| # The original version of this file was downloaded from |
| # http://ed25519.cr.yp.to/software.html, and came with the following copyright |
| # statement: |
| # The Ed25519 software is in the public domain. |
| |
| 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 bytes( |
| [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 bytes( |
| [sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b // 8)]) |
| |
| |
| def bit(h,i): |
| return (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(bytes([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") |