#### slow_ed25519.py2.8 KB Permalink History Raw

 123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115 ``````# This is the ed25519 implementation from # http://ed25519.cr.yp.to/python/ed25519.py . # It is in the public domain. # # It isn't constant-time. Don't use it except for testing. Also, see # warnings about how very slow it is. Only use this for generating # test vectors, I'd suggest. # # Don't edit this file. Mess with ed25519_ref.py 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") ``````