├── README.md
└── rlwe_kex.py


/README.md:
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1 | # RLWE-KEX
2 | 
3 | Simple RLWE-KEX example using Python.
4 | 


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/rlwe_kex.py:
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  1 | import numpy as np
  2 | from numpy.polynomial import polynomial as p
  3 | 
  4 | n = 1024
  5 | q = 2**32-1
  6 | hlpr = [1] + [0] * (n-1) + [1]
  7 | 
  8 | 
  9 | def gen_poly(n,q):
 10 |     global hlpr
 11 |     l = 0 #Gamma Distribution Location (Mean "center" of dist.)
 12 |     poly = np.floor(np.random.normal(l,size=(n)))
 13 |     while (len(poly) != n):
 14 |         poly = np.floor(np.random.normal(l,size=(n)))
 15 |         poly = np.floor(p.polydiv(poly,hlpr)[1]%q)
 16 |     return poly
 17 | 
 18 | 
 19 | 
 20 | #Generate A
 21 | A = np.floor(np.random.random(size=(n))*q)%q
 22 | 
 23 | A = np.floor(p.polydiv(A,hlpr)[1])
 24 | 
 25 | #Alice (Secret & Error)
 26 | sA = gen_poly(n,q)
 27 | eA = gen_poly(n,q)
 28 | 
 29 | bA = p.polymul(A,sA)%q
 30 | bA = np.floor(p.polydiv(sA,hlpr)[1])
 31 | bA = p.polyadd(bA,eA)%q
 32 | 
 33 | 
 34 | #Bob
 35 | sB = gen_poly(n,q)
 36 | eB = gen_poly(n,q)
 37 | 
 38 | 
 39 | bB = p.polymul(A,sB)%q
 40 | bB = np.floor(p.polydiv(sB,hlpr)[1])
 41 | bB = p.polyadd(bB,eB)%q
 42 | 
 43 | 
 44 | #Shared Secret
 45 | #Alice
 46 | sharedAlice = np.floor(p.polymul(sA,bB)%q)
 47 | sharedAlice = np.floor(p.polydiv(sharedAlice,hlpr)[1])%q  #TODO FIX THIS HAS TO BE DIVED BY HELPER
 48 | sharedBob = np.floor(p.polymul(sB,bA)%q)
 49 | sharedBob = np.floor(p.polydiv(sharedBob,hlpr)[1])%q
 50 | 
 51 | #Error Rounding
 52 | #--Bob
 53 | u = np.asarray([0] * n)
 54 | i = 0
 55 | 
 56 | while (i < len(u)):
 57 | 	if (len(bB) <= i): break;
 58 | 	if (int(bB[i]/(q/4)) == 0): u[i] = 0
 59 | 	elif (int(bB[i]/(q/2)) == 0): u[i] = 1
 60 | 	elif (int(bB[i]/(3*q/4)) == 0): u[i] = 0
 61 | 	elif (int(bB[i]/(q)) == 0): u[i] = 1
 62 | 	else:
 63 | 		print "error! (1)"
 64 | 	i+=1
 65 | 
 66 | 
 67 | i = 0
 68 | while (i < len(u)):
 69 | 	#Region 0 (0 --- q/4 and q/2 --- 3q/4)
 70 | 	if (u[i] == 0):
 71 | 		if (sharedBob[i] >= q*0.125 and sharedBob[i] < q*0.625):
 72 | 			sharedBob[i] = 1
 73 | 		else:
 74 | 			sharedBob[i] = 0
 75 | 
 76 | 
 77 | 	#Region 1 (q/4 --- q/2 and 3q/4 --- q)
 78 | 	elif (u[i] == 1):
 79 | 		if (sharedBob[i] >= q*0.875 and sharedBob[i] < q*0.375):
 80 | 			sharedBob[i] = 0
 81 | 		else:
 82 | 			sharedBob[i] = 1
 83 | 
 84 | 	else:
 85 | 		print "error! (2)"
 86 | 
 87 | 	i += 1
 88 | 
 89 | #--Alice
 90 | i = 0
 91 | while (i < len(u)):
 92 | 	#Region 0 (0 --- q/4 and q/2 --- 3q/4)
 93 | 	if (u[i] == 0):
 94 | 		if (sharedAlice[i] >= q*0.125 and sharedAlice[i] < q*0.625):
 95 | 			sharedAlice[i] = 1
 96 | 		else:
 97 | 			sharedAlice[i] = 0
 98 | 
 99 | 
100 | 	#Region 1 (q/4 --- q/2 and 3q/4 --- q)
101 | 	elif (u[i] == 1):
102 | 		if (sharedAlice[i] >= q*0.875 and sharedAlice[i] < q*0.375):
103 | 			sharedAlice[i] = 0
104 | 		else:
105 | 			sharedAlice[i] = 1
106 | 
107 | 	else:
108 | 		print "error! (3)"
109 | 	i += 1
110 | 
111 | 
112 | 
113 | 
114 | 
115 | #
116 | print "A:",len(A),"|",A
117 | print "\n-Alice---"
118 | print " s:",len(sA),"|",sA
119 | print " e:",len(eA),"|",eA
120 | print " b:",len(bA),"|",bA
121 | print "\n-Bob---"
122 | print " s':",len(sB),"|",sB
123 | print " e':",len(eB),"|",eB
124 | print " b':",len(bB),"|",bB
125 | print " u :",len(u),"|",u
126 | print "\n"
127 | print "Shared Secret Alice:",len(sharedAlice),"|",sharedAlice
128 | print "Shared Secret Bob:",len(sharedBob),"|",sharedBob
129 | 
130 | 
131 | print "\n\n--Verification--"
132 | i = 0
133 | while (i < len(sharedBob)):
134 | 	if (sharedAlice[i] != sharedBob[i]):
135 | 		print "Error at index",i
136 | 	i+=1


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