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Montgomery Ladder
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| import random | |
| class Montgomery: | |
| # B*v^2 = u^3 + A*u^2 + u | |
| def __init__(self, A, B, p): | |
| self.A = A | |
| self.B = B | |
| self.p = p | |
| self.a24 = (A + 2) / 4 % self.p | |
| self.mask = pow(2, self.p.bit_length() +1) - 1 | |
| def mladder(self, x1, n): | |
| x2,z2,x3,z3 = 1,0,x1,1 | |
| for i in reversed(range(n.bit_length())): | |
| bit = 1 & (n >> i) | |
| x2,x3 = self.cswap(x2,x3,bit) | |
| z2,z3 = self.cswap(z2,z3,bit) | |
| # x3, z3 = (pow((x2*x3%self.p) - (z2*z3%self.p), 2, self.p), | |
| # x1*pow((x2*z3%self.p)-(z2*x3%self.p), 2, self.p)%self.p) | |
| # x2, z2 = (pow(pow(x2,2,self.p) - pow(z2,2,self.p) %self.p, 2 ,self.p), | |
| # (4*x2*z2* ( pow(x2,2, self.p) + (self.A*x2*z2%self.p) + pow(z2,2, self.p)) % self.p)) | |
| (x2, z2, x3, z3) = self.ladderstep(x1, x2, z2, x3, z3) | |
| x2,x3 = self.cswap(x2,x3,bit) | |
| z2,z3 = self.cswap(z2,z3,bit) | |
| return x2 * pow(z2, self.p-2, self.p) % self.p | |
| def ladderstep(self, XQmP , XP , ZP , XQ, ZQ): | |
| t1 = XP + ZP % self.p | |
| t6 = pow(t1, 2, self.p) | |
| t2 = XP - ZP % self.p | |
| t7 = pow(t2, 2, self.p) | |
| t5 = t6 - t7 % self.p | |
| t3 = XQ + ZQ % self.p | |
| t4 = XQ - ZQ % self.p | |
| t8 = t4 * t1 % self.p | |
| t9 = t3 * t2 % self.p | |
| XPpQ = pow(t8 + t9 % self.p, 2, self.p) | |
| ZPpQ = XQmP * pow(t8 - t9 % self.p, 2, self.p) % self.p | |
| X2P = t6 * t7 % self.p | |
| Z2P = t5 * ((t7 + (self.a24 * t5 % self.p)) % self.p) % self.p | |
| return (X2P , Z2P , XPpQ, ZPpQ) | |
| def generate_keypair(self, base, baseorder): | |
| secret = random.randint(1, baseorder) | |
| public = self.mladder(base, secret) | |
| return (secret, public) | |
| def compute_secret(self, peer_public, self_secret): | |
| return self.mladder(peer_public, self_secret) | |
| def cswap(self, a, b, c): | |
| mask = c * self.mask | |
| return (a & ~mask) | (b & mask) , (b & ~mask) | (a & mask) |
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