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- # The reference Ed25519 software is in the public domain.
- # Source: https://ed25519.cr.yp.to/python/ed25519.py
- # Date accessed: 2 Nov. 2016
- b = 256
- q = 2**255 - 19
- l = 2**252 + 27742317777372353535851937790883648493
- 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 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)])
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