Replace Ed25519 implementation with much faster pyca/ed25519
This commit is contained in:
Michał Sałaban
parent
c5c53adb10
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9aee6564e7
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@ -37,12 +37,15 @@ Released under the BSD 3-Clause License. See `LICENSE.txt`_.
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Copyright (c) 2017-2018 Michał Sałaban <michal@salaban.info> and Contributors: `lalanza808`_, `cryptochangements34`_, `atward`_, `rooterkyberian`_, `brucexiu`_,
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`lialsoftlab`_, `moneroexamples`_.
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Copyright (c) 2016 The MoneroPy Developers (``monero/base58.py`` and ``monero/ed25519.py`` taken from `MoneroPy`_)
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Copyright (c) 2016 The MoneroPy Developers (``monero/base58.py`` taken from `MoneroPy`_)
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Copyright (c) 2011-2013 `pyca/ed25519`_ Developers (``monero/ed25519.py``)
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Copyright (c) 2011 thomasv@gitorious (``monero/seed.py`` based on `Electrum`_)
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.. _`LICENSE.txt`: LICENSE.txt
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.. _`MoneroPy`: https://github.com/bigreddmachine/MoneroPy
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.. _`pyca/ed25519`: https://github.com/pyca/ed25519
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.. _`Electrum`: https://github.com/spesmilo/electrum
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.. _`lalanza808`: https://github.com/lalanza808
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@ -1,16 +1,46 @@
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# The reference Ed25519 software is in the public domain.
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# Source: https://ed25519.cr.yp.to/python/ed25519.py
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# ed25519.py - Optimized version of the reference implementation of Ed25519
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#
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# Parts Copyright (c) 2016 The MoneroPy Developers. Released under the BSD 3-Clause
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# Parts taken from https://github.com/monero-project/mininero/blob/master/ed25519ietf.py
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# Written in 2011? by Daniel J. Bernstein <djb@cr.yp.to>
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# 2013 by Donald Stufft <donald@stufft.io>
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# 2013 by Alex Gaynor <alex.gaynor@gmail.com>
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# 2013 by Greg Price <price@mit.edu>
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# 2019 by Michal Salaban <michal@salaban.info>
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#
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# To the extent possible under law, the author(s) have dedicated all copyright
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# and related and neighboring rights to this software to the public domain
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# worldwide. This software is distributed without any warranty.
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#
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# You should have received a copy of the CC0 Public Domain Dedication along
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# with this software. If not, see
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# <http://creativecommons.org/publicdomain/zero/1.0/>.
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from binascii import hexlify, unhexlify
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import hashlib
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import operator as _oper
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import sys as _sys
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"""
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NB: This code is not safe for use with secret keys or secret data.
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The only safe use of this code is for verifying signatures on public messages.
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# Set up byte handling for Python 2 or 3
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if _sys.version_info.major == 2: # pragma: no cover
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Functions for computing the public key of a secret key and for signing
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a message are included, namely publickey_unsafe and signature_unsafe,
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for testing purposes only.
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The root of the problem is that Python's long-integer arithmetic is
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not designed for use in cryptography. Specifically, it may take more
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or less time to execute an operation depending on the values of the
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inputs, and its memory access patterns may also depend on the inputs.
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This opens it to timing and cache side-channel attacks which can
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disclose data to an attacker. We rely on Python's long-integer
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arithmetic, so we cannot handle secrets without risking their disclosure.
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"""
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import binascii
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import operator
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import sys
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if sys.version_info >= (3,): # pragma: no cover
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indexbytes = operator.getitem
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intlist2bytes = bytes
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int2byte = operator.methodcaller("to_bytes", 1, "big")
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else: # pragma: no cover
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int2byte = chr
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range = xrange
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@ -19,32 +49,51 @@ if _sys.version_info.major == 2: # pragma: no cover
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def intlist2bytes(l):
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return b"".join(chr(c) for c in l)
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else: # pragma: no cover
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indexbytes = _oper.getitem
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intlist2bytes = bytes
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int2byte = _oper.methodcaller("to_bytes", 1, "big")
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b = 256
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q = 2**255 - 19
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l = 2**252 + 27742317777372353535851937790883648493
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q = 2 ** 255 - 19
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l = 2 ** 252 + 27742317777372353535851937790883648493
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def expmod(b, e, m):
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if e == 0: return 1
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t = expmod(b, e//2, m)**2 % m
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if e & 1: t = (t*b) % m
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return t
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def inv(x):
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return expmod(x, q-2, q)
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def pow2(x, p):
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"""== pow(x, 2**p, q)"""
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while p > 0:
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x = x * x % q
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p -= 1
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return x
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def inv(z):
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# Adapted from curve25519_athlon.c in djb's Curve25519.
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z2 = z * z % q # 2
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z9 = pow2(z2, 2) * z % q # 9
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z11 = z9 * z2 % q # 11
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z2_5_0 = (z11 * z11) % q * z9 % q # 31 == 2^5 - 2^0
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z2_10_0 = pow2(z2_5_0, 5) * z2_5_0 % q # 2^10 - 2^0
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z2_20_0 = pow2(z2_10_0, 10) * z2_10_0 % q # ...
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z2_40_0 = pow2(z2_20_0, 20) * z2_20_0 % q
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z2_50_0 = pow2(z2_40_0, 10) * z2_10_0 % q
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z2_100_0 = pow2(z2_50_0, 50) * z2_50_0 % q
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z2_200_0 = pow2(z2_100_0, 100) * z2_100_0 % q
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z2_250_0 = pow2(z2_200_0, 50) * z2_50_0 % q # 2^250 - 2^0
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return pow2(z2_250_0, 5) * z11 % q # 2^255 - 2^5 + 11 = q - 2
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d = -121665 * inv(121666) % q
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I = pow(2, (q - 1) // 4, q)
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d = -121665 * inv(121666)
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I = expmod(2, (q-1)//4, q)
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def xrecover(y):
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xx = (y*y-1) * inv(d*y*y+1)
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x = expmod(xx, (q+3)//8, q)
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if (x*x - xx) % q != 0: x = (x*I) % q
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if x % 2 != 0: x = q-x
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xx = (y * y - 1) * inv(d * y * y + 1)
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x = pow(xx, (q + 3) // 8, q)
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if (x * x - xx) % q != 0:
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x = (x * I) % q
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if x % 2 != 0:
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x = q-x
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return x
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def compress(P):
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@ -56,103 +105,140 @@ def decompress(P):
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By = 4 * inv(5)
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Bx = xrecover(By)
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B = [Bx%q, By%q]
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B = (Bx % q, By % q, 1, (Bx * By) % q)
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ident = (0, 1, 1, 0)
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def edwards(P, Q):
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x1 = P[0]
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y1 = P[1]
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x2 = Q[0]
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y2 = Q[1]
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x3 = (x1*y2+x2*y1) * inv(1+d*x1*x2*y1*y2)
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y3 = (y1*y2+x1*x2) * inv(1-d*x1*x2*y1*y2)
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return [x3%q, y3%q]
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def add(P, Q):
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A = (P[1]-P[0])*(Q[1]-Q[0]) % q
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B = (P[1]+P[0])*(Q[1]+Q[0]) % q
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C = 2 * P[3] * Q[3] * d % q
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D = 2 * P[2] * Q[2] % q
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E = B-A
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F = D-C
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G = D+C
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H = B+A
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return (E*F, G*H, F*G, E*H)
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def edwards_add(P, Q):
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# This is formula sequence 'addition-add-2008-hwcd-3' from
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# http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
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(x1, y1, z1, t1) = P
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(x2, y2, z2, t2) = Q
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a = (y1-x1)*(y2-x2) % q
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b = (y1+x1)*(y2+x2) % q
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c = t1*2*d*t2 % q
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dd = z1*2*z2 % q
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e = b - a
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f = dd - c
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g = dd + c
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h = b + a
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x3 = e*f
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y3 = g*h
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t3 = e*h
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z3 = f*g
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return (x3 % q, y3 % q, z3 % q, t3 % q)
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def edwards_double(P):
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# This is formula sequence 'dbl-2008-hwcd' from
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# http://www.hyperelliptic.org/EFD/g1p/auto-twisted-extended-1.html
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(x1, y1, z1, t1) = P
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a = x1*x1 % q
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b = y1*y1 % q
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c = 2*z1*z1 % q
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# dd = -a
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e = ((x1+y1)*(x1+y1) - a - b) % q
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g = -a + b # dd + b
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f = g - c
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h = -a - b # dd - b
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x3 = e*f
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y3 = g*h
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t3 = e*h
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z3 = f*g
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return (x3 % q, y3 % q, z3 % q, t3 % q)
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def add_compressed(P, Q):
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return compress(add(decompress(P), decompress(Q)))
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def scalarmult(P, e):
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if e == 0: return [0, 1]
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Q = scalarmult(P, e//2)
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Q = edwards(Q, Q)
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if e & 1: Q = edwards(Q, P)
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if e == 0:
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return ident
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Q = scalarmult(P, e // 2)
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Q = edwards_double(Q)
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if e & 1:
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Q = edwards_add(Q, P)
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return Q
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# Bpow[i] == scalarmult(B, 2**i)
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Bpow = []
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def make_Bpow():
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P = B
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for i in range(253):
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Bpow.append(P)
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P = edwards_double(P)
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make_Bpow()
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def scalarmult_B(e):
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"""
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Implements scalarmult(B, e) more efficiently.
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"""
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# scalarmult(B, l) is the identity
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e = e % l
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P = ident
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for i in range(253):
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if e & 1:
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P = edwards_add(P, Bpow[i])
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e = e // 2
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assert e == 0, e
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return P
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def encodeint(y):
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bits = [(y >> i) & 1 for i in range(b)]
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return b''.join([int2byte(sum([bits[i*8 + j] << j for j in range(8)])) for i in range(b//8)])
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return b''.join([
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int2byte(sum([bits[i * 8 + j] << j for j in range(8)]))
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for i in range(b//8)
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])
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def encodepoint(P):
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x = P[0]
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y = P[1]
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bits = [(y >> i) & 1 for i in range(b-1)] + [x & 1]
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return b''.join([int2byte(sum([bits[i * 8 + j] << j for j in range(8)])) for i in range(b//8)])
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(x, y, z, t) = P
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zi = inv(z)
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x = (x * zi) % q
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y = (y * zi) % q
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bits = [(y >> i) & 1 for i in range(b - 1)] + [x & 1]
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return b''.join([
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int2byte(sum([bits[i * 8 + j] << j for j in range(8)]))
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for i in range(b // 8)
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])
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def bit(h, i):
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return (indexbytes(h, i//8) >> (i%8)) & 1
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return (indexbytes(h, i // 8) >> (i % 8)) & 1
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def isoncurve(P):
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x = P[0]
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y = P[1]
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return (-x*x + y*y - 1 - d*x*x*y*y) % q == 0
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(x, y, z, t) = P
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return (z % q != 0 and
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x*y % q == z*t % q and
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(y*y - x*x - z*z - d*t*t) % q == 0)
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def decodeint(s):
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return sum(2**i * bit(s, i) for i in range(0, b))
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return sum(2 ** i * bit(s, i) for i in range(0, b))
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def decodepoint(s):
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y = sum(2**i * bit(s, i) for i in range(0, b-1))
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y = sum(2 ** i * bit(s, i) for i in range(0, b - 1))
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x = xrecover(y)
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if x & 1 != bit(s, b-1): x = q - x
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P = [x, y]
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if not isoncurve(P): raise Exception("decoding point that is not on curve")
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if x & 1 != bit(s, b-1):
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x = q - x
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P = (x, y, 1, (x*y) % q)
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if not isoncurve(P):
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raise ValueError("decoding point that is not on curve")
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return P
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# These are unused but let's keep them
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#def H(m):
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# return hashlib.sha512(m).digest()
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#
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#def Hint(m):
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# h = H(m)
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# return sum(2**i * bit(h, i) for i in range(2*b))
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#
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#def publickey(sk):
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# h = H(sk)
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# a = 2**(b-2) + sum(2**i * bit(h, i) for i in range(3, b-2))
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# A = scalarmult(B, a)
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# return encodepoint(A)
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#
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#def signature(m, sk, pk):
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# h = H(sk)
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# a = 2**(b-2) + sum(2**i * bit(h, i) for i in range(3, b-2))
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# r = Hint(intlist2bytes([indexbytes(h, j) for j in range(b//8, b//4)]) + m)
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# R = scalarmult(B, r)
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# S = (r + Hint(encodepoint(R)+pk+m) * a) % l
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# return encodepoint(R) + encodeint(S)
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#
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#def checkvalid(s, m, pk):
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# if len(s) != b//4: raise Exception("signature length is wrong")
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# if len(pk) != b//8: raise Exception("public-key length is wrong")
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# R = decodepoint(s[0:b//8])
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# A = decodepoint(pk)
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# S = decodeint(s[b//8:b//4])
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# h = Hint(encodepoint(R) + pk + m)
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# if scalarmult(B, S) != edwards(R, scalarmult(A, h)):
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# raise Exception("signature does not pass verification")
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def public_from_secret(k):
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keyInt = decodeint(k)
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aB = scalarmult(B, keyInt)
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aB = scalarmult_B(keyInt)
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return encodepoint(aB)
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def public_from_secret_hex(hk):
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return hexlify(public_from_secret(unhexlify(hk))).decode()
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return binascii.hexlify(public_from_secret(binascii.unhexlify(hk))).decode()
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@ -219,9 +219,9 @@ class Wallet(object):
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struct.pack('<I', major), struct.pack('<I', minor)])
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m = keccak_256(hsdata).digest()
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# D = master_psk + m * B
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D = ed25519.add_compressed(
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D = ed25519.edwards_add(
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ed25519.decodepoint(master_psk),
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ed25519.scalarmult(ed25519.B, ed25519.decodeint(m)))
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ed25519.scalarmult_B(ed25519.decodeint(m)))
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# C = master_svk * D
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C = ed25519.scalarmult(D, ed25519.decodeint(master_svk))
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netbyte = bytearray([
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