zcash-test-vectors/orchard_sinsemilla.py

#!/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 binascii import hexlify
from bitstring import BitArray

# 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=64, 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=64, 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 * 1 * 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):
    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)

    tv1 = Z * u.exp(2)
    tv2 = tv1.exp(2)
    x1 = tv1 + tv2

    x1 = x1.inv()
    e1 = x1 == Fp(0)
    x1 = x1 + Fp(1)

    if e1:
        x1 = c2
    else:
        x1 = x1

    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
    y2 = gx1 if e2 else gx2  # If is_square(gx1), y2 = gx1, else y2 = gx2
    y = y2.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]), map_to_curve_simple_swu(elems[1]) ]

    return (q[0] + q[1]).iso_map()

SINSEMILLA_K = 10

def pad(n, m):
    padding_needed = n * SINSEMILLA_K - m.len
    zeros = BitArray(bin='0' * padding_needed)
    m = m + zeros

    pieces = []
    for i in range(n):
        pieces.append(
            lebs2ip(m[i*SINSEMILLA_K : (i+1)*SINSEMILLA_K])
        )

    return pieces

def sinsemilla_hash_to_point(d, m):
    assert isinstance(m, BitArray)
    n = cldiv(m.len, SINSEMILLA_K)
    m = pad(n, m)
    acc = group_hash(b"z.cash:SinsemillaQ", d)
    #print("acc", acc)

    for m_i in m:
        acc = acc + group_hash(b"z.cash:SinsemillaS", i2leosp(32, m_i)) + acc
        #print("acc", acc)

    return acc

def sinsemilla_hash(d, m):
    return sinsemilla_hash_to_point(d, m).extract()

def sinsemilla_hash_bytes(d, m_bytes):
    assert isinstance(m_bytes, bytes)
    return sinsemilla_hash(d, BitArray(m_bytes))

if __name__ == "__main__":
    # This is the Pallas test vector from the Sage and Rust code (in affine coordinates).
    gh = group_hash(b"z.cash:test", b"Trans rights now!")
    assert gh == Point(Fp(10899331951394555178876036573383466686793225972744812919361819919497009261523),
                       Fp(851679174277466283220362715537906858808436854303373129825287392516025427980))

    # 40 bits, so no padding
    sh = sinsemilla_hash_to_point(b"z.cash:test-Sinsemilla", BitArray(bin='0001011010100110001101100011011011110110'))
    assert sh == Point(Fp(19681977528872088480295086998934490146368213853811658798708435106473481753752),
                       Fp(14670850419772526047574141291705097968771694788047376346841674072293161339903))