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Update elliptic.nim #103

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c201549
Update elliptic.nim
planetis-m Apr 3, 2022
cb951e2
drop 'bi, use more consts
planetis-m Apr 3, 2022
29c83be
fix compilation
planetis-m Apr 9, 2022
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42 changes: 23 additions & 19 deletions examples/elliptic.nim
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Original file line number Diff line number Diff line change
@@ -1,17 +1,18 @@
# By Cyther606: https://forum.nim-lang.org/t/522
# Adapted from: https://github.com/wobine/blackboard101/blob/master/EllipticCurvesPart4-PrivateKeyToPublicKey.py
import bigints
import std/[math, strutils]
import std/[math, strformat]

const
one = 1.initBigInt
two = 2.initBigInt
three = 3.initBigInt
zero = 0.initBigInt

proc `^`(base: int; exp: int): BigInt = pow(base.initBigInt, exp)

# Specs of the Bitcoin's curve - secp256k1
let
const
primeCurve: BigInt = 2^256 - 2^32 - 2^9 - 2^8 - 2^7 - 2^6 - 2^4 - one
numberPoints = initBigInt("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", 16)
Acurve = zero # with Bcurve = 7, coefficients in the elliptic curve equation y^2 = x^3 + Acurve * x + Bcurve
Expand All @@ -29,8 +30,8 @@ proc ecAdd(a: tuple, b: tuple): (BigInt, BigInt) =

proc ecDouble(a: tuple): (BigInt, BigInt) =
var
lam = ((3.initBigInt * a[0] * a[0] + Acurve) * invmod(2.initBigInt * a[1], primeCurve))
x = ((lam * lam) - (2.initBigInt * a[0])) mod primeCurve
lam = (three * a[0] * a[0] + Acurve) * invmod(two * a[1], primeCurve)
x = ((lam * lam) - (two * a[0])) mod primeCurve
y = (lam * (a[0] - x) - a[1]) mod primeCurve
lam = lam mod primeCurve
result = (x, y)
Expand All @@ -49,21 +50,24 @@ proc ecMultiply(genPoint: tuple, scalarHex: BigInt): (BigInt, BigInt) =

proc main() =
let publicKey = ecMultiply(Gpoint, privKey)
let officialKey =
if publicKey[1] mod two == one: "03" & publicKey[0].toString(base = 16)
else: "02" & publicKey[0].toString(base = 16)

echo &"""
******* Public Key Generation *********

the private key:
{privKey}

the uncompressed public key (not address):
{publicKey}

the uncompressed public key (HEX):
04{publicKey[0].toString(base = 16):0>64}{publicKey[1].toString(base = 16):0>64}

echo ""
echo "******* Public Key Generation *********"
echo ""
echo "the private key: "
echo privKey
echo ""
echo "the uncompressed public key (not address):"
echo publicKey
echo ""
echo "the uncompressed public key (HEX):"
echo "04", publicKey[0].toString(base = 16).align(64, '0'), publicKey[1].toString(base = 16).align(64, '0')
echo ""
echo "the official Public Key - compressed:"
echo if publicKey[1] mod two == one: "03" & publicKey[0].toString(base = 16).align(64, '0')
else: "02" & publicKey[0].toString(base = 16).align(64, '0')
the official Public Key - compressed:
{officialKey:0>64}
"""

main()