref10/fe_add.c \
7 | src/ref10/fe_cmov.c \
8 | src/ref10/fe_copy.c \
9 | src/ref10/fe_frombytes.c \
10 | src/ref10/fe_invert.c \
11 | src/ref10/fe_isnegative.c \
12 | src/ref10/fe_isnonzero.c \
13 | src/ref10/fe_mul.c \
14 | src/ref10/fe_neg.c \
15 | src/ref10/fe_pow22523.c \
16 | src/ref10/fe_sq2.c \
17 | src/ref10/fe_sq.c \
18 | src/ref10/fe_sub.c \
19 | src/ref10/fe_tobytes.c \
20 | src/ref10/ge_add.c \
21 | src/ref10/ge_double_scalarmult.c \
22 | src/ref10/ge_frombytes.c \
23 | src/ref10/ge_madd.c \
24 | src/ref10/ge_msub.c \
25 | src/ref10/ge_p1p1_to_p2.c \
26 | src/ref10/ge_p1p1_to_p3.c \
27 | src/ref10/ge_p2_0.c \
28 | src/ref10/ge_p2_dbl.c \
29 | src/ref10/ge_p3_0.c \
30 | src/ref10/ge_p3_dbl.c \
31 | src/ref10/ge_p3_tobytes.c \
32 | src/ref10/ge_p3_to_cached.c \
33 | src/ref10/ge_p3_to_p2.c \
34 | src/ref10/ge_precomp_0.c \
35 | src/ref10/ge_scalarmult_base.c \
36 | src/ref10/ge_sub.c \
37 | src/ref10/ge_tobytes.c \
38 | src/ref10/sc_muladd.c \
39 | src/ref10/sc_reduce.c \
40 | src/ref10/sign.c \
41 | src/ref10/open.c \
42 | src/crypto_verify_32.c \
43 | src/crypto_hash_sha512.c \
44 | src/base32.c \
45 | src/horse25519.c
46 |
47 | OBJS = $(SRCS:.c=.o)
48 |
49 | .c.o:
50 | $(CC) $(CFLAGS) -c $< -o $@
51 |
52 | .PHONEY: all clean
53 |
54 | all: $(OBJS) horse25519
55 |
56 | horse25519: $(OBJS)
57 | $(CC) $(OBJS) $(LDFLAGS) -o horse25519
58 |
59 | clean:
60 | rm -f $(OBJS) horse25519
61 |
--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | ## horse25519 - An Ed25519 vanity public key generator
2 | ### Yawning Angel (yawning at torproject dot org)
3 |
4 | ### What?
5 |
6 | This is a Ed25519 vanity public key search tool in the spirit of shallot. It
7 | attempts to generate a Ed25519 keypair that has a public key with a user
8 | provided prefix when encoded in Base32.
9 |
10 | It is slower than searching for keys via Scallion as it only runs on the CPU.
11 | Porting the relevant math to run on a GPU is left as an exercise for the
12 | student.
13 |
14 | ### Notes
15 |
16 | The Ed25519 implementation is ed25519/ref10 from SUPERCOP (20140924). The
17 | src/ref10 directory contains an unmodified copy, with the portability headers
18 | and routines thrown into src. In theory minor speedups may be obtained by
19 | switching to Floodyberry's ed25519-donna, but as the search phase does not do
20 | the scalar multiplication, this probably will not be that big of a gain.
21 |
22 | The trick for skipping the scalar multiplication, and the basis for the
23 | implementation was shown to be my Nick Mathewson.
24 |
25 | OpenSSL is used for the CSPRNG and a SHA512 implementation. This is subject to
26 | change at a later date since pulling in OpenSSL for either of those things is
27 | approaching overkill.
28 |
29 | The code doesn't take any particular care to scrub values off the heap or stack.
30 | You are using this on a dedicated offline box without swap right?
31 |
32 | The number of fucks I give about Windows or Darwin is equal to the number of
33 | computers I have that run either operating system. Patches for the latter
34 | probably accepted.
35 |
--------------------------------------------------------------------------------
/src/base32.c:
--------------------------------------------------------------------------------
1 | /*
2 | * NB: I stole this from obfsclient, which I stole from the "Public Domain"
3 | * bitpedia Java code. This is somewhat tailored to how I want it to behave
4 | * for horse25519, so if you are not me, stealing it for the third time will
5 | * probably be a *really* bad idea.
6 | */
7 |
8 | #include
9 | #include
10 | #include
11 |
12 | #include "base32.h"
13 |
14 | static uint8_t decode_char(uint8_t c);
15 | static char encode_byte(uint8_t b);
16 |
17 | static
18 | uint8_t decode_char(uint8_t c)
19 | {
20 | if (c >= 'a' && c <= 'z')
21 | c -= 32;
22 |
23 | if (c >= 'A' && c <= 'Z')
24 | return c - 'A';
25 | else if (c >= '2' && c <= '7')
26 | return c - '2' + 26;
27 | else
28 | return 0xff;
29 | }
30 |
31 | static
32 | char encode_byte(uint8_t b)
33 | {
34 | /* The proposed onion format uses lower case. */
35 | if (b <= 25)
36 | return tolower('A' + b);
37 | else if (b <= 31)
38 | return '2' + (b - 26);
39 | else
40 | return 0xff;
41 | }
42 |
43 | ssize_t
44 | base32_decode(const char *encoded, uint8_t *dst, size_t len)
45 | {
46 | size_t offset = 0;
47 | size_t i, enc_len;
48 | int index = 0;
49 |
50 | if (encoded == NULL)
51 | return -1;
52 | if (dst == NULL)
53 | return -1;
54 |
55 | enc_len = strlen(encoded);
56 | if (enc_len * 5 > len * 8)
57 | return -1;
58 | memset(dst, 0, len);
59 |
60 | for (i = 0; i < enc_len; i++) {
61 | uint8_t c = decode_char(encoded[i]);
62 | if (c == 0xff)
63 | return -1;
64 |
65 | if (index <= 3) {
66 | index = (index + 5) & 0x07;
67 | if (index == 0) {
68 | dst[offset] |= c;
69 | offset++;
70 | if (offset >= len)
71 | return -1;
72 | } else
73 | dst[offset] |= c << (8 - index);
74 | } else {
75 | index = (index + 5) & 0x07;
76 | dst[offset] |= (c >> index);
77 | offset++;
78 | if (offset >= len)
79 | return -1;
80 | dst[offset] |= c << (8 - index);
81 | }
82 | }
83 |
84 | return offset;
85 | }
86 |
87 | char *
88 | base32_encode(const uint8_t *buf, size_t len)
89 | {
90 | char *ret;
91 | size_t i = 0;
92 | size_t index = 0;
93 | size_t enc_idx = 0;
94 | uint8_t digit = 0;
95 | uint8_t next_byte = 0;
96 |
97 | ret = calloc(1, (len + 7) * 8 / 5 + 1);
98 |
99 | while (i < len) {
100 | uint8_t currByte = buf[i];
101 |
102 | // Is the current digit going to span a byte boundary?
103 | if (index > 3) {
104 | if ((i + 1) < len)
105 | next_byte = buf[i + 1];
106 | else
107 | next_byte = 0;
108 |
109 | digit = currByte & (0xff >> index);
110 | index = (index + 5) & 0x07;
111 | digit <<= index;
112 | digit |= next_byte >> (8 - index);
113 | i++;
114 | } else {
115 | digit = (currByte >> (8 - (index + 5))) & 0x1f;
116 | index = (index + 5) & 0x07;
117 | if (index == 0)
118 | i++;
119 | }
120 |
121 | ret[enc_idx++] = encode_byte(digit);
122 | }
123 |
124 | /* Padding is for suckas. */
125 |
126 | return ret;
127 | }
128 |
--------------------------------------------------------------------------------
/src/base32.h:
--------------------------------------------------------------------------------
1 | #include
2 | #include
3 |
4 | #ifndef BASE32_H
5 | #define BASE32_H
6 |
7 | ssize_t base32_decode(const char *encoded, uint8_t *dst, size_t len);
8 | char *base32_encode(const uint8_t *buf, size_t len);
9 |
10 | #endif
11 |
--------------------------------------------------------------------------------
/src/crypto_hash_sha512.c:
--------------------------------------------------------------------------------
1 | #include
2 |
3 | #include "crypto_hash_sha512.h"
4 |
5 | int
6 | crypto_hash_sha512(unsigned char *out, const unsigned char *in,
7 | unsigned long long inlen)
8 | {
9 | SHA512(in, inlen, out);
10 | return 0;
11 | }
12 |
--------------------------------------------------------------------------------
/src/crypto_hash_sha512.h:
--------------------------------------------------------------------------------
1 | #ifndef CRYPTO_HASH_SHA512_H
2 | #define CRYPTO_HASH_SHA512_H
3 |
4 | int crypto_hash_sha512(unsigned char *out, const unsigned char *in,
5 | unsigned long long inlen);
6 |
7 | #endif
8 |
--------------------------------------------------------------------------------
/src/crypto_int32.h:
--------------------------------------------------------------------------------
1 | #include
2 |
3 | #ifndef CRYPTO_INT32_H
4 | #define CRYPTO_INT32_H
5 |
6 | typedef int32_t crypto_int32;
7 |
8 | #endif
9 |
--------------------------------------------------------------------------------
/src/crypto_int64.h:
--------------------------------------------------------------------------------
1 | #include
2 |
3 | #ifndef CRYPTO_INT64_H
4 | #define CRYPTO_INT64_H
5 |
6 | typedef int64_t crypto_int64;
7 |
8 | #endif
9 |
--------------------------------------------------------------------------------
/src/crypto_sign.h:
--------------------------------------------------------------------------------
1 | #ifndef CRYPTO_SIGN_H
2 | #define CRYPTO_SIGN_H
3 |
4 | int crypto_sign(
5 | unsigned char *sm,unsigned long long *smlen,
6 | const unsigned char *m,unsigned long long mlen,
7 | const unsigned char *sk
8 | );
9 |
10 | int crypto_sign_open(
11 | unsigned char *m,unsigned long long *mlen,
12 | const unsigned char *sm,unsigned long long smlen,
13 | const unsigned char *pk
14 | );
15 |
16 | #endif
17 |
--------------------------------------------------------------------------------
/src/crypto_uint32.h:
--------------------------------------------------------------------------------
1 | #include
2 |
3 | #ifndef CRYPTO_UINT32_H
4 | #define CRYPTO_UINT32_H
5 |
6 | typedef uint32_t crypto_uint32;
7 |
8 | #endif
9 |
--------------------------------------------------------------------------------
/src/crypto_uint64.h:
--------------------------------------------------------------------------------
1 | #include
2 |
3 | #ifndef CRYPTO_UINT64_H
4 | #define CRYPTO_UINT64_H
5 |
6 | typedef uint64_t crypto_uint64;
7 |
8 | #endif
9 |
--------------------------------------------------------------------------------
/src/crypto_verify_32.c:
--------------------------------------------------------------------------------
1 | #include "crypto_verify_32.h"
2 |
3 | int
4 | crypto_verify_32(const uint8_t *x, const uint8_t *y)
5 | {
6 | uint32_t differentbits = 0;
7 | #define F(i) differentbits |= x[i] ^ y[i];
8 | F(0)
9 | F(1)
10 | F(2)
11 | F(3)
12 | F(4)
13 | F(5)
14 | F(6)
15 | F(7)
16 | F(8)
17 | F(9)
18 | F(10)
19 | F(11)
20 | F(12)
21 | F(13)
22 | F(14)
23 | F(15)
24 | F(16)
25 | F(17)
26 | F(18)
27 | F(19)
28 | F(20)
29 | F(21)
30 | F(22)
31 | F(23)
32 | F(24)
33 | F(25)
34 | F(26)
35 | F(27)
36 | F(28)
37 | F(29)
38 | F(30)
39 | F(31)
40 | return (1 & ((differentbits - 1) >> 8)) - 1;
41 | }
42 |
--------------------------------------------------------------------------------
/src/crypto_verify_32.h:
--------------------------------------------------------------------------------
1 | #include
2 |
3 | #ifndef CRYPTO_VERIFY_32_H
4 | #define CRYPTO_VERIFY_32_H
5 |
6 | int crypto_verify_32(const uint8_t *x,const uint8_t *y);
7 |
8 | #endif
9 |
--------------------------------------------------------------------------------
/src/horse25519.c:
--------------------------------------------------------------------------------
1 | /*
2 | * horse25519.c - Ed25519 vanity key generator.
3 | * Copyright (C) 2014 Yawning Angel.
4 | *
5 | * This is free and unencumbered software released into the public domain.
6 | */
7 |
8 | #include
9 | #include
10 |
11 | #include
12 |
13 | #ifndef __MACH__
14 | # include /* Linux-ism fuck yeah. */
15 | #else
16 | # include
17 | # define htobe64(x) OSSwapHostToBigInt64(x)
18 | # define htole64(x) OSSwapHostToLittleInt64(x)
19 | #endif
20 |
21 | #include
22 | #include
23 | #include
24 | #include
25 | #include
26 | #include
27 | #include
28 | #include
29 |
30 | #include "crypto_hash_sha512.h"
31 | #include "crypto_sign.h"
32 | #include "ref10/ge.h"
33 |
34 | #include "base32.h"
35 |
36 | /*
37 | * Workers will re-check the termination condition every n / 8 iterations.
38 | * MUST be a power of 2 or bad things will happen.
39 | */
40 | #define CHECK_INCR 131072
41 |
42 | /* Maximum supported prefix length (bytes). */
43 | #define MAX_PREFIX_BYTES 12
44 |
45 | /* Maximum supported prefix length (bits). */
46 | #define MAX_PREFIX_BITS 60
47 |
48 | typedef struct {
49 | uint64_t prefix;
50 | uint64_t mask;
51 | size_t nbits;
52 | } bitprefix;
53 |
54 | static bitprefix *bitprefix_from_base32(const char *b32);
55 | static inline int bitprefix_matches(const bitprefix *v, const uint8_t *buf,
56 | size_t len);
57 |
58 | static void usage(const char *execname);
59 | static void random_64bytes(uint8_t *buf);
60 | static void scalar_add(uint8_t r[32], const uint8_t x[32], const uint8_t y[32]);
61 | static void *search_worker(void *arg);
62 | static void test_signature(const uint8_t sk[64], const uint8_t pk[32]);
63 |
64 | static pthread_mutex_t rng_lock = PTHREAD_MUTEX_INITIALIZER;
65 | static pthread_rwlock_t result_lock = PTHREAD_RWLOCK_INITIALIZER;
66 | static int result_found = 0;
67 |
68 | /* The basepoint multiplied by 8. */
69 | static const ge_cached ge_eightpoint = {
70 | /* YplusX */
71 | {
72 | 48496028, -16430416, 15164263, 11885335, 60784617, -4866353, 46481863,
73 | -2771805, 9708580, 2387263
74 | },
75 | /* YmunusX */
76 | {
77 | -10173472, -5540046, 21277639, 4080693, 1932823, -14916249, -9515873,
78 | -21787995, -36575460, 29827857
79 | },
80 | /* Z */
81 | {
82 | 25143927, -10256223, -3515585, 5715072, 19432778, -14905909, 22462083,
83 | -8862871, 13226552, 743677
84 | },
85 | /* T2d */
86 | {
87 | -784818, -8208065, -28479270, 5551579, 15746872, 4911053, 19117091,
88 | 11267669, -24569594, 14624995
89 | }
90 | };
91 |
92 |
93 | static bitprefix *
94 | bitprefix_from_base32(const char *b32)
95 | {
96 | uint8_t decoded[MAX_PREFIX_BYTES] = { 0 };
97 | const uint64_t *p = (uint64_t*)decoded;
98 | bitprefix *v;
99 | size_t nbytes;
100 | size_t i;
101 |
102 | if (b32 == NULL)
103 | return NULL;
104 |
105 | if (base32_decode(b32, decoded, sizeof(decoded)) == -1)
106 | return NULL;
107 | nbytes = strlen(b32);
108 |
109 | v = (bitprefix*)calloc(1, sizeof(*v));
110 | v->nbits = nbytes * 5;
111 |
112 | /*
113 | * Instead of using memcmp() or anything else, we can simplify things and use
114 | * a mask + 64 bit integer compare if we limit the lenght of the prefix to 12
115 | * characters (60 bits). Since it's unlikely that anyone is crazy enough to
116 | * search for prefixes that are that long, use the optimization.
117 | */
118 | for (i = 0; i < nbytes; i++) {
119 | v->mask |= ((uint64_t)0x1f << (64 - 5 * (i + 1)));
120 | }
121 | v->mask = htobe64(v->mask);
122 | v->prefix = *p & v->mask;
123 |
124 | return v;
125 | }
126 |
127 | static inline
128 | int bitprefix_matches(const bitprefix *v, const uint8_t *buf, size_t len)
129 | {
130 | const uint64_t *p = (uint64_t*)buf;
131 |
132 | assert(v != NULL);
133 | assert(buf != NULL);
134 | assert(len * 8 >= v->nbits);
135 | #ifdef NDEBUG
136 | (void)len;
137 | #endif
138 |
139 | return (*p & v->mask) == v->prefix;
140 | }
141 |
142 | static void
143 | usage(const char *execname)
144 | {
145 | fprintf(stderr, "%s [-n cores] prefix\n", execname);
146 | exit(-1);
147 | }
148 |
149 | static void
150 | random_64bytes(uint8_t *buf)
151 | {
152 | uint8_t az[64];
153 |
154 | /* Yes, this is the "wrong" way to make this threadsafe. */
155 | pthread_mutex_lock(&rng_lock);
156 | RAND_bytes(buf, 32);
157 | pthread_mutex_unlock(&rng_lock);
158 | crypto_hash_sha512(az, buf, 32);
159 | memcpy(buf, az, 64);
160 | }
161 |
162 | static void
163 | scalar_add(uint8_t r[32], const uint8_t x[32], const uint8_t y[32])
164 | {
165 | uint32_t v[32];
166 | int carry;
167 | int i;
168 |
169 | for (i = 0; i < 32; i++) {
170 | v[i] = x[i] + y[i];
171 | }
172 | for (i = 0; i < 31; i++) {
173 | carry = v[i] >> 8;
174 | v[i+1] += carry;
175 | v[i] &= 0xff;
176 | }
177 | for (i = 0; i < 32; i++) {
178 | r[i] = v[i];
179 | }
180 | }
181 |
182 | static void *
183 | search_worker(void *arg)
184 | {
185 | const bitprefix *prefix = arg;
186 | uint8_t pk[32];
187 | uint8_t pk_cmp[32];
188 | uint8_t sk[64];
189 | uint8_t sk_base[32];
190 | uint8_t sk_fixup[32];
191 | ge_p3 ge_pk;
192 | uint64_t incr = 0;
193 |
194 | memset(sk_fixup, 0, sizeof(sk_fixup));
195 |
196 | regenerate:
197 | /* Generate the keypair. */
198 | random_64bytes(sk);
199 | memcpy(sk_base, sk, 32);
200 | sk_base[0] &= 248;
201 | sk_base[31] &= 63;
202 | sk_base[31] |= 64;
203 | ge_scalarmult_base(&ge_pk, sk_base);
204 | ge_p3_tobytes(pk, &ge_pk);
205 |
206 | /*
207 | * This is the core of the search algorithm. We increment the public key by
208 | * the basepoint till a public key with the desired prefix is found.
209 | *
210 | * Note: We actually increment the public key by the basepoint 8 times per
211 | * iteration, so that when we go to fixup the private key, we do not end up
212 | * adding a value that will result in a private key that gets screwed up when
213 | * we do the usual masking business.
214 | */
215 | for (incr = 0; incr < UINT64_MAX - 8; incr += 8) {
216 | ge_p1p1 sum;
217 |
218 | /* Only check if the worker should exit once in a while. */
219 | if (__builtin_expect((incr & (CHECK_INCR - 1)) == 0, 0)) {
220 | int found;
221 | pthread_rwlock_rdlock(&result_lock);
222 | found = result_found;
223 | pthread_rwlock_unlock(&result_lock);
224 | if (found)
225 | return NULL;
226 | }
227 |
228 | /* GCC-ism fuck yeah. */
229 | if (__builtin_expect(bitprefix_matches(prefix, pk, sizeof(pk)), 0)) {
230 | uint64_t incr_le = htole64(incr);
231 |
232 | /*
233 | * Fixup the private key by adding the number of times the basepoint was
234 | * incremented, and ensure that it is sane.
235 | *
236 | * Note: The 0th byte should *ALWAYS* be valid due to the increment being
237 | * a multiple of 8. The only way for the last byte to be screwed up is
238 | * if the carry bit propagates all the way across the key. While it is
239 | * possible to filter out keys that can do that in the generation
240 | * phase, the probability of that happening to begin with are
241 | * astronomically low.
242 | */
243 | memcpy(sk_fixup, &incr_le, sizeof(incr_le));
244 | scalar_add(sk, sk_base, sk_fixup);
245 | if (((sk[0] & 248) == sk[0]) && (((sk[31] & 63) | 64) == sk[31])) {
246 | /* These operations should be a no-op. */
247 | sk[0] &= 248;
248 | sk[31] &= 63;
249 | sk[31] |= 64;
250 | goto found;
251 | } else {
252 | /*
253 | * Well shit. Presumably incr is >= 2^56, and the private key that was
254 | * randomly generated is such that the carry bit propagated and screwed
255 | * up the last byte.
256 | */
257 | goto regenerate;
258 | }
259 | }
260 |
261 | ge_add(&sum, &ge_pk, &ge_eightpoint);
262 | ge_p1p1_to_p3(&ge_pk, &sum);
263 | ge_p3_tobytes(pk, &ge_pk);
264 | }
265 | goto regenerate; /* This should *never* happen in a reasonable time. */
266 |
267 | found:
268 | /*
269 | * This will cause all of the other threads to stop work once they go to
270 | * check the termination condition. This is fine because a worker in this
271 | * part of the code means that a key has been found.
272 | */
273 | pthread_rwlock_wrlock(&result_lock);
274 |
275 | /* First result found, print it. */
276 | if (!result_found) {
277 | /* At this point, sk *should* produce pk, which has the prefix. */
278 | ge_scalarmult_base(&ge_pk, sk);
279 | ge_p3_tobytes(pk_cmp, &ge_pk);
280 | if (memcmp(pk_cmp, pk, sizeof(pk_cmp)) == 0) {
281 | char *public_key = base32_encode(pk, sizeof(pk));
282 | char *private_key = base32_encode(sk, sizeof(sk));
283 |
284 | fprintf(stdout, "Expanded Private Key: %s\n", private_key);
285 | fprintf(stdout, "Public Key: %s\n", public_key);
286 |
287 | result_found = 1;
288 |
289 | free(public_key);
290 | free(private_key);
291 |
292 | test_signature(sk, pk);
293 |
294 | } else {
295 | fprintf(stderr, "BUG: Couldn't produce public key from private key.\n");
296 | }
297 | }
298 |
299 | pthread_rwlock_unlock(&result_lock);
300 |
301 | return NULL;
302 | }
303 |
304 | static void
305 | test_signature(const uint8_t sk[64], const uint8_t pk[32])
306 | {
307 | uint8_t m[256];
308 | uint8_t sm[64 + 256];
309 | unsigned long long smlen, mlen = sizeof(m);
310 | size_t i;
311 | int ret;
312 |
313 | /* Sign a test message. */
314 | for (i = 0; i < mlen; i++)
315 | m[i] = i;
316 | crypto_sign(sm, &smlen, m, mlen, sk);
317 |
318 | /* Verify the signature. */
319 | ret = crypto_sign_open(m, &mlen, sm, smlen, pk);
320 | fprintf(stdout, "Test signature verification returned: %d\n", ret);
321 | }
322 |
323 | int
324 | main(int argc, char *argv[])
325 | {
326 | const struct option options[] = {
327 | { "ncores", required_argument, NULL, 'n' },
328 | { NULL, 0, NULL, 0}
329 | };
330 | const char *execname = argv[0];
331 | pthread_t *workers = NULL;
332 | bitprefix *prefix;
333 | unsigned long n;
334 | unsigned int ncores = 1;
335 | unsigned int i;
336 | int ch;
337 |
338 | /* Parse the command line arguments. */
339 | while ((ch = getopt_long(argc, argv, "n:", options, NULL)) != -1) {
340 | switch (ch) {
341 | case 'n':
342 | n = strtoul(optarg, NULL, 10);
343 | if (n == 0 || n == ULONG_MAX || n > UINT_MAX) {
344 | fprintf(stderr, "Failed to parse ncores: [%s]\n", optarg);
345 | return -1;
346 | }
347 | ncores = (int)n;
348 | break;
349 |
350 | default:
351 | usage(execname);
352 | }
353 | }
354 |
355 | /* The prefix is mandatory and can't contain white space because Base32. */
356 | if (optind != argc - 1) {
357 | usage(execname);
358 | }
359 | argc -= optind;
360 | argv += optind;
361 | if (strlen(argv[0]) > MAX_PREFIX_BYTES) {
362 | fprintf(stderr, "Invalid prefix length. (Max: %d)\n", MAX_PREFIX_BYTES);
363 | return -1;
364 | }
365 | prefix = bitprefix_from_base32(argv[0]);
366 | if (prefix == NULL) {
367 | fprintf(stderr, "Failed to decode prefix: [%s]\n", argv[0]);
368 | return -1;
369 | }
370 |
371 | fprintf(stdout, "Searching for prefix: [%s] (%zd bits)\n", argv[0],
372 | prefix->nbits);
373 | fprintf(stdout, "Threads: %u\n", ncores);
374 | fprintf(stdout, "\n");
375 |
376 | /* Kick off the worker threads and start searching. */
377 | ncores -= 1;
378 | if (ncores > 0) {
379 | workers = calloc(ncores, sizeof(*workers));
380 | for (i = 0; i < ncores; i++) {
381 | pthread_create(&workers[i], NULL, &search_worker, prefix);
382 | }
383 | }
384 | search_worker(prefix);
385 |
386 | /* Ensure all of the threads have terminated. */
387 | for (i = 0; i < ncores; i++) {
388 | pthread_join(workers[i], NULL);
389 | }
390 |
391 | if (!result_found) {
392 | fprintf(stderr, "BUG: All threads exited without a result.");
393 | }
394 |
395 | if (workers)
396 | free(workers);
397 | free(prefix);
398 |
399 | return 0;
400 | }
401 |
--------------------------------------------------------------------------------
/src/ref10/api.h:
--------------------------------------------------------------------------------
1 | #define CRYPTO_SECRETKEYBYTES 64
2 | #define CRYPTO_PUBLICKEYBYTES 32
3 | #define CRYPTO_BYTES 64
4 | #define CRYPTO_DETERMINISTIC 1
5 |
--------------------------------------------------------------------------------
/src/ref10/base.h:
--------------------------------------------------------------------------------
1 | {
2 | {
3 | { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
4 | { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
5 | { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
6 | },
7 | {
8 | { -12815894,-12976347,-21581243,11784320,-25355658,-2750717,-11717903,-3814571,-358445,-10211303 },
9 | { -21703237,6903825,27185491,6451973,-29577724,-9554005,-15616551,11189268,-26829678,-5319081 },
10 | { 26966642,11152617,32442495,15396054,14353839,-12752335,-3128826,-9541118,-15472047,-4166697 },
11 | },
12 | {
13 | { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
14 | { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
15 | { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
16 | },
17 | {
18 | { -17036878,13921892,10945806,-6033431,27105052,-16084379,-28926210,15006023,3284568,-6276540 },
19 | { 23599295,-8306047,-11193664,-7687416,13236774,10506355,7464579,9656445,13059162,10374397 },
20 | { 7798556,16710257,3033922,2874086,28997861,2835604,32406664,-3839045,-641708,-101325 },
21 | },
22 | {
23 | { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
24 | { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
25 | { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
26 | },
27 | {
28 | { -15371964,-12862754,32573250,4720197,-26436522,5875511,-19188627,-15224819,-9818940,-12085777 },
29 | { -8549212,109983,15149363,2178705,22900618,4543417,3044240,-15689887,1762328,14866737 },
30 | { -18199695,-15951423,-10473290,1707278,-17185920,3916101,-28236412,3959421,27914454,4383652 },
31 | },
32 | {
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34 | { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
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36 | },
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41 | },
42 | },
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48 | },
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53 | },
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58 | },
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63 | },
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83 | },
84 | },
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90 | },
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95 | },
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100 | },
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105 | },
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110 | },
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114 | { 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 },
115 | },
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120 | },
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125 | },
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137 | },
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162 | },
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167 | },
168 | },
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179 | },
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184 | },
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189 | },
190 | {
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193 | { -30305315,14843444,1539301,11864366,20201677,1900163,13934231,5128323,11213262,9168384 },
194 | },
195 | {
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198 | { 29969567,-2741594,-16711867,-8552442,9175486,-2468974,21556951,3506042,-5933891,-12449708 },
199 | },
200 | {
201 | { -3144746,8744661,19704003,4581278,-20430686,6830683,-21284170,8971513,-28539189,15326563 },
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203 | { -5353335,4488613,-23803248,16314347,7780487,-15638939,-28948358,9601605,33087103,-9011387 },
204 | },
205 | {
206 | { -19443170,-15512900,-20797467,-12445323,-29824447,10229461,-27444329,-15000531,-5996870,15664672 },
207 | { 23294591,-16632613,-22650781,-8470978,27844204,11461195,13099750,-2460356,18151676,13417686 },
208 | { -24722913,-4176517,-31150679,5988919,-26858785,6685065,1661597,-12551441,15271676,-15452665 },
209 | },
210 | },
211 | {
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1306 | { -23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461 },
1307 | { 29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062 },
1308 | },
1309 | {
1310 | { -25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516 },
1311 | { -20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547 },
1312 | { -24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240 },
1313 | },
1314 | {
1315 | { -17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038 },
1316 | { -33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741 },
1317 | { 16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103 },
1318 | },
1319 | {
1320 | { -19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747 },
1321 | { -1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323 },
1322 | { 31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016 },
1323 | },
1324 | {
1325 | { -14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373 },
1326 | { 15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228 },
1327 | { -2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141 },
1328 | },
1329 | {
1330 | { 16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399 },
1331 | { 11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831 },
1332 | { -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 },
1333 | },
1334 | {
1335 | { -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 },
1336 | { -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 },
1337 | { -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 },
1338 | },
1339 | {
1340 | { -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 },
1341 | { 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 },
1342 | { -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 },
1343 | },
1344 | },
1345 |
--------------------------------------------------------------------------------
/src/ref10/base2.h:
--------------------------------------------------------------------------------
1 | {
2 | { 25967493,-14356035,29566456,3660896,-12694345,4014787,27544626,-11754271,-6079156,2047605 },
3 | { -12545711,934262,-2722910,3049990,-727428,9406986,12720692,5043384,19500929,-15469378 },
4 | { -8738181,4489570,9688441,-14785194,10184609,-12363380,29287919,11864899,-24514362,-4438546 },
5 | },
6 | {
7 | { 15636291,-9688557,24204773,-7912398,616977,-16685262,27787600,-14772189,28944400,-1550024 },
8 | { 16568933,4717097,-11556148,-1102322,15682896,-11807043,16354577,-11775962,7689662,11199574 },
9 | { 30464156,-5976125,-11779434,-15670865,23220365,15915852,7512774,10017326,-17749093,-9920357 },
10 | },
11 | {
12 | { 10861363,11473154,27284546,1981175,-30064349,12577861,32867885,14515107,-15438304,10819380 },
13 | { 4708026,6336745,20377586,9066809,-11272109,6594696,-25653668,12483688,-12668491,5581306 },
14 | { 19563160,16186464,-29386857,4097519,10237984,-4348115,28542350,13850243,-23678021,-15815942 },
15 | },
16 | {
17 | { 5153746,9909285,1723747,-2777874,30523605,5516873,19480852,5230134,-23952439,-15175766 },
18 | { -30269007,-3463509,7665486,10083793,28475525,1649722,20654025,16520125,30598449,7715701 },
19 | { 28881845,14381568,9657904,3680757,-20181635,7843316,-31400660,1370708,29794553,-1409300 },
20 | },
21 | {
22 | { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 },
23 | { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 },
24 | { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 },
25 | },
26 | {
27 | { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 },
28 | { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 },
29 | { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 },
30 | },
31 | {
32 | { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 },
33 | { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 },
34 | { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 },
35 | },
36 | {
37 | { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 },
38 | { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 },
39 | { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 },
40 | },
41 |
--------------------------------------------------------------------------------
/src/ref10/d.h:
--------------------------------------------------------------------------------
1 | -10913610,13857413,-15372611,6949391,114729,-8787816,-6275908,-3247719,-18696448,-12055116
2 |
--------------------------------------------------------------------------------
/src/ref10/d2.h:
--------------------------------------------------------------------------------
1 | -21827239,-5839606,-30745221,13898782,229458,15978800,-12551817,-6495438,29715968,9444199
2 |
--------------------------------------------------------------------------------
/src/ref10/fe.h:
--------------------------------------------------------------------------------
1 | #ifndef FE_H
2 | #define FE_H
3 |
4 | #include "crypto_int32.h"
5 |
6 | typedef crypto_int32 fe[10];
7 |
8 | /*
9 | fe means field element.
10 | Here the field is \Z/(2^255-19).
11 | An element t, entries t[0]...t[9], represents the integer
12 | t[0]+2^26 t[1]+2^51 t[2]+2^77 t[3]+2^102 t[4]+...+2^230 t[9].
13 | Bounds on each t[i] vary depending on context.
14 | */
15 |
16 | #define fe_frombytes crypto_sign_ed25519_ref10_fe_frombytes
17 | #define fe_tobytes crypto_sign_ed25519_ref10_fe_tobytes
18 | #define fe_copy crypto_sign_ed25519_ref10_fe_copy
19 | #define fe_isnonzero crypto_sign_ed25519_ref10_fe_isnonzero
20 | #define fe_isnegative crypto_sign_ed25519_ref10_fe_isnegative
21 | #define fe_0 crypto_sign_ed25519_ref10_fe_0
22 | #define fe_1 crypto_sign_ed25519_ref10_fe_1
23 | #define fe_cswap crypto_sign_ed25519_ref10_fe_cswap
24 | #define fe_cmov crypto_sign_ed25519_ref10_fe_cmov
25 | #define fe_add crypto_sign_ed25519_ref10_fe_add
26 | #define fe_sub crypto_sign_ed25519_ref10_fe_sub
27 | #define fe_neg crypto_sign_ed25519_ref10_fe_neg
28 | #define fe_mul crypto_sign_ed25519_ref10_fe_mul
29 | #define fe_sq crypto_sign_ed25519_ref10_fe_sq
30 | #define fe_sq2 crypto_sign_ed25519_ref10_fe_sq2
31 | #define fe_mul121666 crypto_sign_ed25519_ref10_fe_mul121666
32 | #define fe_invert crypto_sign_ed25519_ref10_fe_invert
33 | #define fe_pow22523 crypto_sign_ed25519_ref10_fe_pow22523
34 |
35 | extern void fe_frombytes(fe,const unsigned char *);
36 | extern void fe_tobytes(unsigned char *,const fe);
37 |
38 | extern void fe_copy(fe,const fe);
39 | extern int fe_isnonzero(const fe);
40 | extern int fe_isnegative(const fe);
41 | extern void fe_0(fe);
42 | extern void fe_1(fe);
43 | extern void fe_cswap(fe,fe,unsigned int);
44 | extern void fe_cmov(fe,const fe,unsigned int);
45 |
46 | extern void fe_add(fe,const fe,const fe);
47 | extern void fe_sub(fe,const fe,const fe);
48 | extern void fe_neg(fe,const fe);
49 | extern void fe_mul(fe,const fe,const fe);
50 | extern void fe_sq(fe,const fe);
51 | extern void fe_sq2(fe,const fe);
52 | extern void fe_mul121666(fe,const fe);
53 | extern void fe_invert(fe,const fe);
54 | extern void fe_pow22523(fe,const fe);
55 |
56 | #endif
57 |
--------------------------------------------------------------------------------
/src/ref10/fe_0.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | h = 0
5 | */
6 |
7 | void fe_0(fe h)
8 | {
9 | h[0] = 0;
10 | h[1] = 0;
11 | h[2] = 0;
12 | h[3] = 0;
13 | h[4] = 0;
14 | h[5] = 0;
15 | h[6] = 0;
16 | h[7] = 0;
17 | h[8] = 0;
18 | h[9] = 0;
19 | }
20 |
--------------------------------------------------------------------------------
/src/ref10/fe_1.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | h = 1
5 | */
6 |
7 | void fe_1(fe h)
8 | {
9 | h[0] = 1;
10 | h[1] = 0;
11 | h[2] = 0;
12 | h[3] = 0;
13 | h[4] = 0;
14 | h[5] = 0;
15 | h[6] = 0;
16 | h[7] = 0;
17 | h[8] = 0;
18 | h[9] = 0;
19 | }
20 |
--------------------------------------------------------------------------------
/src/ref10/fe_add.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | h = f + g
5 | Can overlap h with f or g.
6 |
7 | Preconditions:
8 | |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
9 | |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
10 |
11 | Postconditions:
12 | |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
13 | */
14 |
15 | void fe_add(fe h,const fe f,const fe g)
16 | {
17 | crypto_int32 f0 = f[0];
18 | crypto_int32 f1 = f[1];
19 | crypto_int32 f2 = f[2];
20 | crypto_int32 f3 = f[3];
21 | crypto_int32 f4 = f[4];
22 | crypto_int32 f5 = f[5];
23 | crypto_int32 f6 = f[6];
24 | crypto_int32 f7 = f[7];
25 | crypto_int32 f8 = f[8];
26 | crypto_int32 f9 = f[9];
27 | crypto_int32 g0 = g[0];
28 | crypto_int32 g1 = g[1];
29 | crypto_int32 g2 = g[2];
30 | crypto_int32 g3 = g[3];
31 | crypto_int32 g4 = g[4];
32 | crypto_int32 g5 = g[5];
33 | crypto_int32 g6 = g[6];
34 | crypto_int32 g7 = g[7];
35 | crypto_int32 g8 = g[8];
36 | crypto_int32 g9 = g[9];
37 | crypto_int32 h0 = f0 + g0;
38 | crypto_int32 h1 = f1 + g1;
39 | crypto_int32 h2 = f2 + g2;
40 | crypto_int32 h3 = f3 + g3;
41 | crypto_int32 h4 = f4 + g4;
42 | crypto_int32 h5 = f5 + g5;
43 | crypto_int32 h6 = f6 + g6;
44 | crypto_int32 h7 = f7 + g7;
45 | crypto_int32 h8 = f8 + g8;
46 | crypto_int32 h9 = f9 + g9;
47 | h[0] = h0;
48 | h[1] = h1;
49 | h[2] = h2;
50 | h[3] = h3;
51 | h[4] = h4;
52 | h[5] = h5;
53 | h[6] = h6;
54 | h[7] = h7;
55 | h[8] = h8;
56 | h[9] = h9;
57 | }
58 |
--------------------------------------------------------------------------------
/src/ref10/fe_cmov.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | Replace (f,g) with (g,g) if b == 1;
5 | replace (f,g) with (f,g) if b == 0.
6 |
7 | Preconditions: b in {0,1}.
8 | */
9 |
10 | void fe_cmov(fe f,const fe g,unsigned int b)
11 | {
12 | crypto_int32 f0 = f[0];
13 | crypto_int32 f1 = f[1];
14 | crypto_int32 f2 = f[2];
15 | crypto_int32 f3 = f[3];
16 | crypto_int32 f4 = f[4];
17 | crypto_int32 f5 = f[5];
18 | crypto_int32 f6 = f[6];
19 | crypto_int32 f7 = f[7];
20 | crypto_int32 f8 = f[8];
21 | crypto_int32 f9 = f[9];
22 | crypto_int32 g0 = g[0];
23 | crypto_int32 g1 = g[1];
24 | crypto_int32 g2 = g[2];
25 | crypto_int32 g3 = g[3];
26 | crypto_int32 g4 = g[4];
27 | crypto_int32 g5 = g[5];
28 | crypto_int32 g6 = g[6];
29 | crypto_int32 g7 = g[7];
30 | crypto_int32 g8 = g[8];
31 | crypto_int32 g9 = g[9];
32 | crypto_int32 x0 = f0 ^ g0;
33 | crypto_int32 x1 = f1 ^ g1;
34 | crypto_int32 x2 = f2 ^ g2;
35 | crypto_int32 x3 = f3 ^ g3;
36 | crypto_int32 x4 = f4 ^ g4;
37 | crypto_int32 x5 = f5 ^ g5;
38 | crypto_int32 x6 = f6 ^ g6;
39 | crypto_int32 x7 = f7 ^ g7;
40 | crypto_int32 x8 = f8 ^ g8;
41 | crypto_int32 x9 = f9 ^ g9;
42 | b = -b;
43 | x0 &= b;
44 | x1 &= b;
45 | x2 &= b;
46 | x3 &= b;
47 | x4 &= b;
48 | x5 &= b;
49 | x6 &= b;
50 | x7 &= b;
51 | x8 &= b;
52 | x9 &= b;
53 | f[0] = f0 ^ x0;
54 | f[1] = f1 ^ x1;
55 | f[2] = f2 ^ x2;
56 | f[3] = f3 ^ x3;
57 | f[4] = f4 ^ x4;
58 | f[5] = f5 ^ x5;
59 | f[6] = f6 ^ x6;
60 | f[7] = f7 ^ x7;
61 | f[8] = f8 ^ x8;
62 | f[9] = f9 ^ x9;
63 | }
64 |
--------------------------------------------------------------------------------
/src/ref10/fe_copy.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | h = f
5 | */
6 |
7 | void fe_copy(fe h,const fe f)
8 | {
9 | crypto_int32 f0 = f[0];
10 | crypto_int32 f1 = f[1];
11 | crypto_int32 f2 = f[2];
12 | crypto_int32 f3 = f[3];
13 | crypto_int32 f4 = f[4];
14 | crypto_int32 f5 = f[5];
15 | crypto_int32 f6 = f[6];
16 | crypto_int32 f7 = f[7];
17 | crypto_int32 f8 = f[8];
18 | crypto_int32 f9 = f[9];
19 | h[0] = f0;
20 | h[1] = f1;
21 | h[2] = f2;
22 | h[3] = f3;
23 | h[4] = f4;
24 | h[5] = f5;
25 | h[6] = f6;
26 | h[7] = f7;
27 | h[8] = f8;
28 | h[9] = f9;
29 | }
30 |
--------------------------------------------------------------------------------
/src/ref10/fe_frombytes.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 | #include "crypto_int64.h"
3 | #include "crypto_uint64.h"
4 |
5 | static crypto_uint64 load_3(const unsigned char *in)
6 | {
7 | crypto_uint64 result;
8 | result = (crypto_uint64) in[0];
9 | result |= ((crypto_uint64) in[1]) << 8;
10 | result |= ((crypto_uint64) in[2]) << 16;
11 | return result;
12 | }
13 |
14 | static crypto_uint64 load_4(const unsigned char *in)
15 | {
16 | crypto_uint64 result;
17 | result = (crypto_uint64) in[0];
18 | result |= ((crypto_uint64) in[1]) << 8;
19 | result |= ((crypto_uint64) in[2]) << 16;
20 | result |= ((crypto_uint64) in[3]) << 24;
21 | return result;
22 | }
23 |
24 | /*
25 | Ignores top bit of h.
26 | */
27 |
28 | void fe_frombytes(fe h,const unsigned char *s)
29 | {
30 | crypto_int64 h0 = load_4(s);
31 | crypto_int64 h1 = load_3(s + 4) << 6;
32 | crypto_int64 h2 = load_3(s + 7) << 5;
33 | crypto_int64 h3 = load_3(s + 10) << 3;
34 | crypto_int64 h4 = load_3(s + 13) << 2;
35 | crypto_int64 h5 = load_4(s + 16);
36 | crypto_int64 h6 = load_3(s + 20) << 7;
37 | crypto_int64 h7 = load_3(s + 23) << 5;
38 | crypto_int64 h8 = load_3(s + 26) << 4;
39 | crypto_int64 h9 = (load_3(s + 29) & 8388607) << 2;
40 | crypto_int64 carry0;
41 | crypto_int64 carry1;
42 | crypto_int64 carry2;
43 | crypto_int64 carry3;
44 | crypto_int64 carry4;
45 | crypto_int64 carry5;
46 | crypto_int64 carry6;
47 | crypto_int64 carry7;
48 | crypto_int64 carry8;
49 | crypto_int64 carry9;
50 |
51 | carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
52 | carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
53 | carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
54 | carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
55 | carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
56 |
57 | carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
58 | carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
59 | carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
60 | carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
61 | carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
62 |
63 | h[0] = h0;
64 | h[1] = h1;
65 | h[2] = h2;
66 | h[3] = h3;
67 | h[4] = h4;
68 | h[5] = h5;
69 | h[6] = h6;
70 | h[7] = h7;
71 | h[8] = h8;
72 | h[9] = h9;
73 | }
74 |
--------------------------------------------------------------------------------
/src/ref10/fe_invert.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | void fe_invert(fe out,const fe z)
4 | {
5 | fe t0;
6 | fe t1;
7 | fe t2;
8 | fe t3;
9 | int i;
10 |
11 | #include "pow225521.h"
12 |
13 | return;
14 | }
15 |
--------------------------------------------------------------------------------
/src/ref10/fe_isnegative.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | return 1 if f is in {1,3,5,...,q-2}
5 | return 0 if f is in {0,2,4,...,q-1}
6 |
7 | Preconditions:
8 | |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
9 | */
10 |
11 | int fe_isnegative(const fe f)
12 | {
13 | unsigned char s[32];
14 | fe_tobytes(s,f);
15 | return s[0] & 1;
16 | }
17 |
--------------------------------------------------------------------------------
/src/ref10/fe_isnonzero.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 | #include "crypto_verify_32.h"
3 |
4 | /*
5 | return 1 if f == 0
6 | return 0 if f != 0
7 |
8 | Preconditions:
9 | |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
10 | */
11 |
12 | static const unsigned char zero[32];
13 |
14 | int fe_isnonzero(const fe f)
15 | {
16 | unsigned char s[32];
17 | fe_tobytes(s,f);
18 | return crypto_verify_32(s,zero);
19 | }
20 |
--------------------------------------------------------------------------------
/src/ref10/fe_mul.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 | #include "crypto_int64.h"
3 |
4 | /*
5 | h = f * g
6 | Can overlap h with f or g.
7 |
8 | Preconditions:
9 | |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
10 | |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
11 |
12 | Postconditions:
13 | |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
14 | */
15 |
16 | /*
17 | Notes on implementation strategy:
18 |
19 | Using schoolbook multiplication.
20 | Karatsuba would save a little in some cost models.
21 |
22 | Most multiplications by 2 and 19 are 32-bit precomputations;
23 | cheaper than 64-bit postcomputations.
24 |
25 | There is one remaining multiplication by 19 in the carry chain;
26 | one *19 precomputation can be merged into this,
27 | but the resulting data flow is considerably less clean.
28 |
29 | There are 12 carries below.
30 | 10 of them are 2-way parallelizable and vectorizable.
31 | Can get away with 11 carries, but then data flow is much deeper.
32 |
33 | With tighter constraints on inputs can squeeze carries into int32.
34 | */
35 |
36 | void fe_mul(fe h,const fe f,const fe g)
37 | {
38 | crypto_int32 f0 = f[0];
39 | crypto_int32 f1 = f[1];
40 | crypto_int32 f2 = f[2];
41 | crypto_int32 f3 = f[3];
42 | crypto_int32 f4 = f[4];
43 | crypto_int32 f5 = f[5];
44 | crypto_int32 f6 = f[6];
45 | crypto_int32 f7 = f[7];
46 | crypto_int32 f8 = f[8];
47 | crypto_int32 f9 = f[9];
48 | crypto_int32 g0 = g[0];
49 | crypto_int32 g1 = g[1];
50 | crypto_int32 g2 = g[2];
51 | crypto_int32 g3 = g[3];
52 | crypto_int32 g4 = g[4];
53 | crypto_int32 g5 = g[5];
54 | crypto_int32 g6 = g[6];
55 | crypto_int32 g7 = g[7];
56 | crypto_int32 g8 = g[8];
57 | crypto_int32 g9 = g[9];
58 | crypto_int32 g1_19 = 19 * g1; /* 1.959375*2^29 */
59 | crypto_int32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */
60 | crypto_int32 g3_19 = 19 * g3;
61 | crypto_int32 g4_19 = 19 * g4;
62 | crypto_int32 g5_19 = 19 * g5;
63 | crypto_int32 g6_19 = 19 * g6;
64 | crypto_int32 g7_19 = 19 * g7;
65 | crypto_int32 g8_19 = 19 * g8;
66 | crypto_int32 g9_19 = 19 * g9;
67 | crypto_int32 f1_2 = 2 * f1;
68 | crypto_int32 f3_2 = 2 * f3;
69 | crypto_int32 f5_2 = 2 * f5;
70 | crypto_int32 f7_2 = 2 * f7;
71 | crypto_int32 f9_2 = 2 * f9;
72 | crypto_int64 f0g0 = f0 * (crypto_int64) g0;
73 | crypto_int64 f0g1 = f0 * (crypto_int64) g1;
74 | crypto_int64 f0g2 = f0 * (crypto_int64) g2;
75 | crypto_int64 f0g3 = f0 * (crypto_int64) g3;
76 | crypto_int64 f0g4 = f0 * (crypto_int64) g4;
77 | crypto_int64 f0g5 = f0 * (crypto_int64) g5;
78 | crypto_int64 f0g6 = f0 * (crypto_int64) g6;
79 | crypto_int64 f0g7 = f0 * (crypto_int64) g7;
80 | crypto_int64 f0g8 = f0 * (crypto_int64) g8;
81 | crypto_int64 f0g9 = f0 * (crypto_int64) g9;
82 | crypto_int64 f1g0 = f1 * (crypto_int64) g0;
83 | crypto_int64 f1g1_2 = f1_2 * (crypto_int64) g1;
84 | crypto_int64 f1g2 = f1 * (crypto_int64) g2;
85 | crypto_int64 f1g3_2 = f1_2 * (crypto_int64) g3;
86 | crypto_int64 f1g4 = f1 * (crypto_int64) g4;
87 | crypto_int64 f1g5_2 = f1_2 * (crypto_int64) g5;
88 | crypto_int64 f1g6 = f1 * (crypto_int64) g6;
89 | crypto_int64 f1g7_2 = f1_2 * (crypto_int64) g7;
90 | crypto_int64 f1g8 = f1 * (crypto_int64) g8;
91 | crypto_int64 f1g9_38 = f1_2 * (crypto_int64) g9_19;
92 | crypto_int64 f2g0 = f2 * (crypto_int64) g0;
93 | crypto_int64 f2g1 = f2 * (crypto_int64) g1;
94 | crypto_int64 f2g2 = f2 * (crypto_int64) g2;
95 | crypto_int64 f2g3 = f2 * (crypto_int64) g3;
96 | crypto_int64 f2g4 = f2 * (crypto_int64) g4;
97 | crypto_int64 f2g5 = f2 * (crypto_int64) g5;
98 | crypto_int64 f2g6 = f2 * (crypto_int64) g6;
99 | crypto_int64 f2g7 = f2 * (crypto_int64) g7;
100 | crypto_int64 f2g8_19 = f2 * (crypto_int64) g8_19;
101 | crypto_int64 f2g9_19 = f2 * (crypto_int64) g9_19;
102 | crypto_int64 f3g0 = f3 * (crypto_int64) g0;
103 | crypto_int64 f3g1_2 = f3_2 * (crypto_int64) g1;
104 | crypto_int64 f3g2 = f3 * (crypto_int64) g2;
105 | crypto_int64 f3g3_2 = f3_2 * (crypto_int64) g3;
106 | crypto_int64 f3g4 = f3 * (crypto_int64) g4;
107 | crypto_int64 f3g5_2 = f3_2 * (crypto_int64) g5;
108 | crypto_int64 f3g6 = f3 * (crypto_int64) g6;
109 | crypto_int64 f3g7_38 = f3_2 * (crypto_int64) g7_19;
110 | crypto_int64 f3g8_19 = f3 * (crypto_int64) g8_19;
111 | crypto_int64 f3g9_38 = f3_2 * (crypto_int64) g9_19;
112 | crypto_int64 f4g0 = f4 * (crypto_int64) g0;
113 | crypto_int64 f4g1 = f4 * (crypto_int64) g1;
114 | crypto_int64 f4g2 = f4 * (crypto_int64) g2;
115 | crypto_int64 f4g3 = f4 * (crypto_int64) g3;
116 | crypto_int64 f4g4 = f4 * (crypto_int64) g4;
117 | crypto_int64 f4g5 = f4 * (crypto_int64) g5;
118 | crypto_int64 f4g6_19 = f4 * (crypto_int64) g6_19;
119 | crypto_int64 f4g7_19 = f4 * (crypto_int64) g7_19;
120 | crypto_int64 f4g8_19 = f4 * (crypto_int64) g8_19;
121 | crypto_int64 f4g9_19 = f4 * (crypto_int64) g9_19;
122 | crypto_int64 f5g0 = f5 * (crypto_int64) g0;
123 | crypto_int64 f5g1_2 = f5_2 * (crypto_int64) g1;
124 | crypto_int64 f5g2 = f5 * (crypto_int64) g2;
125 | crypto_int64 f5g3_2 = f5_2 * (crypto_int64) g3;
126 | crypto_int64 f5g4 = f5 * (crypto_int64) g4;
127 | crypto_int64 f5g5_38 = f5_2 * (crypto_int64) g5_19;
128 | crypto_int64 f5g6_19 = f5 * (crypto_int64) g6_19;
129 | crypto_int64 f5g7_38 = f5_2 * (crypto_int64) g7_19;
130 | crypto_int64 f5g8_19 = f5 * (crypto_int64) g8_19;
131 | crypto_int64 f5g9_38 = f5_2 * (crypto_int64) g9_19;
132 | crypto_int64 f6g0 = f6 * (crypto_int64) g0;
133 | crypto_int64 f6g1 = f6 * (crypto_int64) g1;
134 | crypto_int64 f6g2 = f6 * (crypto_int64) g2;
135 | crypto_int64 f6g3 = f6 * (crypto_int64) g3;
136 | crypto_int64 f6g4_19 = f6 * (crypto_int64) g4_19;
137 | crypto_int64 f6g5_19 = f6 * (crypto_int64) g5_19;
138 | crypto_int64 f6g6_19 = f6 * (crypto_int64) g6_19;
139 | crypto_int64 f6g7_19 = f6 * (crypto_int64) g7_19;
140 | crypto_int64 f6g8_19 = f6 * (crypto_int64) g8_19;
141 | crypto_int64 f6g9_19 = f6 * (crypto_int64) g9_19;
142 | crypto_int64 f7g0 = f7 * (crypto_int64) g0;
143 | crypto_int64 f7g1_2 = f7_2 * (crypto_int64) g1;
144 | crypto_int64 f7g2 = f7 * (crypto_int64) g2;
145 | crypto_int64 f7g3_38 = f7_2 * (crypto_int64) g3_19;
146 | crypto_int64 f7g4_19 = f7 * (crypto_int64) g4_19;
147 | crypto_int64 f7g5_38 = f7_2 * (crypto_int64) g5_19;
148 | crypto_int64 f7g6_19 = f7 * (crypto_int64) g6_19;
149 | crypto_int64 f7g7_38 = f7_2 * (crypto_int64) g7_19;
150 | crypto_int64 f7g8_19 = f7 * (crypto_int64) g8_19;
151 | crypto_int64 f7g9_38 = f7_2 * (crypto_int64) g9_19;
152 | crypto_int64 f8g0 = f8 * (crypto_int64) g0;
153 | crypto_int64 f8g1 = f8 * (crypto_int64) g1;
154 | crypto_int64 f8g2_19 = f8 * (crypto_int64) g2_19;
155 | crypto_int64 f8g3_19 = f8 * (crypto_int64) g3_19;
156 | crypto_int64 f8g4_19 = f8 * (crypto_int64) g4_19;
157 | crypto_int64 f8g5_19 = f8 * (crypto_int64) g5_19;
158 | crypto_int64 f8g6_19 = f8 * (crypto_int64) g6_19;
159 | crypto_int64 f8g7_19 = f8 * (crypto_int64) g7_19;
160 | crypto_int64 f8g8_19 = f8 * (crypto_int64) g8_19;
161 | crypto_int64 f8g9_19 = f8 * (crypto_int64) g9_19;
162 | crypto_int64 f9g0 = f9 * (crypto_int64) g0;
163 | crypto_int64 f9g1_38 = f9_2 * (crypto_int64) g1_19;
164 | crypto_int64 f9g2_19 = f9 * (crypto_int64) g2_19;
165 | crypto_int64 f9g3_38 = f9_2 * (crypto_int64) g3_19;
166 | crypto_int64 f9g4_19 = f9 * (crypto_int64) g4_19;
167 | crypto_int64 f9g5_38 = f9_2 * (crypto_int64) g5_19;
168 | crypto_int64 f9g6_19 = f9 * (crypto_int64) g6_19;
169 | crypto_int64 f9g7_38 = f9_2 * (crypto_int64) g7_19;
170 | crypto_int64 f9g8_19 = f9 * (crypto_int64) g8_19;
171 | crypto_int64 f9g9_38 = f9_2 * (crypto_int64) g9_19;
172 | crypto_int64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38;
173 | crypto_int64 h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19;
174 | crypto_int64 h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38;
175 | crypto_int64 h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19;
176 | crypto_int64 h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38;
177 | crypto_int64 h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19;
178 | crypto_int64 h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38;
179 | crypto_int64 h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19;
180 | crypto_int64 h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38;
181 | crypto_int64 h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ;
182 | crypto_int64 carry0;
183 | crypto_int64 carry1;
184 | crypto_int64 carry2;
185 | crypto_int64 carry3;
186 | crypto_int64 carry4;
187 | crypto_int64 carry5;
188 | crypto_int64 carry6;
189 | crypto_int64 carry7;
190 | crypto_int64 carry8;
191 | crypto_int64 carry9;
192 |
193 | /*
194 | |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38))
195 | i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8
196 | |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19))
197 | i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9
198 | */
199 |
200 | carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
201 | carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
202 | /* |h0| <= 2^25 */
203 | /* |h4| <= 2^25 */
204 | /* |h1| <= 1.71*2^59 */
205 | /* |h5| <= 1.71*2^59 */
206 |
207 | carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
208 | carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
209 | /* |h1| <= 2^24; from now on fits into int32 */
210 | /* |h5| <= 2^24; from now on fits into int32 */
211 | /* |h2| <= 1.41*2^60 */
212 | /* |h6| <= 1.41*2^60 */
213 |
214 | carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
215 | carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
216 | /* |h2| <= 2^25; from now on fits into int32 unchanged */
217 | /* |h6| <= 2^25; from now on fits into int32 unchanged */
218 | /* |h3| <= 1.71*2^59 */
219 | /* |h7| <= 1.71*2^59 */
220 |
221 | carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
222 | carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
223 | /* |h3| <= 2^24; from now on fits into int32 unchanged */
224 | /* |h7| <= 2^24; from now on fits into int32 unchanged */
225 | /* |h4| <= 1.72*2^34 */
226 | /* |h8| <= 1.41*2^60 */
227 |
228 | carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
229 | carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
230 | /* |h4| <= 2^25; from now on fits into int32 unchanged */
231 | /* |h8| <= 2^25; from now on fits into int32 unchanged */
232 | /* |h5| <= 1.01*2^24 */
233 | /* |h9| <= 1.71*2^59 */
234 |
235 | carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
236 | /* |h9| <= 2^24; from now on fits into int32 unchanged */
237 | /* |h0| <= 1.1*2^39 */
238 |
239 | carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
240 | /* |h0| <= 2^25; from now on fits into int32 unchanged */
241 | /* |h1| <= 1.01*2^24 */
242 |
243 | h[0] = h0;
244 | h[1] = h1;
245 | h[2] = h2;
246 | h[3] = h3;
247 | h[4] = h4;
248 | h[5] = h5;
249 | h[6] = h6;
250 | h[7] = h7;
251 | h[8] = h8;
252 | h[9] = h9;
253 | }
254 |
--------------------------------------------------------------------------------
/src/ref10/fe_neg.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | h = -f
5 |
6 | Preconditions:
7 | |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
8 |
9 | Postconditions:
10 | |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
11 | */
12 |
13 | void fe_neg(fe h,const fe f)
14 | {
15 | crypto_int32 f0 = f[0];
16 | crypto_int32 f1 = f[1];
17 | crypto_int32 f2 = f[2];
18 | crypto_int32 f3 = f[3];
19 | crypto_int32 f4 = f[4];
20 | crypto_int32 f5 = f[5];
21 | crypto_int32 f6 = f[6];
22 | crypto_int32 f7 = f[7];
23 | crypto_int32 f8 = f[8];
24 | crypto_int32 f9 = f[9];
25 | crypto_int32 h0 = -f0;
26 | crypto_int32 h1 = -f1;
27 | crypto_int32 h2 = -f2;
28 | crypto_int32 h3 = -f3;
29 | crypto_int32 h4 = -f4;
30 | crypto_int32 h5 = -f5;
31 | crypto_int32 h6 = -f6;
32 | crypto_int32 h7 = -f7;
33 | crypto_int32 h8 = -f8;
34 | crypto_int32 h9 = -f9;
35 | h[0] = h0;
36 | h[1] = h1;
37 | h[2] = h2;
38 | h[3] = h3;
39 | h[4] = h4;
40 | h[5] = h5;
41 | h[6] = h6;
42 | h[7] = h7;
43 | h[8] = h8;
44 | h[9] = h9;
45 | }
46 |
--------------------------------------------------------------------------------
/src/ref10/fe_pow22523.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | void fe_pow22523(fe out,const fe z)
4 | {
5 | fe t0;
6 | fe t1;
7 | fe t2;
8 | int i;
9 |
10 | #include "pow22523.h"
11 |
12 | return;
13 | }
14 |
--------------------------------------------------------------------------------
/src/ref10/fe_sq.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 | #include "crypto_int64.h"
3 |
4 | /*
5 | h = f * f
6 | Can overlap h with f.
7 |
8 | Preconditions:
9 | |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
10 |
11 | Postconditions:
12 | |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
13 | */
14 |
15 | /*
16 | See fe_mul.c for discussion of implementation strategy.
17 | */
18 |
19 | void fe_sq(fe h,const fe f)
20 | {
21 | crypto_int32 f0 = f[0];
22 | crypto_int32 f1 = f[1];
23 | crypto_int32 f2 = f[2];
24 | crypto_int32 f3 = f[3];
25 | crypto_int32 f4 = f[4];
26 | crypto_int32 f5 = f[5];
27 | crypto_int32 f6 = f[6];
28 | crypto_int32 f7 = f[7];
29 | crypto_int32 f8 = f[8];
30 | crypto_int32 f9 = f[9];
31 | crypto_int32 f0_2 = 2 * f0;
32 | crypto_int32 f1_2 = 2 * f1;
33 | crypto_int32 f2_2 = 2 * f2;
34 | crypto_int32 f3_2 = 2 * f3;
35 | crypto_int32 f4_2 = 2 * f4;
36 | crypto_int32 f5_2 = 2 * f5;
37 | crypto_int32 f6_2 = 2 * f6;
38 | crypto_int32 f7_2 = 2 * f7;
39 | crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
40 | crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
41 | crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
42 | crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
43 | crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
44 | crypto_int64 f0f0 = f0 * (crypto_int64) f0;
45 | crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1;
46 | crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2;
47 | crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3;
48 | crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4;
49 | crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5;
50 | crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6;
51 | crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7;
52 | crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8;
53 | crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9;
54 | crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1;
55 | crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2;
56 | crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2;
57 | crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4;
58 | crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2;
59 | crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6;
60 | crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2;
61 | crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8;
62 | crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
63 | crypto_int64 f2f2 = f2 * (crypto_int64) f2;
64 | crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3;
65 | crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4;
66 | crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5;
67 | crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6;
68 | crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7;
69 | crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
70 | crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38;
71 | crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3;
72 | crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4;
73 | crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2;
74 | crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6;
75 | crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
76 | crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
77 | crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
78 | crypto_int64 f4f4 = f4 * (crypto_int64) f4;
79 | crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5;
80 | crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
81 | crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38;
82 | crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
83 | crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38;
84 | crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38;
85 | crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
86 | crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
87 | crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
88 | crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
89 | crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19;
90 | crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38;
91 | crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
92 | crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38;
93 | crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38;
94 | crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
95 | crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
96 | crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19;
97 | crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38;
98 | crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38;
99 | crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
100 | crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
101 | crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
102 | crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
103 | crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
104 | crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
105 | crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
106 | crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
107 | crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
108 | crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
109 | crypto_int64 carry0;
110 | crypto_int64 carry1;
111 | crypto_int64 carry2;
112 | crypto_int64 carry3;
113 | crypto_int64 carry4;
114 | crypto_int64 carry5;
115 | crypto_int64 carry6;
116 | crypto_int64 carry7;
117 | crypto_int64 carry8;
118 | crypto_int64 carry9;
119 |
120 | carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
121 | carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
122 |
123 | carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
124 | carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
125 |
126 | carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
127 | carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
128 |
129 | carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
130 | carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
131 |
132 | carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
133 | carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
134 |
135 | carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
136 |
137 | carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
138 |
139 | h[0] = h0;
140 | h[1] = h1;
141 | h[2] = h2;
142 | h[3] = h3;
143 | h[4] = h4;
144 | h[5] = h5;
145 | h[6] = h6;
146 | h[7] = h7;
147 | h[8] = h8;
148 | h[9] = h9;
149 | }
150 |
--------------------------------------------------------------------------------
/src/ref10/fe_sq2.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 | #include "crypto_int64.h"
3 |
4 | /*
5 | h = 2 * f * f
6 | Can overlap h with f.
7 |
8 | Preconditions:
9 | |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc.
10 |
11 | Postconditions:
12 | |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc.
13 | */
14 |
15 | /*
16 | See fe_mul.c for discussion of implementation strategy.
17 | */
18 |
19 | void fe_sq2(fe h,const fe f)
20 | {
21 | crypto_int32 f0 = f[0];
22 | crypto_int32 f1 = f[1];
23 | crypto_int32 f2 = f[2];
24 | crypto_int32 f3 = f[3];
25 | crypto_int32 f4 = f[4];
26 | crypto_int32 f5 = f[5];
27 | crypto_int32 f6 = f[6];
28 | crypto_int32 f7 = f[7];
29 | crypto_int32 f8 = f[8];
30 | crypto_int32 f9 = f[9];
31 | crypto_int32 f0_2 = 2 * f0;
32 | crypto_int32 f1_2 = 2 * f1;
33 | crypto_int32 f2_2 = 2 * f2;
34 | crypto_int32 f3_2 = 2 * f3;
35 | crypto_int32 f4_2 = 2 * f4;
36 | crypto_int32 f5_2 = 2 * f5;
37 | crypto_int32 f6_2 = 2 * f6;
38 | crypto_int32 f7_2 = 2 * f7;
39 | crypto_int32 f5_38 = 38 * f5; /* 1.959375*2^30 */
40 | crypto_int32 f6_19 = 19 * f6; /* 1.959375*2^30 */
41 | crypto_int32 f7_38 = 38 * f7; /* 1.959375*2^30 */
42 | crypto_int32 f8_19 = 19 * f8; /* 1.959375*2^30 */
43 | crypto_int32 f9_38 = 38 * f9; /* 1.959375*2^30 */
44 | crypto_int64 f0f0 = f0 * (crypto_int64) f0;
45 | crypto_int64 f0f1_2 = f0_2 * (crypto_int64) f1;
46 | crypto_int64 f0f2_2 = f0_2 * (crypto_int64) f2;
47 | crypto_int64 f0f3_2 = f0_2 * (crypto_int64) f3;
48 | crypto_int64 f0f4_2 = f0_2 * (crypto_int64) f4;
49 | crypto_int64 f0f5_2 = f0_2 * (crypto_int64) f5;
50 | crypto_int64 f0f6_2 = f0_2 * (crypto_int64) f6;
51 | crypto_int64 f0f7_2 = f0_2 * (crypto_int64) f7;
52 | crypto_int64 f0f8_2 = f0_2 * (crypto_int64) f8;
53 | crypto_int64 f0f9_2 = f0_2 * (crypto_int64) f9;
54 | crypto_int64 f1f1_2 = f1_2 * (crypto_int64) f1;
55 | crypto_int64 f1f2_2 = f1_2 * (crypto_int64) f2;
56 | crypto_int64 f1f3_4 = f1_2 * (crypto_int64) f3_2;
57 | crypto_int64 f1f4_2 = f1_2 * (crypto_int64) f4;
58 | crypto_int64 f1f5_4 = f1_2 * (crypto_int64) f5_2;
59 | crypto_int64 f1f6_2 = f1_2 * (crypto_int64) f6;
60 | crypto_int64 f1f7_4 = f1_2 * (crypto_int64) f7_2;
61 | crypto_int64 f1f8_2 = f1_2 * (crypto_int64) f8;
62 | crypto_int64 f1f9_76 = f1_2 * (crypto_int64) f9_38;
63 | crypto_int64 f2f2 = f2 * (crypto_int64) f2;
64 | crypto_int64 f2f3_2 = f2_2 * (crypto_int64) f3;
65 | crypto_int64 f2f4_2 = f2_2 * (crypto_int64) f4;
66 | crypto_int64 f2f5_2 = f2_2 * (crypto_int64) f5;
67 | crypto_int64 f2f6_2 = f2_2 * (crypto_int64) f6;
68 | crypto_int64 f2f7_2 = f2_2 * (crypto_int64) f7;
69 | crypto_int64 f2f8_38 = f2_2 * (crypto_int64) f8_19;
70 | crypto_int64 f2f9_38 = f2 * (crypto_int64) f9_38;
71 | crypto_int64 f3f3_2 = f3_2 * (crypto_int64) f3;
72 | crypto_int64 f3f4_2 = f3_2 * (crypto_int64) f4;
73 | crypto_int64 f3f5_4 = f3_2 * (crypto_int64) f5_2;
74 | crypto_int64 f3f6_2 = f3_2 * (crypto_int64) f6;
75 | crypto_int64 f3f7_76 = f3_2 * (crypto_int64) f7_38;
76 | crypto_int64 f3f8_38 = f3_2 * (crypto_int64) f8_19;
77 | crypto_int64 f3f9_76 = f3_2 * (crypto_int64) f9_38;
78 | crypto_int64 f4f4 = f4 * (crypto_int64) f4;
79 | crypto_int64 f4f5_2 = f4_2 * (crypto_int64) f5;
80 | crypto_int64 f4f6_38 = f4_2 * (crypto_int64) f6_19;
81 | crypto_int64 f4f7_38 = f4 * (crypto_int64) f7_38;
82 | crypto_int64 f4f8_38 = f4_2 * (crypto_int64) f8_19;
83 | crypto_int64 f4f9_38 = f4 * (crypto_int64) f9_38;
84 | crypto_int64 f5f5_38 = f5 * (crypto_int64) f5_38;
85 | crypto_int64 f5f6_38 = f5_2 * (crypto_int64) f6_19;
86 | crypto_int64 f5f7_76 = f5_2 * (crypto_int64) f7_38;
87 | crypto_int64 f5f8_38 = f5_2 * (crypto_int64) f8_19;
88 | crypto_int64 f5f9_76 = f5_2 * (crypto_int64) f9_38;
89 | crypto_int64 f6f6_19 = f6 * (crypto_int64) f6_19;
90 | crypto_int64 f6f7_38 = f6 * (crypto_int64) f7_38;
91 | crypto_int64 f6f8_38 = f6_2 * (crypto_int64) f8_19;
92 | crypto_int64 f6f9_38 = f6 * (crypto_int64) f9_38;
93 | crypto_int64 f7f7_38 = f7 * (crypto_int64) f7_38;
94 | crypto_int64 f7f8_38 = f7_2 * (crypto_int64) f8_19;
95 | crypto_int64 f7f9_76 = f7_2 * (crypto_int64) f9_38;
96 | crypto_int64 f8f8_19 = f8 * (crypto_int64) f8_19;
97 | crypto_int64 f8f9_38 = f8 * (crypto_int64) f9_38;
98 | crypto_int64 f9f9_38 = f9 * (crypto_int64) f9_38;
99 | crypto_int64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38;
100 | crypto_int64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38;
101 | crypto_int64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19;
102 | crypto_int64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38;
103 | crypto_int64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38;
104 | crypto_int64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38;
105 | crypto_int64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19;
106 | crypto_int64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38;
107 | crypto_int64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38;
108 | crypto_int64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2;
109 | crypto_int64 carry0;
110 | crypto_int64 carry1;
111 | crypto_int64 carry2;
112 | crypto_int64 carry3;
113 | crypto_int64 carry4;
114 | crypto_int64 carry5;
115 | crypto_int64 carry6;
116 | crypto_int64 carry7;
117 | crypto_int64 carry8;
118 | crypto_int64 carry9;
119 |
120 | h0 += h0;
121 | h1 += h1;
122 | h2 += h2;
123 | h3 += h3;
124 | h4 += h4;
125 | h5 += h5;
126 | h6 += h6;
127 | h7 += h7;
128 | h8 += h8;
129 | h9 += h9;
130 |
131 | carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
132 | carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
133 |
134 | carry1 = (h1 + (crypto_int64) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25;
135 | carry5 = (h5 + (crypto_int64) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25;
136 |
137 | carry2 = (h2 + (crypto_int64) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26;
138 | carry6 = (h6 + (crypto_int64) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26;
139 |
140 | carry3 = (h3 + (crypto_int64) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25;
141 | carry7 = (h7 + (crypto_int64) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25;
142 |
143 | carry4 = (h4 + (crypto_int64) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26;
144 | carry8 = (h8 + (crypto_int64) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26;
145 |
146 | carry9 = (h9 + (crypto_int64) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25;
147 |
148 | carry0 = (h0 + (crypto_int64) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26;
149 |
150 | h[0] = h0;
151 | h[1] = h1;
152 | h[2] = h2;
153 | h[3] = h3;
154 | h[4] = h4;
155 | h[5] = h5;
156 | h[6] = h6;
157 | h[7] = h7;
158 | h[8] = h8;
159 | h[9] = h9;
160 | }
161 |
--------------------------------------------------------------------------------
/src/ref10/fe_sub.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | h = f - g
5 | Can overlap h with f or g.
6 |
7 | Preconditions:
8 | |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
9 | |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc.
10 |
11 | Postconditions:
12 | |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
13 | */
14 |
15 | void fe_sub(fe h,const fe f,const fe g)
16 | {
17 | crypto_int32 f0 = f[0];
18 | crypto_int32 f1 = f[1];
19 | crypto_int32 f2 = f[2];
20 | crypto_int32 f3 = f[3];
21 | crypto_int32 f4 = f[4];
22 | crypto_int32 f5 = f[5];
23 | crypto_int32 f6 = f[6];
24 | crypto_int32 f7 = f[7];
25 | crypto_int32 f8 = f[8];
26 | crypto_int32 f9 = f[9];
27 | crypto_int32 g0 = g[0];
28 | crypto_int32 g1 = g[1];
29 | crypto_int32 g2 = g[2];
30 | crypto_int32 g3 = g[3];
31 | crypto_int32 g4 = g[4];
32 | crypto_int32 g5 = g[5];
33 | crypto_int32 g6 = g[6];
34 | crypto_int32 g7 = g[7];
35 | crypto_int32 g8 = g[8];
36 | crypto_int32 g9 = g[9];
37 | crypto_int32 h0 = f0 - g0;
38 | crypto_int32 h1 = f1 - g1;
39 | crypto_int32 h2 = f2 - g2;
40 | crypto_int32 h3 = f3 - g3;
41 | crypto_int32 h4 = f4 - g4;
42 | crypto_int32 h5 = f5 - g5;
43 | crypto_int32 h6 = f6 - g6;
44 | crypto_int32 h7 = f7 - g7;
45 | crypto_int32 h8 = f8 - g8;
46 | crypto_int32 h9 = f9 - g9;
47 | h[0] = h0;
48 | h[1] = h1;
49 | h[2] = h2;
50 | h[3] = h3;
51 | h[4] = h4;
52 | h[5] = h5;
53 | h[6] = h6;
54 | h[7] = h7;
55 | h[8] = h8;
56 | h[9] = h9;
57 | }
58 |
--------------------------------------------------------------------------------
/src/ref10/fe_tobytes.c:
--------------------------------------------------------------------------------
1 | #include "fe.h"
2 |
3 | /*
4 | Preconditions:
5 | |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc.
6 |
7 | Write p=2^255-19; q=floor(h/p).
8 | Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))).
9 |
10 | Proof:
11 | Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4.
12 | Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4.
13 |
14 | Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9).
15 | Then 0> 25;
53 | q = (h0 + q) >> 26;
54 | q = (h1 + q) >> 25;
55 | q = (h2 + q) >> 26;
56 | q = (h3 + q) >> 25;
57 | q = (h4 + q) >> 26;
58 | q = (h5 + q) >> 25;
59 | q = (h6 + q) >> 26;
60 | q = (h7 + q) >> 25;
61 | q = (h8 + q) >> 26;
62 | q = (h9 + q) >> 25;
63 |
64 | /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
65 | h0 += 19 * q;
66 | /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
67 |
68 | carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
69 | carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
70 | carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
71 | carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
72 | carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
73 | carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
74 | carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
75 | carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
76 | carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
77 | carry9 = h9 >> 25; h9 -= carry9 << 25;
78 | /* h10 = carry9 */
79 |
80 | /*
81 | Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
82 | Have h0+...+2^230 h9 between 0 and 2^255-1;
83 | evidently 2^255 h10-2^255 q = 0.
84 | Goal: Output h0+...+2^230 h9.
85 | */
86 |
87 | s[0] = h0 >> 0;
88 | s[1] = h0 >> 8;
89 | s[2] = h0 >> 16;
90 | s[3] = (h0 >> 24) | (h1 << 2);
91 | s[4] = h1 >> 6;
92 | s[5] = h1 >> 14;
93 | s[6] = (h1 >> 22) | (h2 << 3);
94 | s[7] = h2 >> 5;
95 | s[8] = h2 >> 13;
96 | s[9] = (h2 >> 21) | (h3 << 5);
97 | s[10] = h3 >> 3;
98 | s[11] = h3 >> 11;
99 | s[12] = (h3 >> 19) | (h4 << 6);
100 | s[13] = h4 >> 2;
101 | s[14] = h4 >> 10;
102 | s[15] = h4 >> 18;
103 | s[16] = h5 >> 0;
104 | s[17] = h5 >> 8;
105 | s[18] = h5 >> 16;
106 | s[19] = (h5 >> 24) | (h6 << 1);
107 | s[20] = h6 >> 7;
108 | s[21] = h6 >> 15;
109 | s[22] = (h6 >> 23) | (h7 << 3);
110 | s[23] = h7 >> 5;
111 | s[24] = h7 >> 13;
112 | s[25] = (h7 >> 21) | (h8 << 4);
113 | s[26] = h8 >> 4;
114 | s[27] = h8 >> 12;
115 | s[28] = (h8 >> 20) | (h9 << 6);
116 | s[29] = h9 >> 2;
117 | s[30] = h9 >> 10;
118 | s[31] = h9 >> 18;
119 | }
120 |
--------------------------------------------------------------------------------
/src/ref10/ge.h:
--------------------------------------------------------------------------------
1 | #ifndef GE_H
2 | #define GE_H
3 |
4 | /*
5 | ge means group element.
6 |
7 | Here the group is the set of pairs (x,y) of field elements (see fe.h)
8 | satisfying -x^2 + y^2 = 1 + d x^2y^2
9 | where d = -121665/121666.
10 |
11 | Representations:
12 | ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
13 | ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
14 | ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
15 | ge_precomp (Duif): (y+x,y-x,2dxy)
16 | */
17 |
18 | #include "fe.h"
19 |
20 | typedef struct {
21 | fe X;
22 | fe Y;
23 | fe Z;
24 | } ge_p2;
25 |
26 | typedef struct {
27 | fe X;
28 | fe Y;
29 | fe Z;
30 | fe T;
31 | } ge_p3;
32 |
33 | typedef struct {
34 | fe X;
35 | fe Y;
36 | fe Z;
37 | fe T;
38 | } ge_p1p1;
39 |
40 | typedef struct {
41 | fe yplusx;
42 | fe yminusx;
43 | fe xy2d;
44 | } ge_precomp;
45 |
46 | typedef struct {
47 | fe YplusX;
48 | fe YminusX;
49 | fe Z;
50 | fe T2d;
51 | } ge_cached;
52 |
53 | #define ge_frombytes_negate_vartime crypto_sign_ed25519_ref10_ge_frombytes_negate_vartime
54 | #define ge_tobytes crypto_sign_ed25519_ref10_ge_tobytes
55 | #define ge_p3_tobytes crypto_sign_ed25519_ref10_ge_p3_tobytes
56 |
57 | #define ge_p2_0 crypto_sign_ed25519_ref10_ge_p2_0
58 | #define ge_p3_0 crypto_sign_ed25519_ref10_ge_p3_0
59 | #define ge_precomp_0 crypto_sign_ed25519_ref10_ge_precomp_0
60 | #define ge_p3_to_p2 crypto_sign_ed25519_ref10_ge_p3_to_p2
61 | #define ge_p3_to_cached crypto_sign_ed25519_ref10_ge_p3_to_cached
62 | #define ge_p1p1_to_p2 crypto_sign_ed25519_ref10_ge_p1p1_to_p2
63 | #define ge_p1p1_to_p3 crypto_sign_ed25519_ref10_ge_p1p1_to_p3
64 | #define ge_p2_dbl crypto_sign_ed25519_ref10_ge_p2_dbl
65 | #define ge_p3_dbl crypto_sign_ed25519_ref10_ge_p3_dbl
66 |
67 | #define ge_madd crypto_sign_ed25519_ref10_ge_madd
68 | #define ge_msub crypto_sign_ed25519_ref10_ge_msub
69 | #define ge_add crypto_sign_ed25519_ref10_ge_add
70 | #define ge_sub crypto_sign_ed25519_ref10_ge_sub
71 | #define ge_scalarmult_base crypto_sign_ed25519_ref10_ge_scalarmult_base
72 | #define ge_double_scalarmult_vartime crypto_sign_ed25519_ref10_ge_double_scalarmult_vartime
73 |
74 | extern void ge_tobytes(unsigned char *,const ge_p2 *);
75 | extern void ge_p3_tobytes(unsigned char *,const ge_p3 *);
76 | extern int ge_frombytes_negate_vartime(ge_p3 *,const unsigned char *);
77 |
78 | extern void ge_p2_0(ge_p2 *);
79 | extern void ge_p3_0(ge_p3 *);
80 | extern void ge_precomp_0(ge_precomp *);
81 | extern void ge_p3_to_p2(ge_p2 *,const ge_p3 *);
82 | extern void ge_p3_to_cached(ge_cached *,const ge_p3 *);
83 | extern void ge_p1p1_to_p2(ge_p2 *,const ge_p1p1 *);
84 | extern void ge_p1p1_to_p3(ge_p3 *,const ge_p1p1 *);
85 | extern void ge_p2_dbl(ge_p1p1 *,const ge_p2 *);
86 | extern void ge_p3_dbl(ge_p1p1 *,const ge_p3 *);
87 |
88 | extern void ge_madd(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
89 | extern void ge_msub(ge_p1p1 *,const ge_p3 *,const ge_precomp *);
90 | extern void ge_add(ge_p1p1 *,const ge_p3 *,const ge_cached *);
91 | extern void ge_sub(ge_p1p1 *,const ge_p3 *,const ge_cached *);
92 | extern void ge_scalarmult_base(ge_p3 *,const unsigned char *);
93 | extern void ge_double_scalarmult_vartime(ge_p2 *,const unsigned char *,const ge_p3 *,const unsigned char *);
94 |
95 | #endif
96 |
--------------------------------------------------------------------------------
/src/ref10/ge_add.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p + q
5 | */
6 |
7 | void ge_add(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
8 | {
9 | fe t0;
10 | #include "ge_add.h"
11 | }
12 |
--------------------------------------------------------------------------------
/src/ref10/ge_add.h:
--------------------------------------------------------------------------------
1 |
2 | /* qhasm: enter ge_add */
3 |
4 | /* qhasm: fe X1 */
5 |
6 | /* qhasm: fe Y1 */
7 |
8 | /* qhasm: fe Z1 */
9 |
10 | /* qhasm: fe Z2 */
11 |
12 | /* qhasm: fe T1 */
13 |
14 | /* qhasm: fe ZZ */
15 |
16 | /* qhasm: fe YpX2 */
17 |
18 | /* qhasm: fe YmX2 */
19 |
20 | /* qhasm: fe T2d2 */
21 |
22 | /* qhasm: fe X3 */
23 |
24 | /* qhasm: fe Y3 */
25 |
26 | /* qhasm: fe Z3 */
27 |
28 | /* qhasm: fe T3 */
29 |
30 | /* qhasm: fe YpX1 */
31 |
32 | /* qhasm: fe YmX1 */
33 |
34 | /* qhasm: fe A */
35 |
36 | /* qhasm: fe B */
37 |
38 | /* qhasm: fe C */
39 |
40 | /* qhasm: fe D */
41 |
42 | /* qhasm: YpX1 = Y1+X1 */
43 | /* asm 1: fe_add(>YpX1=fe#1,YpX1=r->X,Y,X); */
45 | fe_add(r->X,p->Y,p->X);
46 |
47 | /* qhasm: YmX1 = Y1-X1 */
48 | /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */
50 | fe_sub(r->Y,p->Y,p->X);
51 |
52 | /* qhasm: A = YpX1*YpX2 */
53 | /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,YplusX); */
55 | fe_mul(r->Z,r->X,q->YplusX);
56 |
57 | /* qhasm: B = YmX1*YmX2 */
58 | /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,YminusX); */
60 | fe_mul(r->Y,r->Y,q->YminusX);
61 |
62 | /* qhasm: C = T2d2*T1 */
63 | /* asm 1: fe_mul(>C=fe#4,C=r->T,T2d,T); */
65 | fe_mul(r->T,q->T2d,p->T);
66 |
67 | /* qhasm: ZZ = Z1*Z2 */
68 | /* asm 1: fe_mul(>ZZ=fe#1,ZZ=r->X,Z,Z); */
70 | fe_mul(r->X,p->Z,q->Z);
71 |
72 | /* qhasm: D = 2*ZZ */
73 | /* asm 1: fe_add(>D=fe#5,D=t0,X,X); */
75 | fe_add(t0,r->X,r->X);
76 |
77 | /* qhasm: X3 = A-B */
78 | /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */
80 | fe_sub(r->X,r->Z,r->Y);
81 |
82 | /* qhasm: Y3 = A+B */
83 | /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */
85 | fe_add(r->Y,r->Z,r->Y);
86 |
87 | /* qhasm: Z3 = D+C */
88 | /* asm 1: fe_add(>Z3=fe#3,Z3=r->Z,T); */
90 | fe_add(r->Z,t0,r->T);
91 |
92 | /* qhasm: T3 = D-C */
93 | /* asm 1: fe_sub(>T3=fe#4,T3=r->T,T); */
95 | fe_sub(r->T,t0,r->T);
96 |
97 | /* qhasm: return */
98 |
--------------------------------------------------------------------------------
/src/ref10/ge_double_scalarmult.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | static void slide(signed char *r,const unsigned char *a)
4 | {
5 | int i;
6 | int b;
7 | int k;
8 |
9 | for (i = 0;i < 256;++i)
10 | r[i] = 1 & (a[i >> 3] >> (i & 7));
11 |
12 | for (i = 0;i < 256;++i)
13 | if (r[i]) {
14 | for (b = 1;b <= 6 && i + b < 256;++b) {
15 | if (r[i + b]) {
16 | if (r[i] + (r[i + b] << b) <= 15) {
17 | r[i] += r[i + b] << b; r[i + b] = 0;
18 | } else if (r[i] - (r[i + b] << b) >= -15) {
19 | r[i] -= r[i + b] << b;
20 | for (k = i + b;k < 256;++k) {
21 | if (!r[k]) {
22 | r[k] = 1;
23 | break;
24 | }
25 | r[k] = 0;
26 | }
27 | } else
28 | break;
29 | }
30 | }
31 | }
32 |
33 | }
34 |
35 | static ge_precomp Bi[8] = {
36 | #include "base2.h"
37 | } ;
38 |
39 | /*
40 | r = a * A + b * B
41 | where a = a[0]+256*a[1]+...+256^31 a[31].
42 | and b = b[0]+256*b[1]+...+256^31 b[31].
43 | B is the Ed25519 base point (x,4/5) with x positive.
44 | */
45 |
46 | void ge_double_scalarmult_vartime(ge_p2 *r,const unsigned char *a,const ge_p3 *A,const unsigned char *b)
47 | {
48 | signed char aslide[256];
49 | signed char bslide[256];
50 | ge_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */
51 | ge_p1p1 t;
52 | ge_p3 u;
53 | ge_p3 A2;
54 | int i;
55 |
56 | slide(aslide,a);
57 | slide(bslide,b);
58 |
59 | ge_p3_to_cached(&Ai[0],A);
60 | ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t);
61 | ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u);
62 | ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u);
63 | ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u);
64 | ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u);
65 | ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u);
66 | ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u);
67 | ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u);
68 |
69 | ge_p2_0(r);
70 |
71 | for (i = 255;i >= 0;--i) {
72 | if (aslide[i] || bslide[i]) break;
73 | }
74 |
75 | for (;i >= 0;--i) {
76 | ge_p2_dbl(&t,r);
77 |
78 | if (aslide[i] > 0) {
79 | ge_p1p1_to_p3(&u,&t);
80 | ge_add(&t,&u,&Ai[aslide[i]/2]);
81 | } else if (aslide[i] < 0) {
82 | ge_p1p1_to_p3(&u,&t);
83 | ge_sub(&t,&u,&Ai[(-aslide[i])/2]);
84 | }
85 |
86 | if (bslide[i] > 0) {
87 | ge_p1p1_to_p3(&u,&t);
88 | ge_madd(&t,&u,&Bi[bslide[i]/2]);
89 | } else if (bslide[i] < 0) {
90 | ge_p1p1_to_p3(&u,&t);
91 | ge_msub(&t,&u,&Bi[(-bslide[i])/2]);
92 | }
93 |
94 | ge_p1p1_to_p2(r,&t);
95 | }
96 | }
97 |
--------------------------------------------------------------------------------
/src/ref10/ge_frombytes.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | static const fe d = {
4 | #include "d.h"
5 | } ;
6 |
7 | static const fe sqrtm1 = {
8 | #include "sqrtm1.h"
9 | } ;
10 |
11 | int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *s)
12 | {
13 | fe u;
14 | fe v;
15 | fe v3;
16 | fe vxx;
17 | fe check;
18 |
19 | fe_frombytes(h->Y,s);
20 | fe_1(h->Z);
21 | fe_sq(u,h->Y);
22 | fe_mul(v,u,d);
23 | fe_sub(u,u,h->Z); /* u = y^2-1 */
24 | fe_add(v,v,h->Z); /* v = dy^2+1 */
25 |
26 | fe_sq(v3,v);
27 | fe_mul(v3,v3,v); /* v3 = v^3 */
28 | fe_sq(h->X,v3);
29 | fe_mul(h->X,h->X,v);
30 | fe_mul(h->X,h->X,u); /* x = uv^7 */
31 |
32 | fe_pow22523(h->X,h->X); /* x = (uv^7)^((q-5)/8) */
33 | fe_mul(h->X,h->X,v3);
34 | fe_mul(h->X,h->X,u); /* x = uv^3(uv^7)^((q-5)/8) */
35 |
36 | fe_sq(vxx,h->X);
37 | fe_mul(vxx,vxx,v);
38 | fe_sub(check,vxx,u); /* vx^2-u */
39 | if (fe_isnonzero(check)) {
40 | fe_add(check,vxx,u); /* vx^2+u */
41 | if (fe_isnonzero(check)) return -1;
42 | fe_mul(h->X,h->X,sqrtm1);
43 | }
44 |
45 | if (fe_isnegative(h->X) == (s[31] >> 7))
46 | fe_neg(h->X,h->X);
47 |
48 | fe_mul(h->T,h->X,h->Y);
49 | return 0;
50 | }
51 |
--------------------------------------------------------------------------------
/src/ref10/ge_madd.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p + q
5 | */
6 |
7 | void ge_madd(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
8 | {
9 | fe t0;
10 | #include "ge_madd.h"
11 | }
12 |
--------------------------------------------------------------------------------
/src/ref10/ge_madd.h:
--------------------------------------------------------------------------------
1 |
2 | /* qhasm: enter ge_madd */
3 |
4 | /* qhasm: fe X1 */
5 |
6 | /* qhasm: fe Y1 */
7 |
8 | /* qhasm: fe Z1 */
9 |
10 | /* qhasm: fe T1 */
11 |
12 | /* qhasm: fe ypx2 */
13 |
14 | /* qhasm: fe ymx2 */
15 |
16 | /* qhasm: fe xy2d2 */
17 |
18 | /* qhasm: fe X3 */
19 |
20 | /* qhasm: fe Y3 */
21 |
22 | /* qhasm: fe Z3 */
23 |
24 | /* qhasm: fe T3 */
25 |
26 | /* qhasm: fe YpX1 */
27 |
28 | /* qhasm: fe YmX1 */
29 |
30 | /* qhasm: fe A */
31 |
32 | /* qhasm: fe B */
33 |
34 | /* qhasm: fe C */
35 |
36 | /* qhasm: fe D */
37 |
38 | /* qhasm: YpX1 = Y1+X1 */
39 | /* asm 1: fe_add(>YpX1=fe#1,YpX1=r->X,Y,X); */
41 | fe_add(r->X,p->Y,p->X);
42 |
43 | /* qhasm: YmX1 = Y1-X1 */
44 | /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */
46 | fe_sub(r->Y,p->Y,p->X);
47 |
48 | /* qhasm: A = YpX1*ypx2 */
49 | /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,yplusx); */
51 | fe_mul(r->Z,r->X,q->yplusx);
52 |
53 | /* qhasm: B = YmX1*ymx2 */
54 | /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,yminusx); */
56 | fe_mul(r->Y,r->Y,q->yminusx);
57 |
58 | /* qhasm: C = xy2d2*T1 */
59 | /* asm 1: fe_mul(>C=fe#4,C=r->T,xy2d,T); */
61 | fe_mul(r->T,q->xy2d,p->T);
62 |
63 | /* qhasm: D = 2*Z1 */
64 | /* asm 1: fe_add(>D=fe#5,D=t0,Z,Z); */
66 | fe_add(t0,p->Z,p->Z);
67 |
68 | /* qhasm: X3 = A-B */
69 | /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */
71 | fe_sub(r->X,r->Z,r->Y);
72 |
73 | /* qhasm: Y3 = A+B */
74 | /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */
76 | fe_add(r->Y,r->Z,r->Y);
77 |
78 | /* qhasm: Z3 = D+C */
79 | /* asm 1: fe_add(>Z3=fe#3,Z3=r->Z,T); */
81 | fe_add(r->Z,t0,r->T);
82 |
83 | /* qhasm: T3 = D-C */
84 | /* asm 1: fe_sub(>T3=fe#4,T3=r->T,T); */
86 | fe_sub(r->T,t0,r->T);
87 |
88 | /* qhasm: return */
89 |
--------------------------------------------------------------------------------
/src/ref10/ge_msub.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p - q
5 | */
6 |
7 | void ge_msub(ge_p1p1 *r,const ge_p3 *p,const ge_precomp *q)
8 | {
9 | fe t0;
10 | #include "ge_msub.h"
11 | }
12 |
--------------------------------------------------------------------------------
/src/ref10/ge_msub.h:
--------------------------------------------------------------------------------
1 |
2 | /* qhasm: enter ge_msub */
3 |
4 | /* qhasm: fe X1 */
5 |
6 | /* qhasm: fe Y1 */
7 |
8 | /* qhasm: fe Z1 */
9 |
10 | /* qhasm: fe T1 */
11 |
12 | /* qhasm: fe ypx2 */
13 |
14 | /* qhasm: fe ymx2 */
15 |
16 | /* qhasm: fe xy2d2 */
17 |
18 | /* qhasm: fe X3 */
19 |
20 | /* qhasm: fe Y3 */
21 |
22 | /* qhasm: fe Z3 */
23 |
24 | /* qhasm: fe T3 */
25 |
26 | /* qhasm: fe YpX1 */
27 |
28 | /* qhasm: fe YmX1 */
29 |
30 | /* qhasm: fe A */
31 |
32 | /* qhasm: fe B */
33 |
34 | /* qhasm: fe C */
35 |
36 | /* qhasm: fe D */
37 |
38 | /* qhasm: YpX1 = Y1+X1 */
39 | /* asm 1: fe_add(>YpX1=fe#1,YpX1=r->X,Y,X); */
41 | fe_add(r->X,p->Y,p->X);
42 |
43 | /* qhasm: YmX1 = Y1-X1 */
44 | /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */
46 | fe_sub(r->Y,p->Y,p->X);
47 |
48 | /* qhasm: A = YpX1*ymx2 */
49 | /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,yminusx); */
51 | fe_mul(r->Z,r->X,q->yminusx);
52 |
53 | /* qhasm: B = YmX1*ypx2 */
54 | /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,yplusx); */
56 | fe_mul(r->Y,r->Y,q->yplusx);
57 |
58 | /* qhasm: C = xy2d2*T1 */
59 | /* asm 1: fe_mul(>C=fe#4,C=r->T,xy2d,T); */
61 | fe_mul(r->T,q->xy2d,p->T);
62 |
63 | /* qhasm: D = 2*Z1 */
64 | /* asm 1: fe_add(>D=fe#5,D=t0,Z,Z); */
66 | fe_add(t0,p->Z,p->Z);
67 |
68 | /* qhasm: X3 = A-B */
69 | /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */
71 | fe_sub(r->X,r->Z,r->Y);
72 |
73 | /* qhasm: Y3 = A+B */
74 | /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */
76 | fe_add(r->Y,r->Z,r->Y);
77 |
78 | /* qhasm: Z3 = D-C */
79 | /* asm 1: fe_sub(>Z3=fe#3,Z3=r->Z,T); */
81 | fe_sub(r->Z,t0,r->T);
82 |
83 | /* qhasm: T3 = D+C */
84 | /* asm 1: fe_add(>T3=fe#4,T3=r->T,T); */
86 | fe_add(r->T,t0,r->T);
87 |
88 | /* qhasm: return */
89 |
--------------------------------------------------------------------------------
/src/ref10/ge_p1p1_to_p2.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p
5 | */
6 |
7 | extern void ge_p1p1_to_p2(ge_p2 *r,const ge_p1p1 *p)
8 | {
9 | fe_mul(r->X,p->X,p->T);
10 | fe_mul(r->Y,p->Y,p->Z);
11 | fe_mul(r->Z,p->Z,p->T);
12 | }
13 |
--------------------------------------------------------------------------------
/src/ref10/ge_p1p1_to_p3.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p
5 | */
6 |
7 | extern void ge_p1p1_to_p3(ge_p3 *r,const ge_p1p1 *p)
8 | {
9 | fe_mul(r->X,p->X,p->T);
10 | fe_mul(r->Y,p->Y,p->Z);
11 | fe_mul(r->Z,p->Z,p->T);
12 | fe_mul(r->T,p->X,p->Y);
13 | }
14 |
--------------------------------------------------------------------------------
/src/ref10/ge_p2_0.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | void ge_p2_0(ge_p2 *h)
4 | {
5 | fe_0(h->X);
6 | fe_1(h->Y);
7 | fe_1(h->Z);
8 | }
9 |
--------------------------------------------------------------------------------
/src/ref10/ge_p2_dbl.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = 2 * p
5 | */
6 |
7 | void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p)
8 | {
9 | fe t0;
10 | #include "ge_p2_dbl.h"
11 | }
12 |
--------------------------------------------------------------------------------
/src/ref10/ge_p2_dbl.h:
--------------------------------------------------------------------------------
1 |
2 | /* qhasm: enter ge_p2_dbl */
3 |
4 | /* qhasm: fe X1 */
5 |
6 | /* qhasm: fe Y1 */
7 |
8 | /* qhasm: fe Z1 */
9 |
10 | /* qhasm: fe A */
11 |
12 | /* qhasm: fe AA */
13 |
14 | /* qhasm: fe XX */
15 |
16 | /* qhasm: fe YY */
17 |
18 | /* qhasm: fe B */
19 |
20 | /* qhasm: fe X3 */
21 |
22 | /* qhasm: fe Y3 */
23 |
24 | /* qhasm: fe Z3 */
25 |
26 | /* qhasm: fe T3 */
27 |
28 | /* qhasm: XX=X1^2 */
29 | /* asm 1: fe_sq(>XX=fe#1,XX=r->X,X); */
31 | fe_sq(r->X,p->X);
32 |
33 | /* qhasm: YY=Y1^2 */
34 | /* asm 1: fe_sq(>YY=fe#3,YY=r->Z,Y); */
36 | fe_sq(r->Z,p->Y);
37 |
38 | /* qhasm: B=2*Z1^2 */
39 | /* asm 1: fe_sq2(>B=fe#4,B=r->T,Z); */
41 | fe_sq2(r->T,p->Z);
42 |
43 | /* qhasm: A=X1+Y1 */
44 | /* asm 1: fe_add(>A=fe#2,A=r->Y,X,Y); */
46 | fe_add(r->Y,p->X,p->Y);
47 |
48 | /* qhasm: AA=A^2 */
49 | /* asm 1: fe_sq(>AA=fe#5,AA=t0,Y); */
51 | fe_sq(t0,r->Y);
52 |
53 | /* qhasm: Y3=YY+XX */
54 | /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,X); */
56 | fe_add(r->Y,r->Z,r->X);
57 |
58 | /* qhasm: Z3=YY-XX */
59 | /* asm 1: fe_sub(>Z3=fe#3,Z3=r->Z,Z,X); */
61 | fe_sub(r->Z,r->Z,r->X);
62 |
63 | /* qhasm: X3=AA-Y3 */
64 | /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Y); */
66 | fe_sub(r->X,t0,r->Y);
67 |
68 | /* qhasm: T3=B-Z3 */
69 | /* asm 1: fe_sub(>T3=fe#4,T3=r->T,T,Z); */
71 | fe_sub(r->T,r->T,r->Z);
72 |
73 | /* qhasm: return */
74 |
--------------------------------------------------------------------------------
/src/ref10/ge_p3_0.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | void ge_p3_0(ge_p3 *h)
4 | {
5 | fe_0(h->X);
6 | fe_1(h->Y);
7 | fe_1(h->Z);
8 | fe_0(h->T);
9 | }
10 |
--------------------------------------------------------------------------------
/src/ref10/ge_p3_dbl.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = 2 * p
5 | */
6 |
7 | void ge_p3_dbl(ge_p1p1 *r,const ge_p3 *p)
8 | {
9 | ge_p2 q;
10 | ge_p3_to_p2(&q,p);
11 | ge_p2_dbl(r,&q);
12 | }
13 |
--------------------------------------------------------------------------------
/src/ref10/ge_p3_to_cached.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p
5 | */
6 |
7 | static const fe d2 = {
8 | #include "d2.h"
9 | } ;
10 |
11 | extern void ge_p3_to_cached(ge_cached *r,const ge_p3 *p)
12 | {
13 | fe_add(r->YplusX,p->Y,p->X);
14 | fe_sub(r->YminusX,p->Y,p->X);
15 | fe_copy(r->Z,p->Z);
16 | fe_mul(r->T2d,p->T,d2);
17 | }
18 |
--------------------------------------------------------------------------------
/src/ref10/ge_p3_to_p2.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p
5 | */
6 |
7 | extern void ge_p3_to_p2(ge_p2 *r,const ge_p3 *p)
8 | {
9 | fe_copy(r->X,p->X);
10 | fe_copy(r->Y,p->Y);
11 | fe_copy(r->Z,p->Z);
12 | }
13 |
--------------------------------------------------------------------------------
/src/ref10/ge_p3_tobytes.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | void ge_p3_tobytes(unsigned char *s,const ge_p3 *h)
4 | {
5 | fe recip;
6 | fe x;
7 | fe y;
8 |
9 | fe_invert(recip,h->Z);
10 | fe_mul(x,h->X,recip);
11 | fe_mul(y,h->Y,recip);
12 | fe_tobytes(s,y);
13 | s[31] ^= fe_isnegative(x) << 7;
14 | }
15 |
--------------------------------------------------------------------------------
/src/ref10/ge_precomp_0.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | void ge_precomp_0(ge_precomp *h)
4 | {
5 | fe_1(h->yplusx);
6 | fe_1(h->yminusx);
7 | fe_0(h->xy2d);
8 | }
9 |
--------------------------------------------------------------------------------
/src/ref10/ge_scalarmult_base.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 | #include "crypto_uint32.h"
3 |
4 | static unsigned char equal(signed char b,signed char c)
5 | {
6 | unsigned char ub = b;
7 | unsigned char uc = c;
8 | unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */
9 | crypto_uint32 y = x; /* 0: yes; 1..255: no */
10 | y -= 1; /* 4294967295: yes; 0..254: no */
11 | y >>= 31; /* 1: yes; 0: no */
12 | return y;
13 | }
14 |
15 | static unsigned char negative(signed char b)
16 | {
17 | unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */
18 | x >>= 63; /* 1: yes; 0: no */
19 | return x;
20 | }
21 |
22 | static void cmov(ge_precomp *t,ge_precomp *u,unsigned char b)
23 | {
24 | fe_cmov(t->yplusx,u->yplusx,b);
25 | fe_cmov(t->yminusx,u->yminusx,b);
26 | fe_cmov(t->xy2d,u->xy2d,b);
27 | }
28 |
29 | /* base[i][j] = (j+1)*256^i*B */
30 | static ge_precomp base[32][8] = {
31 | #include "base.h"
32 | } ;
33 |
34 | static void select(ge_precomp *t,int pos,signed char b)
35 | {
36 | ge_precomp minust;
37 | unsigned char bnegative = negative(b);
38 | unsigned char babs = b - (((-bnegative) & b) << 1);
39 |
40 | ge_precomp_0(t);
41 | cmov(t,&base[pos][0],equal(babs,1));
42 | cmov(t,&base[pos][1],equal(babs,2));
43 | cmov(t,&base[pos][2],equal(babs,3));
44 | cmov(t,&base[pos][3],equal(babs,4));
45 | cmov(t,&base[pos][4],equal(babs,5));
46 | cmov(t,&base[pos][5],equal(babs,6));
47 | cmov(t,&base[pos][6],equal(babs,7));
48 | cmov(t,&base[pos][7],equal(babs,8));
49 | fe_copy(minust.yplusx,t->yminusx);
50 | fe_copy(minust.yminusx,t->yplusx);
51 | fe_neg(minust.xy2d,t->xy2d);
52 | cmov(t,&minust,bnegative);
53 | }
54 |
55 | /*
56 | h = a * B
57 | where a = a[0]+256*a[1]+...+256^31 a[31]
58 | B is the Ed25519 base point (x,4/5) with x positive.
59 |
60 | Preconditions:
61 | a[31] <= 127
62 | */
63 |
64 | void ge_scalarmult_base(ge_p3 *h,const unsigned char *a)
65 | {
66 | signed char e[64];
67 | signed char carry;
68 | ge_p1p1 r;
69 | ge_p2 s;
70 | ge_precomp t;
71 | int i;
72 |
73 | for (i = 0;i < 32;++i) {
74 | e[2 * i + 0] = (a[i] >> 0) & 15;
75 | e[2 * i + 1] = (a[i] >> 4) & 15;
76 | }
77 | /* each e[i] is between 0 and 15 */
78 | /* e[63] is between 0 and 7 */
79 |
80 | carry = 0;
81 | for (i = 0;i < 63;++i) {
82 | e[i] += carry;
83 | carry = e[i] + 8;
84 | carry >>= 4;
85 | e[i] -= carry << 4;
86 | }
87 | e[63] += carry;
88 | /* each e[i] is between -8 and 8 */
89 |
90 | ge_p3_0(h);
91 | for (i = 1;i < 64;i += 2) {
92 | select(&t,i / 2,e[i]);
93 | ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
94 | }
95 |
96 | ge_p3_dbl(&r,h); ge_p1p1_to_p2(&s,&r);
97 | ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
98 | ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r);
99 | ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r);
100 |
101 | for (i = 0;i < 64;i += 2) {
102 | select(&t,i / 2,e[i]);
103 | ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r);
104 | }
105 | }
106 |
--------------------------------------------------------------------------------
/src/ref10/ge_sub.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | /*
4 | r = p - q
5 | */
6 |
7 | void ge_sub(ge_p1p1 *r,const ge_p3 *p,const ge_cached *q)
8 | {
9 | fe t0;
10 | #include "ge_sub.h"
11 | }
12 |
--------------------------------------------------------------------------------
/src/ref10/ge_sub.h:
--------------------------------------------------------------------------------
1 |
2 | /* qhasm: enter ge_sub */
3 |
4 | /* qhasm: fe X1 */
5 |
6 | /* qhasm: fe Y1 */
7 |
8 | /* qhasm: fe Z1 */
9 |
10 | /* qhasm: fe Z2 */
11 |
12 | /* qhasm: fe T1 */
13 |
14 | /* qhasm: fe ZZ */
15 |
16 | /* qhasm: fe YpX2 */
17 |
18 | /* qhasm: fe YmX2 */
19 |
20 | /* qhasm: fe T2d2 */
21 |
22 | /* qhasm: fe X3 */
23 |
24 | /* qhasm: fe Y3 */
25 |
26 | /* qhasm: fe Z3 */
27 |
28 | /* qhasm: fe T3 */
29 |
30 | /* qhasm: fe YpX1 */
31 |
32 | /* qhasm: fe YmX1 */
33 |
34 | /* qhasm: fe A */
35 |
36 | /* qhasm: fe B */
37 |
38 | /* qhasm: fe C */
39 |
40 | /* qhasm: fe D */
41 |
42 | /* qhasm: YpX1 = Y1+X1 */
43 | /* asm 1: fe_add(>YpX1=fe#1,YpX1=r->X,Y,X); */
45 | fe_add(r->X,p->Y,p->X);
46 |
47 | /* qhasm: YmX1 = Y1-X1 */
48 | /* asm 1: fe_sub(>YmX1=fe#2,YmX1=r->Y,Y,X); */
50 | fe_sub(r->Y,p->Y,p->X);
51 |
52 | /* qhasm: A = YpX1*YmX2 */
53 | /* asm 1: fe_mul(>A=fe#3,A=r->Z,X,YminusX); */
55 | fe_mul(r->Z,r->X,q->YminusX);
56 |
57 | /* qhasm: B = YmX1*YpX2 */
58 | /* asm 1: fe_mul(>B=fe#2,B=r->Y,Y,YplusX); */
60 | fe_mul(r->Y,r->Y,q->YplusX);
61 |
62 | /* qhasm: C = T2d2*T1 */
63 | /* asm 1: fe_mul(>C=fe#4,C=r->T,T2d,T); */
65 | fe_mul(r->T,q->T2d,p->T);
66 |
67 | /* qhasm: ZZ = Z1*Z2 */
68 | /* asm 1: fe_mul(>ZZ=fe#1,ZZ=r->X,Z,Z); */
70 | fe_mul(r->X,p->Z,q->Z);
71 |
72 | /* qhasm: D = 2*ZZ */
73 | /* asm 1: fe_add(>D=fe#5,D=t0,X,X); */
75 | fe_add(t0,r->X,r->X);
76 |
77 | /* qhasm: X3 = A-B */
78 | /* asm 1: fe_sub(>X3=fe#1,X3=r->X,Z,Y); */
80 | fe_sub(r->X,r->Z,r->Y);
81 |
82 | /* qhasm: Y3 = A+B */
83 | /* asm 1: fe_add(>Y3=fe#2,Y3=r->Y,Z,Y); */
85 | fe_add(r->Y,r->Z,r->Y);
86 |
87 | /* qhasm: Z3 = D-C */
88 | /* asm 1: fe_sub(>Z3=fe#3,Z3=r->Z,T); */
90 | fe_sub(r->Z,t0,r->T);
91 |
92 | /* qhasm: T3 = D+C */
93 | /* asm 1: fe_add(>T3=fe#4,T3=r->T,T); */
95 | fe_add(r->T,t0,r->T);
96 |
97 | /* qhasm: return */
98 |
--------------------------------------------------------------------------------
/src/ref10/ge_tobytes.c:
--------------------------------------------------------------------------------
1 | #include "ge.h"
2 |
3 | void ge_tobytes(unsigned char *s,const ge_p2 *h)
4 | {
5 | fe recip;
6 | fe x;
7 | fe y;
8 |
9 | fe_invert(recip,h->Z);
10 | fe_mul(x,h->X,recip);
11 | fe_mul(y,h->Y,recip);
12 | fe_tobytes(s,y);
13 | s[31] ^= fe_isnegative(x) << 7;
14 | }
15 |
--------------------------------------------------------------------------------
/src/ref10/keypair.c:
--------------------------------------------------------------------------------
1 | #include
2 | #include "randombytes.h"
3 | #include "crypto_sign.h"
4 | #include "crypto_hash_sha512.h"
5 | #include "ge.h"
6 |
7 | int crypto_sign_keypair(unsigned char *pk,unsigned char *sk)
8 | {
9 | unsigned char az[64];
10 | ge_p3 A;
11 |
12 | randombytes(sk,32);
13 | crypto_hash_sha512(az,sk,32);
14 | az[0] &= 248;
15 | az[31] &= 63;
16 | az[31] |= 64;
17 |
18 | ge_scalarmult_base(&A,az);
19 | ge_p3_tobytes(pk,&A);
20 |
21 | memmove(sk + 32,pk,32);
22 | return 0;
23 | }
24 |
--------------------------------------------------------------------------------
/src/ref10/open.c:
--------------------------------------------------------------------------------
1 | #include
2 | #include "crypto_sign.h"
3 | #include "crypto_hash_sha512.h"
4 | #include "crypto_verify_32.h"
5 | #include "ge.h"
6 | #include "sc.h"
7 |
8 | int crypto_sign_open(
9 | unsigned char *m,unsigned long long *mlen,
10 | const unsigned char *sm,unsigned long long smlen,
11 | const unsigned char *pk
12 | )
13 | {
14 | unsigned char pkcopy[32];
15 | unsigned char rcopy[32];
16 | unsigned char scopy[32];
17 | unsigned char h[64];
18 | unsigned char rcheck[32];
19 | ge_p3 A;
20 | ge_p2 R;
21 |
22 | if (smlen < 64) goto badsig;
23 | if (sm[63] & 224) goto badsig;
24 | if (ge_frombytes_negate_vartime(&A,pk) != 0) goto badsig;
25 |
26 | memmove(pkcopy,pk,32);
27 | memmove(rcopy,sm,32);
28 | memmove(scopy,sm + 32,32);
29 |
30 | memmove(m,sm,smlen);
31 | memmove(m + 32,pkcopy,32);
32 | crypto_hash_sha512(h,m,smlen);
33 | sc_reduce(h);
34 |
35 | ge_double_scalarmult_vartime(&R,h,&A,scopy);
36 | ge_tobytes(rcheck,&R);
37 | if (crypto_verify_32(rcheck,rcopy) == 0) {
38 | memmove(m,m + 64,smlen - 64);
39 | memset(m + smlen - 64,0,64);
40 | *mlen = smlen - 64;
41 | return 0;
42 | }
43 |
44 | badsig:
45 | *mlen = -1;
46 | memset(m,0,smlen);
47 | return -1;
48 | }
49 |
--------------------------------------------------------------------------------
/src/ref10/pow22523.h:
--------------------------------------------------------------------------------
1 |
2 | /* qhasm: fe z1 */
3 |
4 | /* qhasm: fe z2 */
5 |
6 | /* qhasm: fe z8 */
7 |
8 | /* qhasm: fe z9 */
9 |
10 | /* qhasm: fe z11 */
11 |
12 | /* qhasm: fe z22 */
13 |
14 | /* qhasm: fe z_5_0 */
15 |
16 | /* qhasm: fe z_10_5 */
17 |
18 | /* qhasm: fe z_10_0 */
19 |
20 | /* qhasm: fe z_20_10 */
21 |
22 | /* qhasm: fe z_20_0 */
23 |
24 | /* qhasm: fe z_40_20 */
25 |
26 | /* qhasm: fe z_40_0 */
27 |
28 | /* qhasm: fe z_50_10 */
29 |
30 | /* qhasm: fe z_50_0 */
31 |
32 | /* qhasm: fe z_100_50 */
33 |
34 | /* qhasm: fe z_100_0 */
35 |
36 | /* qhasm: fe z_200_100 */
37 |
38 | /* qhasm: fe z_200_0 */
39 |
40 | /* qhasm: fe z_250_50 */
41 |
42 | /* qhasm: fe z_250_0 */
43 |
44 | /* qhasm: fe z_252_2 */
45 |
46 | /* qhasm: fe z_252_3 */
47 |
48 | /* qhasm: enter pow22523 */
49 |
50 | /* qhasm: z2 = z1^2^1 */
51 | /* asm 1: fe_sq(>z2=fe#1,z2=fe#1,>z2=fe#1); */
52 | /* asm 2: fe_sq(>z2=t0,z2=t0,>z2=t0); */
53 | fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
54 |
55 | /* qhasm: z8 = z2^2^2 */
56 | /* asm 1: fe_sq(>z8=fe#2,z8=fe#2,>z8=fe#2); */
57 | /* asm 2: fe_sq(>z8=t1,z8=t1,>z8=t1); */
58 | fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
59 |
60 | /* qhasm: z9 = z1*z8 */
61 | /* asm 1: fe_mul(>z9=fe#2,z9=t1,z11=fe#1,z11=t0,z22=fe#1,z22=fe#1,>z22=fe#1); */
72 | /* asm 2: fe_sq(>z22=t0,z22=t0,>z22=t0); */
73 | fe_sq(t0,t0); for (i = 1;i < 1;++i) fe_sq(t0,t0);
74 |
75 | /* qhasm: z_5_0 = z9*z22 */
76 | /* asm 1: fe_mul(>z_5_0=fe#1,z_5_0=t0,z_10_5=fe#2,z_10_5=fe#2,>z_10_5=fe#2); */
82 | /* asm 2: fe_sq(>z_10_5=t1,z_10_5=t1,>z_10_5=t1); */
83 | fe_sq(t1,t0); for (i = 1;i < 5;++i) fe_sq(t1,t1);
84 |
85 | /* qhasm: z_10_0 = z_10_5*z_5_0 */
86 | /* asm 1: fe_mul(>z_10_0=fe#1,z_10_0=t0,z_20_10=fe#2,z_20_10=fe#2,>z_20_10=fe#2); */
92 | /* asm 2: fe_sq(>z_20_10=t1,z_20_10=t1,>z_20_10=t1); */
93 | fe_sq(t1,t0); for (i = 1;i < 10;++i) fe_sq(t1,t1);
94 |
95 | /* qhasm: z_20_0 = z_20_10*z_10_0 */
96 | /* asm 1: fe_mul(>z_20_0=fe#2,z_20_0=t1,z_40_20=fe#3,z_40_20=fe#3,>z_40_20=fe#3); */
102 | /* asm 2: fe_sq(>z_40_20=t2,z_40_20=t2,>z_40_20=t2); */
103 | fe_sq(t2,t1); for (i = 1;i < 20;++i) fe_sq(t2,t2);
104 |
105 | /* qhasm: z_40_0 = z_40_20*z_20_0 */
106 | /* asm 1: fe_mul(>z_40_0=fe#2,z_40_0=t1,z_50_10=fe#2,z_50_10=fe#2,>z_50_10=fe#2); */
112 | /* asm 2: fe_sq(>z_50_10=t1,z_50_10=t1,>z_50_10=t1); */
113 | fe_sq(t1,t1); for (i = 1;i < 10;++i) fe_sq(t1,t1);
114 |
115 | /* qhasm: z_50_0 = z_50_10*z_10_0 */
116 | /* asm 1: fe_mul(>z_50_0=fe#1,z_50_0=t0,z_100_50=fe#2,z_100_50=fe#2,>z_100_50=fe#2); */
122 | /* asm 2: fe_sq(>z_100_50=t1,z_100_50=t1,>z_100_50=t1); */
123 | fe_sq(t1,t0); for (i = 1;i < 50;++i) fe_sq(t1,t1);
124 |
125 | /* qhasm: z_100_0 = z_100_50*z_50_0 */
126 | /* asm 1: fe_mul(>z_100_0=fe#2,z_100_0=t1,z_200_100=fe#3,z_200_100=fe#3,>z_200_100=fe#3); */
132 | /* asm 2: fe_sq(>z_200_100=t2,z_200_100=t2,>z_200_100=t2); */
133 | fe_sq(t2,t1); for (i = 1;i < 100;++i) fe_sq(t2,t2);
134 |
135 | /* qhasm: z_200_0 = z_200_100*z_100_0 */
136 | /* asm 1: fe_mul(>z_200_0=fe#2,z_200_0=t1,z_250_50=fe#2,z_250_50=fe#2,>z_250_50=fe#2); */
142 | /* asm 2: fe_sq(>z_250_50=t1,z_250_50=t1,>z_250_50=t1); */
143 | fe_sq(t1,t1); for (i = 1;i < 50;++i) fe_sq(t1,t1);
144 |
145 | /* qhasm: z_250_0 = z_250_50*z_50_0 */
146 | /* asm 1: fe_mul(>z_250_0=fe#1,z_250_0=t0,z_252_2=fe#1,z_252_2=fe#1,>z_252_2=fe#1); */
152 | /* asm 2: fe_sq(>z_252_2=t0,z_252_2=t0,>z_252_2=t0); */
153 | fe_sq(t0,t0); for (i = 1;i < 2;++i) fe_sq(t0,t0);
154 |
155 | /* qhasm: z_252_3 = z_252_2*z1 */
156 | /* asm 1: fe_mul(>z_252_3=fe#12,z_252_3=out,z2=fe#1,z2=fe#1,>z2=fe#1); */
52 | /* asm 2: fe_sq(>z2=t0,z2=t0,>z2=t0); */
53 | fe_sq(t0,z); for (i = 1;i < 1;++i) fe_sq(t0,t0);
54 |
55 | /* qhasm: z8 = z2^2^2 */
56 | /* asm 1: fe_sq(>z8=fe#2,z8=fe#2,>z8=fe#2); */
57 | /* asm 2: fe_sq(>z8=t1,z8=t1,>z8=t1); */
58 | fe_sq(t1,t0); for (i = 1;i < 2;++i) fe_sq(t1,t1);
59 |
60 | /* qhasm: z9 = z1*z8 */
61 | /* asm 1: fe_mul(>z9=fe#2,z9=t1,z11=fe#1,z11=t0,z22=fe#3,z22=fe#3,>z22=fe#3); */
72 | /* asm 2: fe_sq(>z22=t2,z22=t2,>z22=t2); */
73 | fe_sq(t2,t0); for (i = 1;i < 1;++i) fe_sq(t2,t2);
74 |
75 | /* qhasm: z_5_0 = z9*z22 */
76 | /* asm 1: fe_mul(>z_5_0=fe#2,z_5_0=t1,z_10_5=fe#3,z_10_5=fe#3,>z_10_5=fe#3); */
82 | /* asm 2: fe_sq(>z_10_5=t2,z_10_5=t2,>z_10_5=t2); */
83 | fe_sq(t2,t1); for (i = 1;i < 5;++i) fe_sq(t2,t2);
84 |
85 | /* qhasm: z_10_0 = z_10_5*z_5_0 */
86 | /* asm 1: fe_mul(>z_10_0=fe#2,z_10_0=t1,z_20_10=fe#3,z_20_10=fe#3,>z_20_10=fe#3); */
92 | /* asm 2: fe_sq(>z_20_10=t2,z_20_10=t2,>z_20_10=t2); */
93 | fe_sq(t2,t1); for (i = 1;i < 10;++i) fe_sq(t2,t2);
94 |
95 | /* qhasm: z_20_0 = z_20_10*z_10_0 */
96 | /* asm 1: fe_mul(>z_20_0=fe#3,z_20_0=t2,z_40_20=fe#4,z_40_20=fe#4,>z_40_20=fe#4); */
102 | /* asm 2: fe_sq(>z_40_20=t3,z_40_20=t3,>z_40_20=t3); */
103 | fe_sq(t3,t2); for (i = 1;i < 20;++i) fe_sq(t3,t3);
104 |
105 | /* qhasm: z_40_0 = z_40_20*z_20_0 */
106 | /* asm 1: fe_mul(>z_40_0=fe#3,z_40_0=t2,z_50_10=fe#3,z_50_10=fe#3,>z_50_10=fe#3); */
112 | /* asm 2: fe_sq(>z_50_10=t2,z_50_10=t2,>z_50_10=t2); */
113 | fe_sq(t2,t2); for (i = 1;i < 10;++i) fe_sq(t2,t2);
114 |
115 | /* qhasm: z_50_0 = z_50_10*z_10_0 */
116 | /* asm 1: fe_mul(>z_50_0=fe#2,z_50_0=t1,z_100_50=fe#3,z_100_50=fe#3,>z_100_50=fe#3); */
122 | /* asm 2: fe_sq(>z_100_50=t2,z_100_50=t2,>z_100_50=t2); */
123 | fe_sq(t2,t1); for (i = 1;i < 50;++i) fe_sq(t2,t2);
124 |
125 | /* qhasm: z_100_0 = z_100_50*z_50_0 */
126 | /* asm 1: fe_mul(>z_100_0=fe#3,z_100_0=t2,z_200_100=fe#4,z_200_100=fe#4,>z_200_100=fe#4); */
132 | /* asm 2: fe_sq(>z_200_100=t3,z_200_100=t3,>z_200_100=t3); */
133 | fe_sq(t3,t2); for (i = 1;i < 100;++i) fe_sq(t3,t3);
134 |
135 | /* qhasm: z_200_0 = z_200_100*z_100_0 */
136 | /* asm 1: fe_mul(>z_200_0=fe#3,z_200_0=t2,z_250_50=fe#3,z_250_50=fe#3,>z_250_50=fe#3); */
142 | /* asm 2: fe_sq(>z_250_50=t2,z_250_50=t2,>z_250_50=t2); */
143 | fe_sq(t2,t2); for (i = 1;i < 50;++i) fe_sq(t2,t2);
144 |
145 | /* qhasm: z_250_0 = z_250_50*z_50_0 */
146 | /* asm 1: fe_mul(>z_250_0=fe#2,z_250_0=t1,z_255_5=fe#2,z_255_5=fe#2,>z_255_5=fe#2); */
152 | /* asm 2: fe_sq(>z_255_5=t1,z_255_5=t1,>z_255_5=t1); */
153 | fe_sq(t1,t1); for (i = 1;i < 5;++i) fe_sq(t1,t1);
154 |
155 | /* qhasm: z_255_21 = z_255_5*z11 */
156 | /* asm 1: fe_mul(>z_255_21=fe#12,