Merge pull request #17 from zcash-hackworks/sinsemilla-test-vectors

Add iso-Pallas, SWU hash-to-curve, and Sinsemilla
This commit is contained in:
str4d 2021-04-29 02:20:39 +01:00 committed by GitHub
commit 0cc31479cf
No known key found for this signature in database
GPG Key ID: 4AEE18F83AFDEB23
10 changed files with 570 additions and 13 deletions

185
orchard_group_hash.py Normal file
View File

@ -0,0 +1,185 @@
#!/usr/bin/env python3
import sys; assert sys.version_info[0] >= 3, "Python 3 required."
import math
import orchard_iso_pallas
from pyblake2 import blake2b
from orchard_pallas import Fp, p, q, PALLAS_B, Point
from orchard_iso_pallas import PALLAS_ISO_B, PALLAS_ISO_A
from sapling_utils import i2beosp, cldiv, beos2ip, i2leosp, lebs2ip
from tv_output import render_args, render_tv
from tv_rand import Rand
# https://stackoverflow.com/questions/2612720/how-to-do-bitwise-exclusive-or-of-two-strings-in-python
def sxor(s1,s2):
return bytes([a ^ b for a,b in zip(s1,s2)])
def expand_message_xmd(msg, dst, len_in_bytes):
assert len(dst) <= 255
b_in_bytes = 64 # hash function output size
r_in_bytes = 128
ell = cldiv(len_in_bytes, b_in_bytes)
assert ell <= 255
dst_prime = dst + i2beosp(8, len(dst))
z_pad = b"\x00" * r_in_bytes
l_i_b_str = i2beosp(16, len_in_bytes)
msg_prime = z_pad + msg + l_i_b_str + i2beosp(8, 0) + dst_prime
b = []
b0_ctx = blake2b(digest_size=b_in_bytes, person=i2beosp(128,0))
b0_ctx.update(msg_prime)
b.append(b0_ctx.digest())
assert len(b[0]) == b_in_bytes
b1_ctx = blake2b(digest_size=b_in_bytes, person=i2beosp(128,0))
b1_ctx.update(b[0] + i2beosp(8, 1) + dst_prime)
b.append(b1_ctx.digest())
assert len(b[1]) == b_in_bytes
for i in range(2, ell + 1):
bi_input = sxor(b[0], b[i-1])
assert len(bi_input) == b_in_bytes
bi_input += i2beosp(8, i) + dst_prime
bi_ctx = blake2b(digest_size=b_in_bytes, person=i2beosp(128,0))
bi_ctx.update(bi_input)
b.append(bi_ctx.digest())
assert len(b[i]) == b_in_bytes
return b''.join(b[1:])[0:len_in_bytes]
def hash_to_field(msg, dst):
k = 256
count = 2
m = 1
L = cldiv(math.ceil(math.log2(p)) + k, 8)
assert L == 512/8
len_in_bytes = count * m * L
uniform_bytes = expand_message_xmd(msg, dst, len_in_bytes)
elements = []
for i in range(0, count):
for j in range(0, m):
elm_offset = L * (j + i * m)
tv = uniform_bytes[elm_offset:elm_offset+L]
elements.append(Fp(beos2ip(tv), False))
assert len(elements) == count
return elements
def map_to_curve_simple_swu(u):
# The notation below follows Appendix F.2 of the Internet Draft
zero = Fp(0)
assert zero.inv() == Fp(0)
A = PALLAS_ISO_A
B = PALLAS_ISO_B
Z = Fp(-13, False)
c1 = -B / A
c2 = Fp(-1) / Z
tv1 = Z * u.exp(2)
tv2 = tv1.exp(2)
x1 = tv1 + tv2
x1 = x1.inv()
e1 = x1 == Fp(0)
x1 = x1 + Fp(1)
x1 = c2 if e1 else x1 # If (tv1 + tv2) == 0, set x1 = -1 / Z
x1 = x1 * c1 # x1 = (-B / A) * (1 + (1 / (Z^2 * u^4 + Z * u^2)))
gx1 = x1.exp(2)
gx1 = gx1 + A
gx1 = gx1 * x1
gx1 = gx1 + B # gx1 = g(x1) = x1^3 + A * x1 + B
x2 = tv1 * x1 # x2 = Z * u^2 * x1
tv2 = tv1 * tv2
gx2 = gx1 * tv2 # gx2 = (Z * u^2)^3 * gx1
e2 = (gx1.sqrt() is not None)
x = x1 if e2 else x2 # If is_square(gx1), x = x1, else x = x2
yy = gx1 if e2 else gx2 # If is_square(gx1), yy = gx1, else yy = gx2
y = yy.sqrt()
e3 = u.sgn0() == y.sgn0()
y = y if e3 else -y #y = CMOV(-y, y, e3)
return orchard_iso_pallas.Point(x, y)
def group_hash(d, m):
dst = d + b"-" + b"pallas" + b"_XMD:BLAKE2b_SSWU_RO_"
elems = hash_to_field(m, dst)
assert len(elems) == 2
q = [map_to_curve_simple_swu(elems[0]).iso_map(), map_to_curve_simple_swu(elems[1]).iso_map()]
return q[0] + q[1]
def main():
fixed_test_vectors = [
# This is the Pallas test vector from the Sage and Rust code (in affine coordinates).
(b"z.cash:test", b"Trans rights now!", Point(Fp(10899331951394555178876036573383466686793225972744812919361819919497009261523),
Fp(851679174277466283220362715537906858808436854303373129825287392516025427980))),
]
for (domain, msg, point) in fixed_test_vectors:
gh = group_hash(domain, msg)
assert gh == point
test_vectors = [(domain, msg) for (domain, msg, _) in fixed_test_vectors]
from random import Random
rng = Random(0xabad533d)
def randbytes(l):
ret = []
while len(ret) < l:
ret.append(rng.randrange(0, 256))
return bytes(ret)
rand = Rand(randbytes)
# Generate test vectors with the following properties:
# - One of two domains.
# - Random message lengths between 0 and 255 bytes.
# - Random message contents.
for _ in range(10):
domain = b"z.cash:test-longer" if rand.bool() else b"z.cash:test"
msg_len = rand.u8()
msg = bytes([rand.u8() for _ in range(msg_len)])
test_vectors.append((domain, msg))
render_tv(
render_args(),
'orchard_group_hash',
(
('domain', 'Vec<u8>'),
('msg', 'Vec<u8>'),
('point', '[u8; 32]'),
),
[{
'domain': domain,
'msg': msg,
'point': bytes(group_hash(domain, msg)),
} for (domain, msg) in test_vectors],
)
if __name__ == "__main__":
main()

180
orchard_iso_pallas.py Executable file
View File

@ -0,0 +1,180 @@
#!/usr/bin/env python3
# -*- coding: utf8 -*-
import sys; assert sys.version_info[0] >= 3, "Python 3 required."
import orchard_pallas
from orchard_pallas import Fp, p, q, Scalar
#
# Point arithmetic
#
PALLAS_ISO_B = Fp(1265)
PALLAS_ISO_A = Fp(0x18354a2eb0ea8c9c49be2d7258370742b74134581a27a59f92bb4b0b657a014b)
class Point(object):
@staticmethod
def from_bytes(buf):
assert len(buf) == 32
if buf == bytes([0]*32):
return Point.identity()
y_sign = buf[31] >> 7
buf = buf[:31] + bytes([buf[31] & 0b01111111])
try:
x = Fp.from_bytes(buf)
except ValueError:
return None
x3 = x * x * x
y2 = x3 + PALLAS_ISO_A * x + PALLAS_ISO_B
y = y2.sqrt()
if y is None:
return None
if y.s % 2 != y_sign:
y = -y
return Point(x, y)
# Maps a point on iso-Pallas to a point on Pallas
def iso_map(self):
c = [
None, # make the indices 1-based
Fp(0x0e38e38e38e38e38e38e38e38e38e38e4081775473d8375b775f6034aaaaaaab),
Fp(0x3509afd51872d88e267c7ffa51cf412a0f93b82ee4b994958cf863b02814fb76),
Fp(0x17329b9ec525375398c7d7ac3d98fd13380af066cfeb6d690eb64faef37ea4f7),
Fp(0x1c71c71c71c71c71c71c71c71c71c71c8102eea8e7b06eb6eebec06955555580),
Fp(0x1d572e7ddc099cff5a607fcce0494a799c434ac1c96b6980c47f2ab668bcd71f),
Fp(0x325669becaecd5d11d13bf2a7f22b105b4abf9fb9a1fc81c2aa3af1eae5b6604),
Fp(0x1a12f684bda12f684bda12f684bda12f7642b01ad461bad25ad985b5e38e38e4),
Fp(0x1a84d7ea8c396c47133e3ffd28e7a09507c9dc17725cca4ac67c31d8140a7dbb),
Fp(0x3fb98ff0d2ddcadd303216cce1db9ff11765e924f745937802e2be87d225b234),
Fp(0x025ed097b425ed097b425ed097b425ed0ac03e8e134eb3e493e53ab371c71c4f),
Fp(0x0c02c5bcca0e6b7f0790bfb3506defb65941a3a4a97aa1b35a28279b1d1b42ae),
Fp(0x17033d3c60c68173573b3d7f7d681310d976bbfabbc5661d4d90ab820b12320a),
Fp(0x40000000000000000000000000000000224698fc094cf91b992d30ecfffffde5)
]
if self == Point.identity():
return orchard_pallas.identity()
else:
numerator_a = c[1] * self.x * self.x * self.x + c[2] * self.x * self.x + c[3] * self.x + c[4]
denominator_a = self.x * self.x + c[5] * self.x + c[6]
numerator_b = (c[7] * self.x * self.x * self.x + c[8] * self.x * self.x + c[9] * self.x + c[10]) * self.y
denominator_b = self.x * self.x * self.x + c[11] * self.x * self.x + c[12] * self.x + c[13]
return orchard_pallas.Point(numerator_a / denominator_a, numerator_b / denominator_b)
def __init__(self, x, y, is_identity=False):
self.x = x
self.y = y
self.is_identity = is_identity
if is_identity:
assert self.x == Fp.ZERO
assert self.y == Fp.ZERO
else:
assert self.y * self.y == self.x * self.x * self.x + PALLAS_ISO_A * self.x + PALLAS_ISO_B
def identity():
p = Point(Fp.ZERO, Fp.ZERO, True)
return p
def __neg__(self):
if self.is_identity:
return self
else:
return Point(Fp(self.x.s), -Fp(self.y.s))
def __add__(self, a):
if self.is_identity:
return a
elif a.is_identity:
return self
else:
# Hüseyin Hışıl. “Elliptic Curves, Group Law, and Efficient Computation”. PhD thesis.
# <https://core.ac.uk/download/pdf/10898289.pdf> section 4.1
(x1, y1) = (self.x, self.y)
(x2, y2) = (a.x, a.y)
if x1 == x2:
if (y1 != y2) or (y1 == Fp(0)):
return Point.identity()
else:
return self.double()
else:
λ = (y1 - y2) / (x1 - x2)
x3 = λ*λ - x1 - x2
y3 = λ*(x1 - x3) - y1
return Point(x3, y3)
def __sub__(self, a):
return (-a) + self
def double(self):
if self.is_identity:
return self
# Hüseyin Hışıl. “Elliptic Curves, Group Law, and Efficient Computation”. PhD thesis.
# <https://core.ac.uk/download/pdf/10898289.pdf> section 4.1
λ = (Fp(3) * self.x * self.x + PALLAS_ISO_A) / (self.y + self.y)
x3 = λ*λ - self.x - self.x
y3 = λ*(self.x - x3) - self.y
return Point(x3, y3)
def __mul__(self, s):
s = format(s.s, '0256b')
ret = self.ZERO
for c in s:
ret = ret.double()
if int(c):
ret = ret + self
return ret
def __bytes__(self):
if self.is_identity:
return bytes([0] * 32)
buf = bytes(self.x)
if self.y.s % 2 == 1:
buf = buf[:31] + bytes([buf[31] | (1 << 7)])
return buf
def __eq__(self, a):
if a is None:
return False
if not (self.is_identity or a.is_identity):
return self.x == a.x and self.y == a.y
else:
return self.is_identity == a.is_identity
def __str__(self):
if self.is_identity:
return 'Point(identity)'
else:
return 'Point(%s, %s)' % (self.x, self.y)
Point.ZERO = Point.identity()
# This is an arbitrarily-chosen generator for testing purposes only, NOT a
# formally-selected common generator for iso-Pallas.
x = Fp(2)
y2 = x * x * x + PALLAS_ISO_A * x + PALLAS_ISO_B
y = y2.sqrt()
assert y is not None
Point.GENERATOR = Point(x, y)
assert Point.ZERO + Point.ZERO == Point.ZERO
assert Point.GENERATOR - Point.GENERATOR == Point.ZERO
assert Point.GENERATOR + Point.GENERATOR + Point.GENERATOR == Point.GENERATOR * Scalar(3)
assert Point.GENERATOR + Point.GENERATOR - Point.GENERATOR == Point.GENERATOR
assert Point.from_bytes(bytes([0]*32)) == Point.ZERO
assert Point.from_bytes(bytes(Point.GENERATOR)) == Point.GENERATOR

56
orchard_map_to_curve.py Executable file
View File

@ -0,0 +1,56 @@
#!/usr/bin/env python3
from orchard_group_hash import map_to_curve_simple_swu
from orchard_iso_pallas import Point as IsoPoint
from orchard_pallas import Fp
from sapling_utils import leos2ip
from tv_output import render_args, render_tv
from tv_rand import Rand
def main():
fixed_test_vectors = [
(Fp(0), IsoPoint(Fp(19938918781445865934736160264407396416050199005817793816893455093350997047296),
Fp(1448774895934493446148762800986014913165975534940595774801697325542407056356))),
(Fp(1), IsoPoint(Fp(5290181550357368025040301950220623271393946308300025648720253222947454165280),
Fp(24520995241805476578231005891941079870703368870355132644748659103632565232759))),
(Fp(0x123456789abcdef123456789abcdef123456789abcdef123456789abcdef0123),
IsoPoint(Fp(16711718778908753690082328243251803703269853000652055785581237369882690082595),
Fp(1764705856161931038824461929646873031992914829456409784642560948827969833589))),
]
for (u, point) in fixed_test_vectors:
P = map_to_curve_simple_swu(u)
assert P == point
test_vectors = [u for (u, _) in fixed_test_vectors]
from random import Random
rng = Random(0xabad533d)
def randbytes(l):
ret = []
while len(ret) < l:
ret.append(rng.randrange(0, 256))
return bytes(ret)
rand = Rand(randbytes)
# Generate random test vectors
for _ in range(10):
test_vectors.append(Fp(leos2ip(rand.b(32))))
render_tv(
render_args(),
'orchard_map_to_curve',
(
('u', '[u8; 32]'),
('point', '[u8; 32]'),
),
[{
'u': bytes(u),
'point': bytes(map_to_curve_simple_swu(u)),
} for u in test_vectors],
)
if __name__ == "__main__":
main()

View File

@ -37,6 +37,10 @@ class Fp(FieldElement):
def __str__(self):
return 'Fp(%s)' % self.s
def sgn0(self):
# https://tools.ietf.org/html/draft-irtf-cfrg-hash-to-curve-10#section-4.1
return (self.s % 2) == 1
def sqrt(self):
# Tonelli-Shank's algorithm for p mod 16 = 1
# https://eprint.iacr.org/2012/685.pdf (page 12, algorithm 5)
@ -138,14 +142,19 @@ class Point(object):
return Point(x, y)
def __init__(self, x, y):
def __init__(self, x, y, is_identity=False):
self.x = x
self.y = y
self.is_identity = False
self.is_identity = is_identity
if is_identity:
assert self.x == Fp.ZERO
assert self.y == Fp.ZERO
else:
assert self.y * self.y == self.x * self.x * self.x + PALLAS_B
def identity():
p = Point(Fp.ZERO, Fp.ZERO)
p.is_identity = True
p = Point(Fp.ZERO, Fp.ZERO, True)
return p
def __neg__(self):
@ -174,6 +183,13 @@ class Point(object):
else:
return self.double()
def checked_incomplete_add(self, a):
assert self != a
assert self != -a
assert self != Point.identity()
assert a != Point.identity()
return self + a
def __sub__(self, a):
return (-a) + self
@ -186,6 +202,11 @@ class Point(object):
x = λ*λ - self.x - self.x
y = λ*(self.x - x) - self.y
return Point(x, y)
def extract(self):
if self.is_identity:
return Fp.ZERO
return self.x
def __mul__(self, s):
s = format(s.s, '0256b')

99
orchard_sinsemilla.py Executable file
View File

@ -0,0 +1,99 @@
#!/usr/bin/env python3
import sys; assert sys.version_info[0] >= 3, "Python 3 required."
import math
import orchard_iso_pallas
from orchard_pallas import Fp, Point
from sapling_utils import cldiv, lebs2ip, i2leosp
from orchard_group_hash import group_hash
from tv_output import render_args, render_tv
from tv_rand import Rand
SINSEMILLA_K = 10
# Interprets a string or a list as a sequence of bits.
def str_to_bits(s):
for c in s:
assert c in ['0', '1', 0, 1, False, True]
# Regular Python truthiness is fine here except for bool('0') == True.
return [c != '0' and bool(c) for c in s]
def pad(n, m):
padding_needed = n * SINSEMILLA_K - len(m)
zeros = [0] * padding_needed
m = list(m) + zeros
return [lebs2ip(str_to_bits(m[i*SINSEMILLA_K : (i+1)*SINSEMILLA_K])) for i in range(n)]
def sinsemilla_hash_to_point(d, m):
n = cldiv(len(m), SINSEMILLA_K)
m = pad(n, m)
acc = group_hash(b"z.cash:SinsemillaQ", d)
for m_i in m:
acc = acc.checked_incomplete_add(
group_hash(b"z.cash:SinsemillaS", i2leosp(32, m_i))
).checked_incomplete_add(acc)
return acc
def sinsemilla_hash(d, m):
return sinsemilla_hash_to_point(d, m).extract()
def main():
test_vectors = [
# 40 bits, so no padding
(b"z.cash:test-Sinsemilla", [0,0,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0,1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,1,1,0,1,1,0]),
]
sh = sinsemilla_hash_to_point(test_vectors[0][0], test_vectors[0][1])
assert sh == Point(Fp(19681977528872088480295086998934490146368213853811658798708435106473481753752),
Fp(14670850419772526047574141291705097968771694788047376346841674072293161339903))
from random import Random
rng = Random(0xabad533d)
def randbytes(l):
ret = []
while len(ret) < l:
ret.append(rng.randrange(0, 256))
return bytes(ret)
rand = Rand(randbytes)
# Generate test vectors with the following properties:
# - One of two domains.
# - Random message lengths between 0 and 255 bytes.
# - Random message bits.
for _ in range(10):
domain = b"z.cash:test-Sinsemilla-longer" if rand.bool() else b"z.cash:test-Sinsemilla"
msg_len = rand.u8()
msg = bytes([rand.bool() for _ in range(msg_len)])
test_vectors.append((domain, msg))
test_vectors = [{
'domain': domain,
'msg': msg,
'point': bytes(sinsemilla_hash_to_point(domain, msg)),
'hash': bytes(sinsemilla_hash(domain, msg)),
} for (domain, msg) in test_vectors]
render_tv(
render_args(),
'orchard_sinsemilla',
(
('domain', 'Vec<u8>'),
('msg', {
'rust_type': 'Vec<bool>',
'rust_fmt': lambda x: str_to_bits(x),
}),
('point', '[u8; 32]'),
('hash', '[u8; 32]'),
),
test_vectors,
)
if __name__ == "__main__":
main()

View File

@ -155,7 +155,7 @@ RAND_OPCODES = [
class Script(object):
def __init__(self, rand):
self._script = bytes([
rand.a(RAND_OPCODES) for i in range(rand.u8() % 10)
rand.a(RAND_OPCODES) for i in range(rand.i8() % 10)
])
def raw(self):
@ -212,11 +212,11 @@ class Transaction(object):
self.nVersion = rand.u32() & ((1 << 31) - 1)
self.vin = []
for i in range(rand.u8() % 3):
for i in range(rand.i8() % 3):
self.vin.append(TxIn(rand))
self.vout = []
for i in range(rand.u8() % 3):
for i in range(rand.i8() % 3):
self.vout.append(TxOut(rand))
self.nLockTime = rand.u32()
@ -227,14 +227,14 @@ class Transaction(object):
self.vShieldedSpends = []
self.vShieldedOutputs = []
if self.nVersion >= SAPLING_TX_VERSION:
for _ in range(rand.u8() % 5):
for _ in range(rand.i8() % 5):
self.vShieldedSpends.append(SpendDescription(rand))
for _ in range(rand.u8() % 5):
for _ in range(rand.i8() % 5):
self.vShieldedOutputs.append(OutputDescription(rand))
self.vJoinSplit = []
if self.nVersion >= 2:
for i in range(rand.u8() % 3):
for i in range(rand.i8() % 3):
self.vJoinSplit.append(JoinSplit(rand, self.fOverwintered and self.nVersion >= SAPLING_TX_VERSION))
if len(self.vJoinSplit) > 0:
self.joinSplitPubKey = rand.b(32) # Potentially invalid

View File

@ -75,6 +75,17 @@ def tv_vec_bytes_rust(name, value, pad):
pad,
))
def tv_vec_bool_rust(name, value, pad):
print('''%s%s: vec![
%s%s
%s],''' % (
pad,
name,
pad,
', '.join(['true' if x else 'false' for x in value]),
pad,
))
def tv_option_bytes_rust(name, value, pad):
if value:
print('''%s%s: Some([
@ -121,6 +132,8 @@ def tv_part_rust(name, value, config, indent=3):
tv_option_vec_bytes_rust(name, value, pad)
elif config['rust_type'] == 'Vec<u8>':
tv_vec_bytes_rust(name, value, pad)
elif config['rust_type'] == 'Vec<bool>':
tv_vec_bool_rust(name, value, pad)
elif config['rust_type'].startswith('Option<['):
tv_option_bytes_rust(name, value, pad)
elif type(value) == bytes:

View File

@ -12,9 +12,12 @@ class Rand(object):
def v(self, l, f):
return struct.unpack(f, self.b(l))[0]
def u8(self):
def i8(self):
return self.v(1, 'b')
def u8(self):
return self.v(1, 'B')
def u32(self):
return self.v(4, '<I')

View File

@ -113,7 +113,7 @@ def main():
for i in range(10):
tx = Transaction(rand, OVERWINTER_TX_VERSION)
scriptCode = Script(rand)
nIn = rand.u8() % (len(tx.vin) + 1)
nIn = rand.i8() % (len(tx.vin) + 1)
if nIn == len(tx.vin):
nIn = NOT_AN_INPUT
nHashType = SIGHASH_ALL if nIn == NOT_AN_INPUT else rand.a([

View File

@ -120,7 +120,7 @@ def main():
for _ in range(10):
tx = Transaction(rand, SAPLING_TX_VERSION)
scriptCode = Script(rand)
nIn = rand.u8() % (len(tx.vin) + 1)
nIn = rand.i8() % (len(tx.vin) + 1)
if nIn == len(tx.vin):
nIn = NOT_AN_INPUT
nHashType = SIGHASH_ALL if nIn == NOT_AN_INPUT else rand.a([