diff --git a/src/Crypt/ed25519.py b/src/Crypt/ed25519.py new file mode 100644 index 00000000..7c0161dc --- /dev/null +++ b/src/Crypt/ed25519.py @@ -0,0 +1,292 @@ +# The following is copied from... +# +# https://github.com/pyca/ed25519 +# +# This is under the CC0 license. For more information please see... +# +# https://github.com/pyca/cryptography/issues/5068 + + +# ed25519.py - Optimized version of the reference implementation of Ed25519 +# +# Written in 2011? by Daniel J. Bernstein +# 2013 by Donald Stufft +# 2013 by Alex Gaynor +# 2013 by Greg Price +# +# To the extent possible under law, the author(s) have dedicated all copyright +# and related and neighboring rights to this software to the public domain +# worldwide. This software is distributed without any warranty. +# +# You should have received a copy of the CC0 Public Domain Dedication along +# with this software. If not, see +# . + +""" +NB: This code is not safe for use with secret keys or secret data. +The only safe use of this code is for verifying signatures on public messages. + +Functions for computing the public key of a secret key and for signing +a message are included, namely publickey_unsafe and signature_unsafe, +for testing purposes only. + +The root of the problem is that Python's long-integer arithmetic is +not designed for use in cryptography. Specifically, it may take more +or less time to execute an operation depending on the values of the +inputs, and its memory access patterns may also depend on the inputs. +This opens it to timing and cache side-channel attacks which can +disclose data to an attacker. We rely on Python's long-integer +arithmetic, so we cannot handle secrets without risking their disclosure. +""" + +import hashlib +import operator + + +__version__ = "1.0.dev0" + +b = 256 +q = 2 ** 255 - 19 +l = 2 ** 252 + 27742317777372353535851937790883648493 +int2byte = operator.methodcaller("to_bytes", 1, "big") + + +def H(m): + return hashlib.sha512(m).digest() + + +def pow2(x, p): + """== pow(x, 2**p, q)""" + while p > 0: + x = x * x % q + p -= 1 + return x + + +def inv(z): + """$= z^{-1} \mod q$, for z != 0""" + # Adapted from curve25519_athlon.c in djb's Curve25519. + z2 = z * z % q # 2 + z9 = pow2(z2, 2) * z % q # 9 + z11 = z9 * z2 % q # 11 + z2_5_0 = (z11 * z11) % q * z9 % q # 31 == 2^5 - 2^0 + z2_10_0 = pow2(z2_5_0, 5) * z2_5_0 % q # 2^10 - 2^0 + z2_20_0 = pow2(z2_10_0, 10) * z2_10_0 % q # ... + z2_40_0 = pow2(z2_20_0, 20) * z2_20_0 % q + z2_50_0 = pow2(z2_40_0, 10) * z2_10_0 % q + z2_100_0 = pow2(z2_50_0, 50) * z2_50_0 % q + z2_200_0 = pow2(z2_100_0, 100) * z2_100_0 % q + z2_250_0 = pow2(z2_200_0, 50) * z2_50_0 % q # 2^250 - 2^0 + return pow2(z2_250_0, 5) * z11 % q # 2^255 - 2^5 + 11 = q - 2 + + +d = -121665 * inv(121666) % q +I = pow(2, (q - 1) // 4, q) + + +def xrecover(y): + xx = (y * y - 1) * inv(d * y * y + 1) + x = pow(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, 1, (Bx * By) % q) +ident = (0, 1, 1, 0) + + +def edwards_add(P, Q): + # This is formula sequence 'addition-add-2008-hwcd-3' from + # http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html + (x1, y1, z1, t1) = P + (x2, y2, z2, t2) = Q + + a = (y1-x1)*(y2-x2) % q + b = (y1+x1)*(y2+x2) % q + c = t1*2*d*t2 % q + dd = z1*2*z2 % q + e = b - a + f = dd - c + g = dd + c + h = b + a + x3 = e*f + y3 = g*h + t3 = e*h + z3 = f*g + + return (x3 % q, y3 % q, z3 % q, t3 % q) + + +def edwards_double(P): + # This is formula sequence 'dbl-2008-hwcd' from + # http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html + (x1, y1, z1, t1) = P + + a = x1*x1 % q + b = y1*y1 % q + c = 2*z1*z1 % q + # dd = -a + e = ((x1+y1)*(x1+y1) - a - b) % q + g = -a + b # dd + b + f = g - c + h = -a - b # dd - b + x3 = e*f + y3 = g*h + t3 = e*h + z3 = f*g + + return (x3 % q, y3 % q, z3 % q, t3 % q) + + +def scalarmult(P, e): + if e == 0: + return ident + Q = scalarmult(P, e // 2) + Q = edwards_double(Q) + if e & 1: + Q = edwards_add(Q, P) + return Q + + +# Bpow[i] == scalarmult(B, 2**i) +Bpow = [] + + +def make_Bpow(): + P = B + for i in range(253): + Bpow.append(P) + P = edwards_double(P) +make_Bpow() + + +def scalarmult_B(e): + """ + Implements scalarmult(B, e) more efficiently. + """ + # scalarmult(B, l) is the identity + e = e % l + P = ident + for i in range(253): + if e & 1: + P = edwards_add(P, Bpow[i]) + e = e // 2 + assert e == 0, e + return P + + +def encodeint(y): + bits = [(y >> i) & 1 for i in range(b)] + return b''.join([ + int2byte(sum([bits[i * 8 + j] << j for j in range(8)])) + for i in range(b//8) + ]) + + +def encodepoint(P): + (x, y, z, t) = P + zi = inv(z) + x = (x * zi) % q + y = (y * zi) % q + bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1] + return b''.join([ + int2byte(sum([bits[i * 8 + j] << j for j in range(8)])) + for i in range(b // 8) + ]) + + +def bit(h, i): + return (operator.getitem(h, i // 8) >> (i % 8)) & 1 + + +def publickey_unsafe(sk): + """ + Not safe to use with secret keys or secret data. + + See module docstring. This function should be used for testing only. + """ + 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_unsafe(m, sk, pk): + """ + Not safe to use with secret keys or secret data. + + See module docstring. This function should be used for testing only. + """ + h = H(sk) + a = 2 ** (b - 2) + sum(2 ** i * bit(h, i) for i in range(3, b - 2)) + r = Hint( + bytes([operator.getitem(h, j) for j 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, y, z, t) = P + return (z % q != 0 and + x*y % q == z*t % q and + (y*y - x*x - z*z - d*t*t) % 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, 1, (x*y) % q) + if not isoncurve(P): + raise ValueError("decoding point that is not on curve") + return P + + +class SignatureMismatch(Exception): + pass + + +def checkvalid(s, m, pk): + """ + Not safe to use when any argument is secret. + + See module docstring. This function should be used only for + verifying public signatures of public messages. + """ + if len(s) != b // 4: + raise ValueError("signature length is wrong") + + if len(pk) != b // 8: + raise ValueError("public-key length is wrong") + + R = decodepoint(s[:b // 8]) + A = decodepoint(pk) + S = decodeint(s[b // 8:b // 4]) + h = Hint(encodepoint(R) + pk + m) + + (x1, y1, z1, t1) = P = scalarmult_B(S) + (x2, y2, z2, t2) = Q = edwards_add(R, scalarmult(A, h)) + + if (not isoncurve(P) or not isoncurve(Q) or + (x1*z2 - x2*z1) % q != 0 or (y1*z2 - y2*z1) % q != 0): + raise SignatureMismatch("signature does not pass verification")