Hyun-Sung Kim and Il-Soo Jeon
Kyungil University, Computer Engineering,
712-701, Kyungsansi, Kyungpook Province, Korea
email: hskim@purple.knu.ac.kr
Finite field GF(2m) arithmetic is fundamental to the implementation of a number of modern cryptographic systems and schemes of certain cryptographic systems[1]. Most arithmetic operations, such as exponentiation, inversion, and division operations, can be carried out using just a modular multiplier.
CA (Cellular Automata), first introduced by John Von Neumann in the 1950s, have been accepted as a good computational model for the simulation of complex physical systems. CA are finite state machines, defined as uniform arrays of simple cells in n-dimensional space. This property is very easily combined with finite field GF(2m) arithmetic.
Accordingly, the purpose of this paper is to propose two new modular multipliers based on cellular automata over GF(2m). They deploy the mixture of the advantages from the previous architectures in the perspective of area and time complexity. First multiplier uses a generalized irreducible polynomial contrast with the second one using a specialized irreducible polynomial. They are easy to implement VLSI hardware and could be used in IC cards as the multipliers have a particularly simple architecture.