Skip to main content

Klefki is a playground for researching elliptic curve group based algorithms & applications, such as MPC, HE, ZKP, and Bitcoin/Ethereum. All data types & structures are based on mathematical defination of abstract algebra.

Project description

Klefki

travis Maintenance PyPI version klefki PyPI license PyPI status Generic badge

klefki


Klefki (Japanese: クレッフィ Cleffy) is a dual-type Steel/Fairy Pokémon introduced in Generation VI. It is not known to evolve into or from any other Pokémon.


TL; DR

Klefki is a playground for researching elliptic curve group based algorithms & applications, such as MPC, HE, ZKP, and Bitcoin/Ethereum. All data types & structures are based on mathematical defination of abstract algebra.

Check the Document

Try it!

For Installation (require python>=3.6):

pip3 install klefki

klefki shell

Have Fun!!!!

Elliptic Curve Group Example

  • Test pairing
from klefki.curves.barreto_naehrig import bn128

G1 = bn128.ECGBN128.G1
G2 = bn128.ECGBN128.G2
G = G1
e = bn128.ECGBN128.e

one = bn128.BN128FP12.one()
p1 = e(G2, G1)
p2 = e(G2, G1 @ 2)
assert p1 * p1 == p2
  • Create Custom Groups
import klefki.const as const
from klefki.algebra.fields import FiniteField
from klefki.algebra.groups import EllipticCurveGroup
from klefki.algebra.groups import EllipicCyclicSubgroup
from klefki.curves.arith import short_weierstrass_form_curve_addition2


class FiniteFieldSecp256k1(FiniteField):
    P = const.SECP256K1_P


class FiniteFieldCyclicSecp256k1(FiniteField):
    P = const.SECP256K1_N


class EllipticCurveGroupSecp256k1(EllipticCurveGroup):
    """
    y^2 = x^3 + A * x + B
    """

    N = const.SECP256K1_N
    A = const.SECP256K1_A
    B = const.SECP256K1_B

    def op(self, g):
        field = self.id[0].__class__
        x, y = short_weierstrass_form_curve_addition2(
            self.x, self.y,
            g.x, g.y,
            field.zero(),
            field.zero(),
            field.zero(),
            field(self.A),
            field(self.B),
            field
        )
        if x == y == field(0):
            return self.__class__(0)
        return self.__class__((x, y))

ZKP Examples

  • Play with r1cs
from klefki.zkp.r1cs import R1CS
from functools import partial



@R1CS.r1cs
def t(x):
    y = x**3
    return y + x + 5


s = t.witness(3)
assert R1CS.verify(s, *t.r1cs)
assert s[2] == t(3)

MPC Examples (SSSS/VSS)

from klefki.crypto.ssss import SSSS
from klefki.const import SECP256K1_P as P
from klefki.algebra.utils import randfield
from klefki.algebra.meta import field
import random


def test_ssss():
    F = field(P)
    s = SSSS(F)
    k = random.randint(1, 100)
    n = k * 3
    secret = randfield(F)

    s.setup(secret, k, n)

    assert s.decrypt([s.join() for _ in range(k-1)]) != secret
    assert s.decrypt([s.join() for _ in range(k+1)]) == secret
    assert s.decrypt([s.join() for _ in range(k+2)]) == secret

PubKey/PrivKey Examples

With AAT(Abstract Algebra Type) you can easily implement the bitcoin priv/pub key and sign/verify algorithms like this:

import random
from klefki.utils import to_sha256int
from klefki.algebra.concrete import (
    JacobianGroupSecp256k1 as JG,
    EllipticCurveCyclicSubgroupSecp256k1 as CG,
    EllipticCurveGroupSecp256k1 as ECG,
    FiniteFieldCyclicSecp256k1 as CF
)


N = CG.N
G = CG.G


def random_privkey() -> CF:
    return CF(random.randint(1, N))


def pubkey(priv: CF) -> ECG:
    return ECG(JG(G @ priv))


def sign(priv: CF, m: str) -> tuple:
    k = CF(random.randint(1, N))
    z = CF(to_sha256int(m))
    r = CF((G @ k).value[0])  # From Secp256k1Field to CyclicSecp256k1Field
    s = z / k + priv * r / k
    return r, s



def verify(pub: ECG, sig: tuple, mhash: int):
    r, s = sig
    z = CF(mhash)
    u1 = z / s
    u2 = r / s
    rp = G @ u1 + pub @ u2
    return r == rp.value[0]

Even proof the Sign/Verify algorithm mathematically.

def proof():
    priv = random_privkey()
    m = 'test'
    k = CF(random_privkey())
    z = CF(to_sha256int(m))
    r = CF((G @ k).value[0])
    s = z / k + priv * r / k

    assert k == z / s + priv * r / s
    assert G @ k == G @ (z / s + priv * r / s)
    assert G @ k == G @ (z / s) + G @ priv @ (r / s)

    pub = G @ priv
    assert pub == pubkey(priv)
    assert G @ k == G @ (z / s) + pub @ (r / s)
    u1 = z / s
    u2 = r / s
    assert G @ k == G @ u1 + pub @ u2

Or transform your Bitcoin Private Key to EOS Private/Pub key (or back)

from klefki.bitcoin.private import decode_privkey
from klefki.eos.public import gen_pub_key
from klefki.eos.private import encode_privkey


def test_to_eos(priv):
    key = decode_privkey(priv)
    eos_priv = encode_privkey(key)
    eos_pub = gen_pub_key(key)
    print(eos_priv, eos_pub)

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Files for klefki, version 1.7.1
Filename, size File type Python version Upload date Hashes
Filename, size klefki-1.7.1-py3-none-any.whl (85.3 kB) File type Wheel Python version py3 Upload date Hashes View

Supported by

AWS AWS Cloud computing Datadog Datadog Monitoring DigiCert DigiCert EV certificate Facebook / Instagram Facebook / Instagram PSF Sponsor Fastly Fastly CDN Google Google Object Storage and Download Analytics Microsoft Microsoft PSF Sponsor Pingdom Pingdom Monitoring Salesforce Salesforce PSF Sponsor Sentry Sentry Error logging StatusPage StatusPage Status page