Efficient Implementation of Elliptic Curve Cryptography on FPGAs

Abstract

This work presents the design strategies of an FPGA-based elliptic curve co-processor. Elliptic curve cryptography is an important topic in cryptography due to its relatively short key length and higher efficiency as compared to other well-known public key crypto-systems like RSA. The most important contributions of this work are:<br /> - Analyzing how different representations of finite fields and points on elliptic curves effect the performance of an elliptic curve co-processor and implementing a high performance co-processor.<br /> - Proposing a novel dynamic programming approach to find the optimum combination of different recursive polynomial multiplication methods. Here optimum means the method which has the smallest number of bit operations.<br /> - Designing a new normal-basis multiplier which is based on polynomial multipliers. The most important part of this multiplier is a circuit of size $O(n \log n)$ for changing the representation between polynomial and normal basis.