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-------------------------------------------------------------------------------- 1 | ## gomorph 2 | 3 | Repository is currently maintained by current user (transfer from my old to new account) 4 | 5 | **Gomorph** tries to implement a set of Homomorphic Crypto systems in pure Go-lang 6 | 7 | - Gaillier is a Golang implementation of [Paillier Cryptosystem](https://www.wikiwand.com/en/Paillier_cryptosystem) 8 | 9 | ## For citations 10 | 11 | ``` 12 | @MISC {Gomoprh, 13 | author = "Achraf B", 14 | title = "Go-morph - a pure Golang implementation of the Paillier cryptosystem", 15 | howpublished = "https://github.com/actuallyachraf/gomorph", 16 | month = "March", 17 | year = "2019", 18 | } 19 | ``` 20 | -------------------------------------------------------------------------------- /gaillier/gaillier.go: -------------------------------------------------------------------------------- 1 | /* 2 | This package implements a Paillier cryptosystem 3 | 4 | Provides primitives for Public & Private Key Generation / Encryption / Decryption 5 | Provides Functions to operate on the Cyphertext according to Paillier algorithm 6 | 7 | @author: radicalrafi 8 | @license: Apache 2.0 9 | 10 | */ 11 | 12 | // Homomorphic Properties of Paillier Cryptosystem 13 | // 14 | // * The product of two ciphers decrypts to the sum of the plain text 15 | // * The product of a cipher with a non-cipher raising g will decrypt to their sum 16 | // * A Cipher raised to a non-cipher decrypts to their product 17 | // * Any cipher raised to an integer k will decrypt to the product of the deciphered and k 18 | 19 | package gaillier 20 | 21 | import ( 22 | "crypto/rand" 23 | "errors" 24 | "io" 25 | "math/big" 26 | ) 27 | 28 | //Errors definition 29 | 30 | // The Paillier crypto system picks two keys p & q and denotes n = p*q 31 | // Messages have to be in the ring Z/nZ (integers modulo n) 32 | // Therefore a Message can't be bigger than n 33 | var ErrLongMessage = errors.New("message should be smaller than choosen public key size") 34 | 35 | var one = big.NewInt(1) 36 | 37 | // PubKey is a struct to hold the public key used to encrypt 38 | type PubKey struct { 39 | Len int 40 | N *big.Int //n = p*q (where p & q are two primes) 41 | G *big.Int //g random integer in Z\*\n^2 42 | Nsq *big.Int //N^2 43 | } 44 | 45 | // PrivKey is a struct to hold the private key used to decrypt 46 | type PrivKey struct { 47 | Len int 48 | PubKey 49 | L *big.Int //lcm((p-1)*(q-1)) 50 | U *big.Int //L^-1 modulo n mu = U = (L(g^L mod N^2)^-1) 51 | } 52 | 53 | // GenerateKeyPair generates a key pair using a random source and a number of bits 54 | func GenerateKeyPair(random io.Reader, bits int) (*PubKey, *PrivKey, error) { 55 | 56 | p, err := rand.Prime(random, bits/2) 57 | 58 | if err != nil { 59 | return nil, nil, err 60 | } 61 | 62 | q, err := rand.Prime(random, bits/2) 63 | 64 | if err != nil { 65 | return nil, nil, err 66 | } 67 | 68 | //N = p*q 69 | 70 | n := new(big.Int).Mul(p, q) 71 | 72 | nSquared := new(big.Int).Mul(n, n) 73 | 74 | g := new(big.Int).Add(n, one) 75 | 76 | //p-1 77 | pMin := new(big.Int).Sub(p, one) 78 | //q-1 79 | qMin := new(big.Int).Sub(q, one) 80 | //(p-1)*(q-1) 81 | l := new(big.Int).Mul(pMin, qMin) 82 | //l^-1 mod n 83 | u := new(big.Int).ModInverse(l, n) 84 | pub := &PubKey{Len: bits, N: n, Nsq: nSquared, G: g} 85 | return pub, &PrivKey{PubKey: *pub, Len: bits, L: l, U: u}, nil 86 | } 87 | 88 | // Encrypt function to encrypt the message into a paillier cipher text 89 | // using the following rule : 90 | // cipher = g^m * r^n mod n^2 91 | // r is random integer such as 0 <= r <= n 92 | // m is the message 93 | func Encrypt(pubkey *PubKey, message []byte) ([]byte, error) { 94 | // We need to generate an r such that 0 < r < n is true and r and n are relatively prime 95 | r, err := generateRelativelyPrimeInt(pubkey.N) 96 | if err != nil { 97 | return nil, err 98 | } 99 | 100 | m := new(big.Int).SetBytes(message) 101 | if pubkey.N.Cmp(m) < 1 { 102 | return nil, ErrLongMessage 103 | } 104 | //c = g^m * r^nmod n^2 105 | 106 | //g^m 107 | gm := new(big.Int).Exp(pubkey.G, m, pubkey.Nsq) 108 | //r^n 109 | rn := new(big.Int).Exp(r, pubkey.N, pubkey.Nsq) 110 | //prod = g^m * r^n 111 | prod := new(big.Int).Mul(gm, rn) 112 | 113 | c := new(big.Int).Mod(prod, pubkey.Nsq) 114 | 115 | return c.Bytes(), nil 116 | } 117 | 118 | // Decrypts a given ciphertext following the rule: 119 | // m = L(c^lambda mod n^2).mu mod n 120 | // lambda : L 121 | // mu : U 122 | func Decrypt(privkey *PrivKey, cipher []byte) ([]byte, error) { 123 | 124 | c := new(big.Int).SetBytes(cipher) 125 | 126 | if privkey.Nsq.Cmp(c) < 1 { 127 | return nil, ErrLongMessage 128 | } 129 | 130 | //c^l mod n^2 131 | a := new(big.Int).Exp(c, privkey.L, privkey.Nsq) 132 | 133 | //L(x) = x-1 / n we compute L(a) 134 | l := new(big.Int).Div(new(big.Int).Sub(a, one), privkey.N) 135 | 136 | //computing m 137 | m := new(big.Int).Mod(new(big.Int).Mul(l, privkey.U), privkey.N) 138 | 139 | return m.Bytes(), nil 140 | 141 | } 142 | 143 | //Add two ciphers together 144 | func Add(pubkey *PubKey, c1, c2 []byte) []byte { 145 | 146 | a := new(big.Int).SetBytes(c1) 147 | b := new(big.Int).SetBytes(c2) 148 | 149 | // a * b mod n^² 150 | res := new(big.Int).Mod(new(big.Int).Mul(a, b), pubkey.Nsq) 151 | 152 | return res.Bytes() 153 | } 154 | 155 | //Add a constant & a cipher 156 | func AddConstant(pubkey *PubKey, cipher, constant []byte) []byte { 157 | 158 | c := new(big.Int).SetBytes(cipher) 159 | k := new(big.Int).SetBytes(constant) 160 | 161 | //result = c * g^k mod n^2 162 | res := new(big.Int).Mod( 163 | new(big.Int).Mul(c, new(big.Int).Exp(pubkey.G, k, pubkey.Nsq)), pubkey.Nsq) 164 | 165 | return res.Bytes() 166 | 167 | } 168 | 169 | //Multiplication by a constant integer 170 | func Mul(pubkey *PubKey, cipher, constant []byte) []byte { 171 | 172 | c := new(big.Int).SetBytes(cipher) 173 | k := new(big.Int).SetBytes(constant) 174 | 175 | //res = c^k mod n^2 176 | res := new(big.Int).Exp(c, k, pubkey.Nsq) 177 | 178 | return res.Bytes() 179 | } 180 | 181 | // Generates an Int that is relatively prime with the input Int. Relative primeness is defined by gcd(r, n) = 1. 182 | // So we enter an infinite loop to generate r's until this is true. It is very unlikely that we will ever iterate 183 | // through this loop more than once since our search space is so large. 184 | func generateRelativelyPrimeInt(n *big.Int) (*big.Int, error) { 185 | for { 186 | randR, err := rand.Int(rand.Reader, n) 187 | if err != nil { 188 | return nil, err 189 | } 190 | 191 | // We only care about z here, but need references to x & y because of the GCD function 192 | x, y, z := new(big.Int), new(big.Int), new(big.Int) 193 | z.GCD(x, y, n, randR) 194 | 195 | // Check that the GCD is 1 196 | if z.Cmp(one) == 0 { 197 | // If so, we are done 198 | return randR, nil 199 | } 200 | } 201 | } 202 | -------------------------------------------------------------------------------- /gaillier/gaillier_test.go: -------------------------------------------------------------------------------- 1 | package gaillier 2 | 3 | import ( 4 | "crypto/rand" 5 | "math/big" 6 | "testing" 7 | ) 8 | 9 | func TestKeyGen(t *testing.T) { 10 | puba, priva, err1 := GenerateKeyPair(rand.Reader, 1024) 11 | pubb, privb, err2 := GenerateKeyPair(rand.Reader, 2048) 12 | pubc, privc, err3 := GenerateKeyPair(rand.Reader, 4096) 13 | 14 | if err1 != nil || err2 != nil || err3 != nil { 15 | t.Errorf("Error Generating Keypair :\n Size:1024 %v\nSize:2048 %v\nSize 4096 %v\n", err1, err2, err3) 16 | } 17 | if puba.Len != 1024 || priva.Len != 1024 { 18 | t.Errorf("Error generating correct keypair of size 1024 byte got %d want 1024", puba.Len) 19 | } 20 | if pubb.Len != 2048 || privb.Len != 2048 { 21 | t.Errorf("Error generating correct keypair of size 1024 byte got %d want 2048", puba.Len) 22 | } 23 | if pubc.Len != 4096 || privc.Len != 4096 { 24 | t.Errorf("Error generating correct keypair of size 1024 byte got %d want 4096", puba.Len) 25 | } 26 | 27 | } 28 | func TestEncryptDecrypt(t *testing.T) { 29 | 30 | case1 := new(big.Int).SetInt64(9132) 31 | case2 := new(big.Int).SetInt64(1492) 32 | 33 | pub, priv, err := GenerateKeyPair(rand.Reader, 512) 34 | 35 | if err != nil { 36 | t.Errorf("Error Generating Keypair") 37 | } 38 | encCase1, errCase1 := Encrypt(pub, case1.Bytes()) 39 | encCase2, errCase2 := Encrypt(pub, case2.Bytes()) 40 | 41 | if errCase1 != nil || errCase2 != nil { 42 | t.Errorf("Error encrypting keypair %v \n %v", errCase1, errCase2) 43 | } 44 | 45 | d1, errDec1 := Decrypt(priv, encCase1) 46 | d2, errDec2 := Decrypt(priv, encCase2) 47 | 48 | decCase1 := new(big.Int).SetBytes(d1) 49 | decCase2 := new(big.Int).SetBytes(d2) 50 | if decCase1.Cmp(case1) != 0 || decCase2.Cmp(case2) != 0 { 51 | t.Errorf("Error Decrypting the message %v \n %v", errDec1, errDec2) 52 | } 53 | 54 | } 55 | 56 | func TestAdd(t *testing.T) { 57 | case1 := new(big.Int).SetInt64(1) 58 | case2 := new(big.Int).SetInt64(1) 59 | 60 | pub, priv, err := GenerateKeyPair(rand.Reader, 512) 61 | 62 | if err != nil { 63 | t.Errorf("Error Generating Keypair") 64 | } 65 | //Encrypt 66 | encCase1, err1 := Encrypt(pub, case1.Bytes()) 67 | encCase2, err2 := Encrypt(pub, case2.Bytes()) 68 | 69 | if err1 != nil || err2 != nil { 70 | t.Errorf("Error Encrypting Integers") 71 | } 72 | 73 | res := Add(pub, encCase1, encCase2) 74 | 75 | corr := new(big.Int).SetInt64(2) 76 | 77 | decRes, err := Decrypt(priv, res) 78 | if err != nil { 79 | t.Errorf("Failed to Decrypt Result got %v want %v with Error : %v", decRes, corr, err) 80 | } 81 | 82 | resB := new(big.Int).SetBytes(decRes) 83 | 84 | if resB.Cmp(corr) != 0 { 85 | t.Errorf("Failed to Add two ciphers got %v want %v", resB, corr) 86 | } 87 | 88 | } 89 | 90 | func TestAddConstant(t *testing.T) { 91 | 92 | k := new(big.Int).SetInt64(10) 93 | c := new(big.Int).SetInt64(32) 94 | 95 | pub, priv, err := GenerateKeyPair(rand.Reader, 102) 96 | 97 | if err != nil { 98 | t.Errorf("Failed to generated keypair %v", err) 99 | } 100 | 101 | //encrypt 102 | encC, err := Encrypt(pub, c.Bytes()) 103 | if err != nil { 104 | t.Errorf("Failed to encrypt c") 105 | } 106 | res := AddConstant(pub, encC, k.Bytes()) 107 | 108 | decRes, err := Decrypt(priv, res) 109 | if err != nil { 110 | t.Errorf("Failed to decrypt result") 111 | } 112 | 113 | result := new(big.Int).SetBytes(decRes) 114 | corr := new(big.Int).SetInt64(42) 115 | if result.Cmp(corr) != 0 { 116 | t.Errorf("Error Add Constant function want %d , got %d", corr, result) 117 | } 118 | 119 | } 120 | 121 | func TestMul(t *testing.T) { 122 | 123 | k := new(big.Int).SetInt64(10) 124 | c := new(big.Int).SetInt64(32) 125 | 126 | pub, priv, err := GenerateKeyPair(rand.Reader, 102) 127 | 128 | if err != nil { 129 | t.Errorf("Failed to generated keypair %v", err) 130 | } 131 | 132 | //encrypt 133 | encC, err := Encrypt(pub, c.Bytes()) 134 | if err != nil { 135 | t.Errorf("Failed to encrypt c") 136 | } 137 | res := Mul(pub, encC, k.Bytes()) 138 | 139 | decRes, err := Decrypt(priv, res) 140 | if err != nil { 141 | t.Errorf("Failed to decrypt result") 142 | } 143 | 144 | result := new(big.Int).SetBytes(decRes) 145 | corr := new(big.Int).SetInt64(320) 146 | if result.Cmp(corr) != 0 { 147 | t.Errorf("Error Mul function want %d , got %d", corr, result) 148 | } 149 | } 150 | func BenchmarkEncrypt(b *testing.B) { 151 | pubKey, _, _ := GenerateKeyPair(rand.Reader, 2048) 152 | val := new(big.Int).SetInt64(int64(1234)).Bytes() 153 | 154 | b.ResetTimer() 155 | for i := 0; i < b.N; i++ { 156 | _, err := Encrypt(pubKey, val) 157 | if err != nil { 158 | b.Fail() 159 | } 160 | } 161 | } 162 | -------------------------------------------------------------------------------- /go.mod: -------------------------------------------------------------------------------- 1 | module github.com/actuallyachraf/gomorph 2 | 3 | go 1.16 4 | --------------------------------------------------------------------------------