Topic: Calculate ‘X’ coordinates that share the same ‘Y’ (Read 125 times)

p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f

n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141

E = EllipticCurve(GF(p), [0, 7])

G = E.point( (0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798,0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8))   # Base point

## Input
y = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8

## Field parameters
# Field modulus
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
# Cube root of 1
beta = 60197513588986302554485582024885075108884032450952339817679072026166228089408
 
## Actual code
xcubed = (y*y - 7) % p
print ("xcubed = 0x%x" % xcubed)

x = pow(xcubed, (p + 2) / 9, p)
print ("x1 = 0x%x" % x)
print ("x2 = 0x%x" % (x * beta % p))
print ("x3 = 0x%x" % (x * beta * beta % p))
x1=x * beta % p
x2=(x * beta * beta % p)
P=E.point((x,y))
P2=E.point((x1,y))
P3=E.point((x2,y))

assert G*78074008874160198520644763525212887401909906723592317393988542598630163514318 == P
assert G*37718080363155996902926221483475020450927657555482586988616620542887997980018 == P2

## Input
y = 0x3199555CE45C38B856C9F64AC6DB27000AB6CEA10CAD76B2B6E246C9A020E707

## Field parameters
# Field modulus
p = 0xfffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f
# Cube root of 1
beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee

## Actual code
xcubed = (y*y - 7) % p
print ("xcubed = 0x%x" % xcubed)

x = pow(xcubed, (p + 2) / 9, p)
print ("x1 = 0x%x" % x)
print ("x2 = 0x%x" % (x * beta % p))
print ("x3 = 0x%x" % (x * beta * beta % p))

import ecdsa
from ecdsa.ellipticcurve import Point
from sympy import symbols, Eq, solve

target = "0379be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798"

if target.startswith("04"):
    Upub = target[2:]
    y_value = int(Upub[64:], 16)
elif target.startswith("02") or target.startswith("03"):
    x = int(target[2:], 16)
    curve = ecdsa.SECP256k1.curve
    y_square = (x**3 + curve.a() * x + curve.b()) % curve.p()
    y_value = pow(y_square, (curve.p() + 1) // 4, curve.p())
    if (target.startswith("03") and y_value % 2 == 0) or (target.startswith("02") and y_value % 2 != 0):
        y_value = curve.p() - y_value
    Upub = '04' + hex(x)[2:].zfill(64) + hex(y_value)[2:].zfill(64)
else:
    raise ValueError("null")

p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F 
beta = 0x7ae96a2b657c07106e64479eac3434e99cf0497512f58995c1396c28719501ee

xcubed = (y_value * y_value - 7) % p
print("xcubed = 0x%x" % xcubed)

x1 = pow(xcubed, (p + 2) // 9, p)
x2 = (x1 * beta) % p
x3 = (x2 * beta) % p

UncompressedPublicKey1 = '04' + hex(x1)[2:].zfill(64) + hex(y_value)[2:].zfill(64)
compressedPublicKey1 = ('02' if y_value % 2 == 0 else '03') + hex(x1)[2:].zfill(64)

UncompressedPublicKey2 = '04' + hex(x2)[2:].zfill(64) + hex(y_value)[2:].zfill(64)
compressedPublicKey2 = ('02' if y_value % 2 == 0 else '03') + hex(x2)[2:].zfill(64)

UncompressedPublicKey3 = '04' + hex(x3)[2:].zfill(64) + hex(y_value)[2:].zfill(64)
compressedPublicKey3 = ('02' if y_value % 2 == 0 else '03') + hex(x3)[2:].zfill(64)

print("point 1:")
print(f"Uncompressed: {UncompressedPublicKey1}")
print(f"Compressed: {compressedPublicKey1}\n")

print("point 2:")
print(f"Uncompressed: {UncompressedPublicKey2}")
print(f"Compressed: {compressedPublicKey2}\n")

print("point 3:")
print(f"Uncompressed: {UncompressedPublicKey3}")
print(f"Compressed: {compressedPublicKey3}")

cPub: 0379be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

X= 79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798

Y= b7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777

cPub: 0379be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
H160: adde4c73c7b9cee17da6c7b3e2b2eea1a0dcbe67
Addr: 1GrLCmVQXoyJXaPJQdqssNqwxvha1eUo2E

cPub: 03bcace2e99da01887ab0102b696902325872844067f15e98da7bba04400b88fcb

X= bcace2e99da01887ab0102b696902325872844067f15e98da7bba04400b88fcb 

Y= b7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777

cPub: 03bcace2e99da01887ab0102b696902325872844067f15e98da7bba04400b88fcb
H160: 516becf48ea6f02f20591504925d87bc62e9014f
Addr: 18RX2Lmi8cm2Bab8eABwyPgr9h8GSDjond

cPub: 03c994b69768832bcbff5e9ab39ae8d1d3763bbf1e531bed98fe51de5ee84f50fb

X= c994b69768832bcbff5e9ab39ae8d1d3763bbf1e531bed98fe51de5ee84f50fb

Y= b7c52588d95c3b9aa25b0403f1eef75702e84bb7597aabe663b82f6f04ef2777

cPub: 03c994b69768832bcbff5e9ab39ae8d1d3763bbf1e531bed98fe51de5ee84f50fb
H160: 9226f4f38f59b60ad6d41fd78c7dcadb40cf1515
Addr: 1EKnKn1b4vQF81CxpBb2v2QiUhrjJsA4RK

private_key = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364140


N = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
lambda_value = 0x5363ad4cc05c30e0a5261c028812645a122e22ea20816678df02967c1b23bd72
private_key_x2 = (private_key * pow(lambda_value , 1, N)) % N
private_key_x3 = (private_key * pow(lambda_value , 2, N)) % N

print("Private key x1: 0x%x" % private_key)
print("Private key x2: 0x%x" % private_key_x2)
print("Private key x3: 0x%x" % private_key_x3)