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A lightweight and fast pure Java ECDSA

Overview

This is a pure Java implementation of the Elliptic Curve Digital Signature Algorithm (ECDSA). It is compatible with Java 8+ and OpenSSL. It uses elegant math such as Jacobian Coordinates to speed up the ECDSA on pure Java.

Security

starkbank-ecdsa includes the following security features:

  • RFC 6979 deterministic nonces: Eliminates the catastrophic risk of nonce reuse that leaks private keys
  • Low-S signature normalization: Prevents signature malleability (BIP-62)
  • Public key on-curve validation: Blocks invalid-curve attacks during verification
  • Montgomery ladder scalar multiplication: Constant-operation point multiplication to mitigate timing side channels
  • Hash truncation: Correctly handles hash functions larger than the curve order (e.g. SHA-512 with secp256k1)
  • Fermat's little theorem for modular inverse: More uniform execution time than the extended Euclidean algorithm

Installation

Maven Central

In pom.xml:

<dependency>
    <groupId>com.starkbank</groupId>
    <artifactId>starkbank-ecdsa</artifactId>
    <version>2.0.0</version>
</dependency>

Then run:

mvn clean install

Curves

We currently support secp256k1 and prime256v1 (P-256), but you can add more curves to the project. Just use Curve.add().

Speed

We ran a test on JDK 21.0.10 on a MAC Pro. The libraries were run 100 times and the averages displayed below were obtained:

Library sign verify
starkbank-ecdsa 0.8ms 1.3ms

Performance is driven by Jacobian coordinates, a branch-balanced Montgomery ladder for variable-base scalar multiplication, a precomputed affine table of powers-of-two multiples of the generator ([G, 2G, 4G, ..., 2^n*G]) combined with a width-2 NAF of the scalar to eliminate doublings during signing, a mixed affine+Jacobian addition fast path, curve-specific shortcuts in point doubling (A=0 for secp256k1, A=-3 for prime256v1), the secp256k1 GLV endomorphism to split 256-bit scalars into two ~128-bit halves for a 4-scalar simultaneous multi-exponentiation during verification, Shamir's trick with Joint Sparse Form as the fallback path for curves without an efficient endomorphism, and the extended Euclidean algorithm for modular inversion.

Sample Code

How to sign a json message for Stark Bank:

import com.starkbank.ellipticcurve.PrivateKey;
import com.starkbank.ellipticcurve.PublicKey;
import com.starkbank.ellipticcurve.Signature;
import com.starkbank.ellipticcurve.Ecdsa;


// Generate privateKey from PEM string
PrivateKey privateKey = PrivateKey.fromPem("-----BEGIN EC PRIVATE KEY-----\n...\n-----END EC PRIVATE KEY-----");

String message = "{\"transfers\": [{\"amount\": 100000000}]}";

Signature signature = Ecdsa.sign(message, privateKey);

// Generate Signature in base64
System.out.println(signature.toBase64());

// To double check if the message matches the signature:
PublicKey publicKey = privateKey.publicKey();
System.out.println(Ecdsa.verify(message, signature, publicKey));

Simple use:

import com.starkbank.ellipticcurve.PrivateKey;
import com.starkbank.ellipticcurve.PublicKey;
import com.starkbank.ellipticcurve.Signature;
import com.starkbank.ellipticcurve.Ecdsa;


// Generate new Keys
PrivateKey privateKey = new PrivateKey();
PublicKey publicKey = privateKey.publicKey();

String message = "My test message";

// Generate Signature
Signature signature = Ecdsa.sign(message, privateKey);

// To verify if the signature is valid
System.out.println(Ecdsa.verify(message, signature, publicKey));

How to add more curves:

import com.starkbank.ellipticcurve.Curve;
import com.starkbank.ellipticcurve.PrivateKey;
import com.starkbank.ellipticcurve.PublicKey;
import java.math.BigInteger;

Curve newCurve = new Curve(
    new BigInteger("f1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c00", 16),
    new BigInteger("ee353fca5428a9300d4aba754a44c00fdfec0c9ae4b1a1803075ed967b7bb73f", 16),
    new BigInteger("f1fd178c0b3ad58f10126de8ce42435b3961adbcabc8ca6de8fcf353d86e9c03", 16),
    new BigInteger("f1fd178c0b3ad58f10126de8ce42435b53dc67e140d2bf941ffdd459c6d655e1", 16),
    new BigInteger("b6b3d4c356c139eb31183d4749d423958c27d2dcaf98b70164c97a2dd98f5cff", 16),
    new BigInteger("6142e0f7c8b204911f9271f0f3ecef8c2701c307e8e4c9e183115a1554062cfb", 16),
    "frp256v1",
    new long[]{1, 2, 250, 1, 223, 101, 256, 1}
);

Curve.add(newCurve);

PrivateKey privateKey = new PrivateKey(newCurve, null);
PublicKey publicKey = privateKey.publicKey();
System.out.println(publicKey.toPem());

How to generate compressed public key:

import com.starkbank.ellipticcurve.PrivateKey;
import com.starkbank.ellipticcurve.PublicKey;

PrivateKey privateKey = new PrivateKey();
PublicKey publicKey = privateKey.publicKey();
String compressedPublicKey = publicKey.toCompressed();

System.out.println(compressedPublicKey);

How to recover a compressed public key:

import com.starkbank.ellipticcurve.PublicKey;

String compressedPublicKey = "0252972572d465d016d4c501887b8df303eee3ed602c056b1eb09260dfa0da0ab2";
PublicKey publicKey = PublicKey.fromCompressed(compressedPublicKey);

System.out.println(publicKey.toPem());

OpenSSL

This library is compatible with OpenSSL, so you can use it to generate keys:

openssl ecparam -name secp256k1 -genkey -out privateKey.pem
openssl ec -in privateKey.pem -pubout -out publicKey.pem

Create a message.txt file and sign it:

openssl dgst -sha256 -sign privateKey.pem -out signatureDer.txt message.txt

To verify, do this:

import com.starkbank.ellipticcurve.Ecdsa;
import com.starkbank.ellipticcurve.PublicKey;
import com.starkbank.ellipticcurve.Signature;
import com.starkbank.ellipticcurve.utils.ByteString;
import com.starkbank.ellipticcurve.utils.File;

String publicKeyPem = File.read("publicKey.pem");
byte[] signatureBin = File.readBytes("signatureDer.txt");
String message = File.read("message.txt");

PublicKey publicKey = PublicKey.fromPem(publicKeyPem);
Signature signature = Signature.fromDer(new ByteString(signatureBin));

System.out.println(Ecdsa.verify(message, signature, publicKey));

You can also verify it on terminal:

openssl dgst -sha256 -verify publicKey.pem -signature signatureDer.txt message.txt

NOTE: If you want to create a Digital Signature to use with Stark Bank, you need to convert the binary signature to base64.

openssl base64 -in signatureDer.txt -out signatureBase64.txt

You can do the same with this library:

import com.starkbank.ellipticcurve.Signature;
import com.starkbank.ellipticcurve.utils.ByteString;
import com.starkbank.ellipticcurve.utils.File;

byte[] signatureBin = File.readBytes("signatureDer.txt");
Signature signature = Signature.fromDer(new ByteString(signatureBin));

System.out.println(signature.toBase64());

Run unit tests

gradle test

Run benchmark

gradle run