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#ed25519.cr.yp.to/python/ed25519.py
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 radix255(x):
x = x % q
if x + x > q: x -= q
x = [x,0,0,0,0,0,0,0,0,0]
bits = [26,25,26,25,26,25,26,25,26,25]
for i in range(9):
carry = (x[i] + 2**(bits[i]-1)) / 2**bits[i]
x[i] -= carry * 2**bits[i]
x[i + 1] += carry
result = ""
for i in range(9):
result = result+str(x[i])+","
result = result+str(x[9])
return result
def theD():
return d
def computeA():
return 2 *((1 - d) % q) * inv((1 + d) % q) % 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
def sqroot(xx):
x = expmod(xx,(q+3)/8,q)
if (x*x - xx) % q != 0:
x = (x*I) % q
if (x*x - xx) % q != 0:
print("no square root!")
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 edwards_Minus(P, Q): #added
x1 = P[0]
y1 = P[1]
x2 = (-1 * Q[0]) % q
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
#added scalarmultbase
def scalarmultbase(e):
if e == 0: return [0,1]
Q = scalarmult(B,e/2)
Q = edwards(Q,Q)
if e & 1: Q = edwards(Q,B)
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 decodepointcheck(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]
#print("actually checking if it's on curve!")
if not isoncurve(P):
#print("not on curve")
quit()
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")
return False
if len(pk) != b/8:
raise Exception("public-key length is wrong")
return False
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
return True