Fast finite field multipliers for public key cryptosystems

Abstract

The security strength of Public Key Cryptosystems (PKCs) is attributed to the complex computations that are employed in the encryption and decryption algorithms. These algorithms are executed by cryptoprocessors which are used as embedded co-processors in devices like smartcards, smart cameras etc. Speed of operation, circuit area and security strength variability are vital design considerations in such applications. These criteria call for efficient hardware implementation of the underlying arithmetic operations of the algorithms. Multiplication in finite fields, widely known as finite field multiplication or modular multiplication, forms the core computational engine of all algorithms involved in PKCs. The research work in this thesis aims at developing efficient architectures for finite field multiplications in the prime field GF(N) and the extended binary field GF(2m).