elliptic-curve-solidity
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Elliptic Curve arithmetic for up to 256-bit curves written in solidity
elliptic-curve-solidity is an open source implementation of Elliptic Curve arithmetic operations written in Solidity.
DISCLAIMER: This is experimental software. Use it at your own risk!
The solidity contracts have been generalized in order to support any elliptic curve based on prime numbers up to 256 bits.
elliptic-curve-solidity has been designed as a library with only pure functions aiming at decreasing gas consumption as much as possible. Additionally, gas consumption comparison can be found in the benchmark section. This library does not check whether the points passed as arguments to the library belong to the curve. However, the library exposes a method called isOnCurve that can be utilized before using the library functions.
It contains 2 solidity libraries:
EllipticCurve.sol: provides main elliptic curve operations in affine and Jacobian coordinates.FastEcMul.sol: provides a fast elliptic curve multiplication by using scalar decomposition and wNAF scalar representation.EllipticCurve library provides functions for:
FastEcMul library provides support for:
The elliptic-curve-solidity contract supports up to 256-bit curves. However, it has been extensively tested for the following curves:
secp256k1secp224k1secp192k1secp256r1 (aka P256)secp192r1 (aka P192)secp224r1 (aka P224)Known limitations:
deriveY function do not work with the curves secp224r1 and secp224k1 because of the selected derivation algorithm. The computations for this curve are done with a modulo prime p such that p mod 4 = 1, thus a more complex algorithm is required (e.g. Tonelli-Shanks algorithm). Note that deriveY is just an auxiliary function, and thus does not limit the functionality of curve arithmetic operations.cofactor = 1 (all supported curves have a cofactor = 1).EllipticCurve.sol library can be used directly by importing it.
The Secp256k1 example depicts how to use the library by providing a function to derive a public key from a secret key:
pragma solidity 0.6.12;
import "elliptic-curve-solidity/contracts/EllipticCurve.sol";
contract Secp256k1 {
uint256 public constant GX = 0x79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798;
uint256 public constant GY = 0x483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8;
uint256 public constant AA = 0;
uint256 public constant BB = 7;
uint256 public constant PP = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F;
function derivePubKey(uint256 privKey) public pure returns(uint256 qx, uint256 qy) {
(qx, qy) = EllipticCurve.ecMul(
privKey,
GX,
GY,
AA,
PP
);
}
}
The cost of a key derivation operation in Secp256k1 is around 550k gas.
·--------------------------------------------------|--------------------------·
| Gas · Block limit: 6721975 gas │
···················································|···························
| · 100 gwei/gas · 592.30 usd/eth │
··················|··········|··········|··········|············|··············
| Method · Min · Max · Avg · # calls · usd (avg) │
··················|··········|··········|··········|············|··············
| derivePubKey · 476146 · 518863 · 499884 · 18 · 29.61 │
··················|··········|··········|··········|············|··············
The cost of a simultaneous multiplication (using wNAF) consumes around 35% of the gas required by 2 EC multiplications.
Gas consumption and USD price estimation with a gas price of 100 Gwei, derived from ETH Gas Station:
·----------------------------------------|---------------------------|-------------|----------------------------·
| Solc version: 0.6.12+commit.27d51765 · Optimizer enabled: true · Runs: 200 · Block limit: 6718946 gas │
·········································|···························|·············|·····························
| Methods · 100 gwei/gas · 613.52 usd/eth │
··················|······················|·············|·············|·············|··············|··············
| Contract · Method · Min · Max · Avg · # calls · usd (avg) │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · decomposeScalar · 55811 · 65399 · 61939 · 134 · 3.80 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · deriveY · 45275 · 55545 · 50410 · 4 · 3.09 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · ecAdd · 24305 · 56323 · 49119 · 472 · 3.01 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · ecInv · 22906 · 23074 · 22990 · 2 · 1.41 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · ecMul · 24911 · 623087 · 350939 · 561 · 21.53 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · ecSimMul · 76465 · 488165 · 243763 · 125 · 14.96 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · ecSub · 42634 · 56236 · 49717 · 228 · 3.05 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · invMod · 22153 · 49255 · 39627 · 12 · 2.43 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · isOnCurve · 23400 · 24071 · 23623 · 16 · 1.45 │
··················|······················|·············|·············|·············|··············|··············
| EllipticCurve · toAffine · 50145 · 50850 · 50498 · 4 · 3.10 │
·----------------------------------------|-------------|-------------|-------------|--------------|-------------·
Some functions of the contract are based on:
Numerology by NuCyphersolidity-arithmetic by Gnosisecsol written by Jordi Baylinastandard contracts written by Andreas Olofssonelliptic-curve-solidity is published under the MIT license.
FAQs
Elliptic Curve arithmetic for up to 256-bit curves written in solidity
We found that elliptic-curve-solidity demonstrated a not healthy version release cadence and project activity because the last version was released a year ago. It has 5 open source maintainers collaborating on the project.
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