commit d10e1bdec4415a0676e12f9f909509a38c5d5b39 Author: Nick Mathewson nickm@torproject.org Date: Sat Aug 30 12:29:35 2014 -0400
Add the pure-python ed25519 implementation, for testing. --- src/test/slow_ed25519.py | 111 ++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 111 insertions(+)
diff --git a/src/test/slow_ed25519.py b/src/test/slow_ed25519.py new file mode 100644 index 0000000..3380079 --- /dev/null +++ b/src/test/slow_ed25519.py @@ -0,0 +1,111 @@ +# 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. + +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") +