Topic: Pollard's kangaroo ECDLP solver - page 13. (Read 59389 times)

def shiftdown(pubkey, divisor, file, convert=True):
    Q = pub2point(pubkey) if convert else pubkey
    # k = 1/divisor
    k = pow(divisor, N - 2, N)
    R = Point.identity(curve=curve.secp256k1)
    for i in range(divisor):
        R += Q # Equivalent to subtracting (divisor - i) * G
        P = k * R
        if (P.y % 2 == 0):
            prefix = "02"
        else:
            prefix = "03"
        hx = hex(P.x)[2:].zfill(64)
        hy = hex(P.y)[2:].zfill(64)
        file.write(prefix+ " " + hx+"\n") # Writes compressed key to file
    file.write("\n") # Writes compressed key to file

from fastecdsa import curve
from fastecdsa.point import Point
import bit

G = curve.secp256k1.G
N = curve.secp256k1.q

def pub2point(pub_hex):
    x = int(pub_hex[2:66], 16)
    if len(pub_hex) < 70:
        y = bit.format.x_to_y(x, int(pub_hex[:2], 16) % 2)
    else:
        y = int(pub_hex[66:], 16)
    return Point(x, y, curve=curve.secp256k1)

# This function makes all the downscaled pubkeys obtained from subtracting
# numbers between 0 and divisor, before dividing the pubkeys by divisor.
def shiftdown(pubkey, divisor, file, convert=True):
    Q = pub2point(pubkey) if convert else pubkey
    # k = 1/divisor
    k = pow(divisor, N - 2, N)
    for i in range(divisor):
        P = Q - (i * G)
        P = k * P
        if (P.y % 2 == 0):
            prefix = "02"
        else:
            prefix = "03"
        hx = hex(P.x)[2:].zfill(64)
        hy = hex(P.y)[2:].zfill(64)
        file.write(prefix+ " " + hx+"\n") # Writes compressed key to file
    file.write("\n") # Writes compressed key to file

with open("input.txt", "r") as f, open("output.txt", "w") as outf:
    line = f.readline().strip()
    while line != '':
        outf.write("original: " +line + "\n")
        shiftdown(line, pow(2,1), outf)
        line = f.readline().strip()

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022f8bde4d1a07209355b4a7250a5c5128e88b84bddc619ab7cba8d569b240efe4