LightECC

LightECC is a lightweight elliptic curve cryptography library for its arithmetic for python. It is a hybrid library wrapping many elliptic curve forms such as Weierstrass, Koblitz and Edwards, and many pre-defined curves for those forms. LightECC simplifies these arithmetic operations. You don't need to understand the underlying principles forms. Once you define an elliptic curve in a given form, you can perform addition, subtraction, multiplication, and division of points using standard operators.

Installation

The easiest way to install the LightECC package is to install it from python package index (PyPI).

pip install lightecc

Then you will be able to import the library and use its functionalities.

from lightecc import LightECC

Elliptic Curve Arithmetic

Building an elliptic curve cryptosystem is very straightforward in LightECC. You basically need to initialize a LightECC object with a form name and a curve name. By default, it constructs elliptic curves in Weierstras form.After that, you can retrieve the base point of the curve and perform various elliptic curve arithmetic operations, including addition, subtraction, multiplication, and division.

from lightecc import LightECC

# build an elliptic curve
ec = LightECC(
    form_name = "edwards", # or weierstrass, koblitz. default is weierstrass.
    curve_name = "ed25519", # check out supported curves section
)

# get the base point
G = ec.G

# addition
_2G = G + G
_3G = _2G + G
_5G = _3G + _2G
_10G = _5G + _5G

# subtraction
_9G = _10G - G

# multiplication
_20G = 20 * G
_50G = 50 * G

# division
_25G = _50G / G

Here, addition and subtraction require only basic formulas and can be performed in constant time 𝒪(1).

Supportingly, the double-and-add method is adopted for multiplication, allowing it to be performed very quickly in linear time with 𝒪(log(n)), regardless of the size of the multiplier.

On the other hand, division requires solving the elliptic curve discrete logarithm problem, which is computationally difficult. Its time complexity is 𝒪(n) with brute force.

Point at Infinity or Neutral & Identity Element

The order of the elliptic curve is defined by the argument n in the constructed LightECC object. This represents the total number of points on the curve. It also serves as the neutral or identity element in Edwards curves and point at infinity in Weierstass and Koblitz forms, meaning that adding this point to any other point does not change the result. Additionally, elliptic curves exhibit cyclic group properties beyond this point.

ec = LightECC()

# order of elliptic curve
n = ec.n

# neutral element
neutral = n * G

# scalar multiplication
_17G = 17 * G
minus17G = -1 * _17G

# proof of work for neutralism
assert _17G == _17G + neutral
assert _17G + minus17G == neutral

# proof of work for cyclic group
assert (n + 1) * G == G
assert (n + 2) * G == 2 * G

Supported Curves

Below is a list of elliptic curves supported by LightECC. Each curve has a specific order (n), which defines the number of points in the finite field. The order directly impacts the cryptosystem's security strength. A higher order typically corresponds to a stronger cryptosystem, making it more resistant to cryptographic attacks.

Edwards Curves

form	curve	field	n (bits)
edwards	e521	prime	519
edwards	id-tc26-gost-3410-2012-512-paramsetc	prime	510
edwards	numsp512t1	prime	510
edwards	ed448	prime	446
edwards	curve41417	prime	411
edwards	numsp384t1	prime	382
edwards	id-tc26-gost-3410-2012-256-paramseta	prime	255
edwards	ed25519 (default)	prime	254
edwards	mdc201601	prime	254
edwards	numsp256t1	prime	254
edwards	jubjub	prime	252

Weierstass Form

form	curve	field	n (bits)
weierstrass	bn638	prime	638
weierstrass	bn606	prime	606
weierstrass	bn574	prime	574
weierstrass	bn542	prime	542
weierstrass	p521	prime	521
weierstrass	brainpoolp512r1	prime	512
weierstrass	brainpoolp512t1	prime	512
weierstrass	fp512bn	prime	512
weierstrass	numsp512d1	prime	512
weierstrass	eccfrog512ck2	prime	512
weierstrass	gost512	prime	511
weierstrass	bn510	prime	510
weierstrass	bn478	prime	478
weierstrass	bn446	prime	446
weierstrass	bls12-638	prime	427
weierstrass	bn414	prime	414
weierstrass	brainpoolp384r1	prime	384
weierstrass	brainpoolp384t1	prime	384
weierstrass	fp384bn	prime	384
weierstrass	numsp384d1	prime	384
weierstrass	p384	prime	384
weierstrass	bls24-477	prime	383
weierstrass	bn382	prime	382
weierstrass	curve67254	prime	380
weierstrass	bn350	prime	350
weierstrass	brainpoolp320r1	prime	320
weierstrass	brainpoolp320t1	prime	320
weierstrass	bn318	prime	318
weierstrass	bls12-455	prime	305
weierstrass	bls12-446	prime	299
weierstrass	bn286	prime	286
weierstrass	brainpoolp256r1	prime	256
weierstrass	brainpoolp256t1	prime	256
weierstrass	fp256bn	prime	256
weierstrass	gost256	prime	256
weierstrass	numsp256d1	prime	256
weierstrass	p256	prime	256
weierstrass	secp256k1 (default)	prime	256
weierstrass	tom256	prime	256
weierstrass	bls12-381	prime	255
weierstrass	pallas	prime	255
weierstrass	tweedledee	prime	255
weierstrass	tweedledum	prime	255
weierstrass	vesta	prime	255
weierstrass	bn254	prime	254
weierstrass	fp254bna	prime	254
weierstrass	fp254bnb	prime	254
weierstrass	bls12-377	prime	253
weierstrass	curve1174	prime	249
weierstrass	mnt4	prime	240
weierstrass	mnt5-1	prime	240
weierstrass	mnt5-2	prime	240
weierstrass	mnt5-3	prime	240
weierstrass	prime239v1	prime	239
weierstrass	prime239v2	prime	239
weierstrass	prime239v3	prime	239
weierstrass	secp224k1	prime	225
weierstrass	brainpoolp224r1	prime	224
weierstrass	brainpoolp224t1	prime	224
weierstrass	curve4417	prime	224
weierstrass	fp224bn	prime	224
weierstrass	p224	prime	224
weierstrass	bn222	prime	222
weierstrass	curve22103	prime	218
weierstrass	brainpoolp192r1	prime	192
weierstrass	brainpoolp192t1	prime	192
weierstrass	p192	prime	192
weierstrass	prime192v2	prime	192
weierstrass	prime192v3	prime	192
weierstrass	secp192k1	prime	192
weierstrass	bn190	prime	190
weierstrass	secp160k1	prime	161
weierstrass	secp160r1	prime	161
weierstrass	secp160r2	prime	161
weierstrass	brainpoolp160r1	prime	160
weierstrass	brainpoolp160t1	prime	160
weierstrass	mnt3-1	prime	160
weierstrass	mnt3-2	prime	160
weierstrass	mnt3-3	prime	160
weierstrass	mnt2-1	prime	159
weierstrass	mnt2-2	prime	159
weierstrass	bn158	prime	158
weierstrass	mnt1	prime	156
weierstrass	secp128r1	prime	128
weierstrass	secp128r2	prime	126
weierstrass	secp112r1	prime	112
weierstrass	secp112r2	prime	110

Koblitz Form

form	curve	field	n (bits)
koblitz	b571	binary	570
koblitz	k571	binary	570
koblitz	c2tnb431r1	binary	418
koblitz	b409	binary	409
koblitz	k409	binary	407
koblitz	c2pnb368w1	binary	353
koblitz	c2tnb359v1	binary	353
koblitz	c2pnb304w1	binary	289
koblitz	b283	binary	282
koblitz	k283	binary	281
koblitz	c2pnb272w1	binary	257
koblitz	ansit239k1	binary	238
koblitz	c2tnb239v1	binary	238
koblitz	c2tnb239v2	binary	237
koblitz	c2tnb239v3	binary	236
koblitz	b233	binary	233
koblitz	k233	binary	232
koblitz	ansit193r1	binary	193
koblitz	ansit193r2	binary	193
koblitz	c2pnb208w1	binary	193
koblitz	c2tnb191v1	binary	191
koblitz	c2tnb191v2	binary	190
koblitz	c2tnb191v3	binary	189
koblitz	b163	binary	163
koblitz	c2pnb163v1	binary	163
koblitz	k163 (default)	binary	163
koblitz	ansit163r1	binary	162
koblitz	c2pnb163v2	binary	162
koblitz	c2pnb163v3	binary	162
koblitz	c2pnb176w1	binary	161
koblitz	sect131r1	binary	131
koblitz	sect131r2	binary	131
koblitz	sect113r1	binary	113
koblitz	sect113r2	binary	113
koblitz	wap-wsg-idm-ecid-wtls1	binary	112

Applications

Explore the LightPHE library for its encryption and decryption implementation, which also demonstrates additive homomorphic properties with Elliptic Curve ElGamal algorithm. Additionally, check out LightDSA for elliptic curve based digital signature implementations such as ECDSA and EdDSA. These are both built on LightECC's fundamentals.

Contributing

All PRs are more than welcome! If you are planning to contribute a large patch, please create an issue first to get any upfront questions or design decisions out of the way first.

You should be able run make test and make lint commands successfully before committing. Once a PR is created, GitHub test workflow will be run automatically and unit test results will be available in GitHub actions before approval.

Support

There are many ways to support a project - starring⭐️ the GitHub repo is just one 🙏

You can also support this work on Patreon, GitHub Sponsors or Buy Me a Coffee.

Also, your company's logo will be shown on README on GitHub if you become sponsor in gold, silver or bronze tiers.

Citation

Please cite LightECC in your publications if it helps your research. Here is its BibTex entry:

@misc{serengil2025lightecc
    author       = {Serengil, Sefik Ilkin},
    title        = {LightECC: A Lightweight Elliptic Curve Cryptography Arithmetic Library for Python with Support for Prime and Binary Fields},
    year         = {2025},
    publisher    = {GitHub},
    howpublished = {https://github.com/serengil/LightECC},
}

License

LightECC is licensed under the MIT License - see LICENSE for more details.

LightECC's logo, designed by Identidea, is inspired from Edwards curves graphs.