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recover_pk: remove sslcrypto dep
This commit is contained in:
Philippe Teuwen
parent
3e67ad0b0f
commit
58eb9faa84
1 changed files with 299 additions and 7 deletions
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@ -1,26 +1,318 @@
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#!/usr/bin/env python3
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# MIT License
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# Copyright (c) 2020 @doegox
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# @doegox -- 2020
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import sslcrypto
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import binascii
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import sys
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debug = False
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#######################################################################
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# Using external sslcrypto library:
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# import sslcrypto
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# ... sslcrypto.ecc.get_curve()
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# But to get this script autonomous, i.e. for CI, we embedded the
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# code snippets we needed:
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#######################################################################
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# code snippets from JacobianCurve:
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# This code is public domain. Everyone has the right to do whatever they want with it for any purpose.
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# Copyright (c) 2013 Vitalik Buterin
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class JacobianCurve:
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def __init__(self, p, n, a, b, g):
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self.p = p
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self.n = n
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self.a = a
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self.b = b
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self.g = g
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self.n_length = len(bin(self.n).replace("0b", ""))
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def to_jacobian(self, p):
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return p[0], p[1], 1
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def jacobian_double(self, p):
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if not p[1]:
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return 0, 0, 0
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ysq = (p[1] ** 2) % self.p
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s = (4 * p[0] * ysq) % self.p
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m = (3 * p[0] ** 2 + self.a * p[2] ** 4) % self.p
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nx = (m ** 2 - 2 * s) % self.p
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ny = (m * (s - nx) - 8 * ysq ** 2) % self.p
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nz = (2 * p[1] * p[2]) % self.p
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return nx, ny, nz
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def jacobian_add(self, p, q):
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if not p[1]:
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return q
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if not q[1]:
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return p
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u1 = (p[0] * q[2] ** 2) % self.p
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u2 = (q[0] * p[2] ** 2) % self.p
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s1 = (p[1] * q[2] ** 3) % self.p
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s2 = (q[1] * p[2] ** 3) % self.p
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if u1 == u2:
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if s1 != s2:
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return (0, 0, 1)
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return self.jacobian_double(p)
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h = u2 - u1
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r = s2 - s1
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h2 = (h * h) % self.p
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h3 = (h * h2) % self.p
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u1h2 = (u1 * h2) % self.p
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nx = (r ** 2 - h3 - 2 * u1h2) % self.p
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ny = (r * (u1h2 - nx) - s1 * h3) % self.p
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nz = (h * p[2] * q[2]) % self.p
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return (nx, ny, nz)
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def from_jacobian(self, p):
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z = inverse(p[2], self.p)
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return (p[0] * z ** 2) % self.p, (p[1] * z ** 3) % self.p
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def jacobian_shamir(self, a, n, b, m):
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ab = self.jacobian_add(a, b)
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if n < 0 or n >= self.n:
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n %= self.n
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if m < 0 or m >= self.n:
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m %= self.n
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res = 0, 0, 1 # point on infinity
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for i in range(self.n_length - 1, -1, -1):
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res = self.jacobian_double(res)
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has_n = n & (1 << i)
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has_m = m & (1 << i)
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if has_n:
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if has_m == 0:
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res = self.jacobian_add(res, a)
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if has_m != 0:
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res = self.jacobian_add(res, ab)
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else:
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if has_m == 0:
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res = self.jacobian_add(res, (0, 0, 1)) # Try not to leak
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if has_m != 0:
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res = self.jacobian_add(res, b)
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return res
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def fast_shamir(self, a, n, b, m):
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return self.from_jacobian(self.jacobian_shamir(self.to_jacobian(a), n, self.to_jacobian(b), m))
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#######################################################################
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# code snippets from sslcrypto
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# MIT License
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# Copyright (c) 2019 Ivan Machugovskiy
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import hmac
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import os
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import hashlib
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import struct
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def int_to_bytes(raw, length):
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data = []
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for _ in range(length):
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data.append(raw % 256)
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raw //= 256
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return bytes(data[::-1])
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def bytes_to_int(data):
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raw = 0
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for byte in data:
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raw = raw * 256 + byte
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return raw
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def legendre(a, p):
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res = pow(a, (p - 1) // 2, p)
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if res == p - 1:
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return -1
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else:
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return res
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def inverse(a, n):
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if a == 0:
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return 0
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lm, hm = 1, 0
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low, high = a % n, n
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while low > 1:
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r = high // low
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nm, new = hm - lm * r, high - low * r
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lm, low, hm, high = nm, new, lm, low
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return lm % n
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def square_root_mod_prime(n, p):
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if n == 0:
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return 0
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if p == 2:
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return n # We should never get here but it might be useful
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if legendre(n, p) != 1:
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raise ValueError("No square root")
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# Optimizations
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if p % 4 == 3:
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return pow(n, (p + 1) // 4, p)
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# 1. By factoring out powers of 2, find Q and S such that p - 1 =
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# Q * 2 ** S with Q odd
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q = p - 1
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s = 0
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while q % 2 == 0:
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q //= 2
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s += 1
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# 2. Search for z in Z/pZ which is a quadratic non-residue
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z = 1
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while legendre(z, p) != -1:
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z += 1
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m, c, t, r = s, pow(z, q, p), pow(n, q, p), pow(n, (q + 1) // 2, p)
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while True:
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if t == 0:
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return 0
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elif t == 1:
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return r
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# Use repeated squaring to find the least i, 0 < i < M, such
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# that t ** (2 ** i) = 1
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t_sq = t
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i = 0
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for i in range(1, m):
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t_sq = t_sq * t_sq % p
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if t_sq == 1:
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break
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else:
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raise ValueError("Should never get here")
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# Let b = c ** (2 ** (m - i - 1))
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b = pow(c, 2 ** (m - i - 1), p)
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m = i
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c = b * b % p
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t = t * b * b % p
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r = r * b % p
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return r
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# name: (nid, p, n, a, b, (Gx, Gy)),
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CURVES = {
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"secp128r1": (
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706,
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0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF,
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0xFFFFFFFE0000000075A30D1B9038A115,
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0xFFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC,
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0xE87579C11079F43DD824993C2CEE5ED3,
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(
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0x161FF7528B899B2D0C28607CA52C5B86,
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0xCF5AC8395BAFEB13C02DA292DDED7A83
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)
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),
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"secp224r1": (
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713,
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0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001,
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0xFFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D,
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0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE,
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0xB4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4,
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(
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0xB70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21,
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0xBD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34
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)
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),
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}
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def get_curve(name):
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if name not in CURVES:
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raise ValueError("Unknown curve {}".format(name))
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nid, p, n, a, b, g = CURVES[name]
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params = {"p": p, "n": n, "a": a, "b": b, "g": g}
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return EllipticCurve(nid, p, n, a, b, g)
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class EllipticCurve:
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def __init__(self, nid, p, n, a, b, g):
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self.p, self.n, self.a, self.b, self.g = p, n, a, b, g
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self.jacobian = JacobianCurve(self.p, self.n, self.a, self.b, self.g)
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self.public_key_length = (len(bin(p).replace("0b", "")) + 7) // 8
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self.order_bitlength = len(bin(n).replace("0b", ""))
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def _int_to_bytes(self, raw, len=None):
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return int_to_bytes(raw, len or self.public_key_length)
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def _subject_to_int(self, subject):
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return bytes_to_int(subject[:(self.order_bitlength + 7) // 8])
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def recover(self, signature, data, hash="sha256"):
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# Sanity check: is this signature recoverable?
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if len(signature) != 1 + 2 * self.public_key_length:
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raise ValueError("Cannot recover an unrecoverable signature")
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subject = self._digest(data, hash)
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z = self._subject_to_int(subject)
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recid = signature[0] - 27 if signature[0] < 31 else signature[0] - 31
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r = bytes_to_int(signature[1:self.public_key_length + 1])
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s = bytes_to_int(signature[self.public_key_length + 1:])
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# Verify bounds
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if not 0 <= recid < 2 * (self.p // self.n + 1):
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raise ValueError("Invalid recovery ID")
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if r >= self.n:
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raise ValueError("r is out of bounds")
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if s >= self.n:
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raise ValueError("s is out of bounds")
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rinv = inverse(r, self.n)
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u1 = (-z * rinv) % self.n
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u2 = (s * rinv) % self.n
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# Recover R
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rx = r + (recid // 2) * self.n
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if rx >= self.p:
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raise ValueError("Rx is out of bounds")
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# Almost copied from decompress_point
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ry_square = (pow(rx, 3, self.p) + self.a * rx + self.b) % self.p
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try:
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ry = square_root_mod_prime(ry_square, self.p)
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except Exception:
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raise ValueError("Invalid recovered public key") from None
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# Ensure the point is correct
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if ry % 2 != recid % 2:
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# Fix Ry sign
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ry = self.p - ry
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x, y = self.jacobian.fast_shamir(self.g, u1, (rx, ry), u2)
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x, y = self._int_to_bytes(x), self._int_to_bytes(y)
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is_compressed = signature[0] >= 31
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if is_compressed:
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return bytes([0x02 + (y[-1] % 2)]) + x
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else:
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return bytes([0x04]) + x + y
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def _digest(self, data, hash):
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if hash is None:
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return data
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elif callable(hash):
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return hash(data)
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elif hash == "sha1":
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return hashlib.sha1(data).digest()
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elif hash == "sha256":
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return hashlib.sha256(data).digest()
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elif hash == "sha512":
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return hashlib.sha512(data).digest()
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else:
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raise ValueError("Unknown hash/derivation method")
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#######################################################################
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def recover(data, signature, alghash=None):
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recovered = set()
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if len(signature) == 32:
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curve = sslcrypto.ecc.get_curve("secp128r1")
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curve = get_curve("secp128r1")
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recoverable = False
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elif len(signature) == 33:
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curve = sslcrypto.ecc.get_curve("secp128r1")
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curve = get_curve("secp128r1")
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recoverable = True
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elif len(signature) == 56:
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curve = sslcrypto.ecc.get_curve("secp224r1")
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curve = get_curve("secp224r1")
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recoverable = False
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elif len(signature) == 57:
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curve = sslcrypto.ecc.get_curve("secp224r1")
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curve = get_curve("secp224r1")
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recoverable = True
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else:
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print("Unsupported signature size %i" % len(signature))
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