ECDH-Algorithm

This is an implementation of the Elliptic-Curve Diffie-Hellman Cryptographic Algorithm.

This repo was initially a part of the course project CSCI-GA 3033-020 Practical Computer Security at New York University under Prof. T. Srivatanakul, but can be further extended to research in the field of IoT.

The goal of the project was to try and reduce the computational resources used by an cryptographic algortihm such that it is suitable for use in IoT devices,by in turn sacrificing some acceptable amount of resources used in the operational scheme of the device. The code in the repository consists of two implementations of the Elliptic Curve Diffie-Hellman (ECDH) algorithms-

1. The base implementation is done using OpenSSL APIs, which serves as a benchmark since it is a popular library for encrypting messages over the network. This implementation is in the ecdh-openssl.c file. It requires OpenSSL library and headers to be installed.

2. The implementation that we developed as part of the project is in ecdh.c, ecdh.h and primefield.h files. It uses GMP for arbitrary precision arithmetic(i.e limited by the host machine). GMP is required to run and compile the code.

Compilation

This code is meant only for systems running Linux or with a Linux-compatible /dev/urandom device available on the system.

The code requires OpenSSL library and development headers and gmplib. Install them using your package manager, if not already installed.

| To compile both implementations, run make. | To compile only OpenSSL version, run make ecdh-openssl. | To compile only our version, run make ecdh.

A recent version of gcc is required for compilation. If the compiler complains about -Wall as unrecognized option or the complains about -std=c99, run the command as CC=gcc CFLAGS='-std=c99' make

Running

To run the code, execute ./ecdh. The code will generate two keypairs and validate the ecdh exchange between them. To see the keypairs generated, execute ./ecdh -v.

To run the OpenSSL version, execute ./ecdh-openssl. There is no option to see the keypairs generated here.

Benchmarking

To get statistics on memory and CPU usage, run ./utils/benchmark [executable] [iterations]. The benchmark script requires GNU time to run, not the shell built-in time.

(Kindly refer to the PDF for further information.)