EC-ElGamal

This repository contains a C implementation of the additive homomorphic elliptic curve based EL-Gamal cryptographic scheme and a corresponding Java JNI wrapper. The elliptic curve operations of OpenSSL are used for the implementation. Ciphertexts can be added toghether such that the decrypted result corresponds to the sum of the plaintexts (i.e. p1 + p2 = Dec(Enc(p1) ++ Enc(p2)))) similar to the Paillier-cryptosystem.

Content

The native folder contains the C implementation of the scheme and the src folder contains the Java wrapper library.

Prerequisites

Make sure you have the following installed:

• CMake
• OpenSSL
• Maven
• Java JDK 1.8

C Library

The C library contains two versions of EC-Elgamal, a basic version and a Chinese Remainder Thereom (CRT) based optimized version, as introduced by Pilatus. The library builds with cmake. To compile the library and run the benchmark run:

cd native
cmake .
make
./out/ecelgamal

Java Wrapper

The Java library wraps the CRT based EC-ElGamal scheme implemented in C in a Java class with the JNI. The Java wrapper contains a prebuilt version of the library for linux64 and darwin64 (src/main/resources). To build the jar package, maven is required. The following command builds the library:

mvn package

Here an example on how to use the library.

ECElGamal.CRTParams params32 = ECElGamal.getDefault32BitParams();
ECElGamal.ECElGamalKey key32 = ECElGamal.generateNewKey(params32)
ECElGamal.ECElGamalCiphertext cipher1,cipher2;
int val1 = 2, val2 = -3;
cipher1 = ECElGamal.encrypt(BigInteger.valueOf(val1), key32);
cipher2 = ECElGamal.encrypt(BigInteger.valueOf(val2), key32);
cipher1 = ECElGamal.add(cipher1, cipher2);
int decriptedVal = ECElGamal.decrypt32(cipher1, key32);
assertEquals(val1 + val2, decriptedVal);

Performance

On a 256-bit curve and with an AWS EC2 micro instance in ms. (OpenSSL 1.0.2g)

Plain EC-ElGamal 32-bit integers
Avg ENC Time 0.238853ms Avg DEC Time 275.811 ms

CRT optimized EC-ElGamal 32-bit integers
Avg ENC Time 0.61461ms Avg DEC Time 0.339739ms 

CRT optimized EC-ElGamal 64-bit integers
Avg ENC Time 1.00067ms Avg DEC Time 0.560923ms 

Security

This library is for academic purposes, gives no security guarantees and may contain implementation vulnerabilities.