# This code is a (slightly modified) version of the code published here:
# http://ed25519.cr.yp.to/python/ed25519.py (fetched 2015-02-15)
# And described here:
# http://ed25519.cr.yp.to/software.html (fetched 2015-02-15)
#
# Specifically, the authors state:
# "Copyrights: The Ed25519 software is in the public domain."
#
# The modification made here to the code published at ed25519.cr.yp.to are not
# regarded by its author to be significant enough to constitute a derivative
# work, protected on its own, and thus the same rights should hold that applies
# to files published by the original authors.
import hashlib
b = 256
q = 2**255 - 19
l = 2**252 + 27742317777372353535851937790883648493
[docs]def H(m):
return bytearray(hashlib.sha512(m).digest())
[docs]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
[docs]def inv(x):
return expmod(x, q-2, q)
d = -121665 * inv(121666)
I = expmod(2, (q-1)//4, q)
[docs]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]
[docs]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]
[docs]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
[docs]def encodeint(y):
bits = [(y >> i) & 1 for i in range(b)]
return bytearray([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b//8)])
[docs]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)])
return bytearray([sum([bits[i * 8 + j] << j for j in range(8)]) for i in range(b//8)])
[docs]def bit(h, i):
return (h[i//8] >> (i % 8)) & 1
[docs]def publickey(sk):
sk = bytearray(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)
[docs]def Hint(m):
h = H(m)
return sum(2**i * bit(h, i) for i in range(2*b))
[docs]def signature(m, sk, pk):
sk = bytearray(sk)
pk = bytearray(pk)
m = bytearray(m,'utf-8')
h = H(sk)
a = 2**(b-2) + sum(2**i * bit(h, i) for i in range(3, b-2))
r = Hint(bytearray([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)
[docs]def isoncurve(P):
x = P[0]
y = P[1]
return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0
[docs]def decodeint(s):
return sum(2**i * bit(s, i) for i in range(0, b))
[docs]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
[docs]def checkvalid(s, m, pk):
s = bytearray(s)
pk = bytearray(pk)
m = bytearray(m,'utf-8')
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")
return False
else:
return True
# Extra checks
assert b >= 10
assert 8 * len(H(bytearray("hash input",'utf-8'))) == 2 * b
assert expmod(2, q-1, q) == 1
assert q % 4 == 1
assert expmod(2, l-1, l) == 1
assert l >= 2**(b-4)
assert l <= 2**(b-3)
assert expmod(d, (q-1)//2, q) == q-1
assert expmod(I, 2, q) == q-1
assert isoncurve(B)
assert scalarmult(B, l) == [0, 1]
[docs]def main():
import os, base64, subprocess
print("This runs some tests of the ed25519 python implementation")
message = "This is my message."
my_secret_key = bytearray("swordfish",'utf-8')
print("Generating public key")
my_public_key = publickey(my_secret_key)
print("Signing message")
my_signature = signature(message, my_secret_key, my_public_key)
print("base64 encoding of signature")
b64signature = base64.b64encode(my_signature)
print("Signature is")
print(b64signature)
assert(bytearray(b64signature) == bytearray('EiK38c3M9nFH9niBnqg6kxQg+VqHVXf11028CjBmaY4Ua+SOAM/qQc52OhcJTo23oOyWdPzbvXNlNr5PF6ldDQ==','utf-8'))
print("base64 encoding of signature")
my_signature = base64.b64decode(b64signature)
print("Check if signature is valid")
result = checkvalid(my_signature, message, my_public_key)
assert(result == True)
forged_message = "This is not my message."
print("Check if forged message is valid")
result = checkvalid(my_signature, forged_message, my_public_key)
assert(result==False)
#print("Check if implementation matches original python 2 implementation")
#output = subprocess.check_output("python2 -c 'import base64; from _ed25519_orig import *; my_secret_key = \"swordfish\"; print base64.b64encode(publickey(my_secret_key))'", shell=True)
#my_public_key_orig = bytearray(base64.b64decode(output))
#assert(my_public_key_orig == my_public_key)
print("Finished")
if __name__ == "__main__":
main()