diff --git a/ed25519.py b/ed25519.py deleted file mode 100644 index 69a0af3..0000000 --- a/ed25519.py +++ /dev/null @@ -1,104 +0,0 @@ -import hashlib - -b = 256 -q = 2**255 - 19 -l = 2**252 + 27742317777372353535851937790883648493 - -def H(m): - return hashlib.sha512(m).digest() - -def expmod(b,e,m): - if e == 0: return 1 - t = expmod(b,e//2,m)**2 % m - if e & 1: t = (t*b) % m - return t - -def inv(x): - return expmod(x,q-2,q) - -d = -121665 * inv(121666) -I = expmod(2,(q-1)//4,q) - -def xrecover(y): - xx = (y*y-1) * inv(d*y*y+1) - x = expmod(xx,(q+3)//8,q) - if (x*x - xx) % q != 0: x = (x*I) % q - if x % 2 != 0: x = q-x - return x - -By = 4 * inv(5) -Bx = xrecover(By) -B = [Bx % q,By % q] - -def edwards(P,Q): - x1 = P[0] - y1 = P[1] - x2 = Q[0] - y2 = Q[1] - x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2) - y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2) - return [x3 % q,y3 % q] - -def scalarmult(P,e): - if e == 0: return [0,1] - Q = scalarmult(P,e//2) - Q = edwards(Q,Q) - if e & 1: Q = edwards(Q,P) - return Q - -def encodeint(y): - bits = [(y >> i) & 1 for i in range(b)] - return ''.join([chr(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b//8)]) - -def encodepoint(P): - x = P[0] - y = P[1] - bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1] - return ''.join([chr(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b//8)]) - -def bit(h,i): - return (ord(h[i//8]) >> (i%8)) & 1 - -def publickey(sk): - h = H(sk) - a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2)) - A = scalarmult(B,a) - return encodepoint(A) - -def Hint(m): - h = H(m) - return sum(2**i * bit(h,i) for i in range(2*b)) - -def signature(m,sk,pk): - h = H(sk) - a = 2**(b-2) + sum(2**i * bit(h,i) for i in range(3,b-2)) - r = Hint(''.join([h[i] for i in range(b//8,b//4)]) + m) - R = scalarmult(B,r) - S = (r + Hint(encodepoint(R) + pk + m) * a) % l - return encodepoint(R) + encodeint(S) - -def isoncurve(P): - x = P[0] - y = P[1] - return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0 - -def decodeint(s): - return sum(2**i * bit(s,i) for i in range(0,b)) - -def decodepoint(s): - y = sum(2**i * bit(s,i) for i in range(0,b-1)) - x = xrecover(y) - if x & 1 != bit(s,b-1): x = q-x - P = [x,y] - if not isoncurve(P): raise Exception("decoding point that is not on curve") - return P - -def checkvalid(s,m,pk): - if len(s) != b//4: raise Exception("signature length is wrong") - if len(pk) != b//8: raise Exception("public-key length is wrong") - R = decodepoint(s[0:b//8]) - A = decodepoint(pk) - S = decodeint(s[b//8:b//4]) - h = Hint(encodepoint(R) + pk + m) - if scalarmult(B,S) != edwards(R,scalarmult(A,h)): - raise Exception("signature does not pass verification") diff --git a/reference.py b/reference.py deleted file mode 100755 index 56f7940..0000000 --- a/reference.py +++ /dev/null @@ -1,9 +0,0 @@ -#!/usr/bin/env python - -import binascii -import ed25519 - - -s = "mike" -print ed25519.publickey(s) -