Arithmetic operations over binary extension fields GF(2 m ) have many important applications in domains such as cryptography, code theory and digital signal processing. These must be fast, so low-delay implementations of arithmetic circuits are required. Among operations, field multiplication is...

<p style='text-indent:20px;'>Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic secure and efficient way. However, while implementation is simple, parameterization not trivial relies suitable choice of the polynomial which PMNS operates. The initial proposals were based...

s of invited lectures Extended differential properties of cryptographic functions ANNE CANTEAUT (INRIA-Rocquencournt, France) Differential cryptanalysis is one of the very first attack proposed against block ciphers. This attack exploits the fact that some derivatives of the cipher (or of a reduced version of the cipher) have a nonrandom output distribution. Since this distribution highly depen...

Throughout this paper, we refer to the non-cyclotomic part of a polynomial f(x) 2 Z[x] as f(x) with its cyclotomic factors removed. More speci cally, if g1(x); : : : ; gr(x) are non-cyclotomic irreducible polynomials in Z[x] and gr+1(x); : : : ; gs(x) are cyclotomic polynomials such that f(x) = g1(x) gr(x) gr+1(x) gs(x), then g1(x) gr(x) is the non-cyclotomic part of f(x). We refer to a polynom...

Novel systolic and super-systolic architectures are presented for polynomial basis multiplication over GF (2) based on irreducible trinomials. By suitable cut-set retiming, we have derived here an efficient bit-level-pipelined bit-parallel systolic design for binary field multiplication which requires less number of gates and registers, and involves nearly half the timecomplexity of the corresp...

A famous conjecture about group algebras of torsion-free groups states that there is no zero divisor in such algebras. recent approach to settle the show non-existence divisors with respect length possible ones, where by we mean size support an element algebra. The case $2$ cannot be happen. first unsettled existence $3$. Here study $3$ rational and over field $p$ elements for some prime $p$.

Based on the shifted polynomial basis (SPB), a high efficient bit-parallel multiplier for the field GF(2m) defined by an equallyspaced trinomial (EST) is proposed. The use of SPB significantly reduces time delay of the proposed multiplier and at the same time Karatsuba method is combined with SPB to decrease space complexity. As a result, with the same time complexity, approximately 3/4 gates o...

By selecting the largest possible value of k ∈ (n/2, 2n/3], we further reduce the AND and XOR gate complexities of the CRT-based hybrid parallel GF (2) polynomial basis multipliers for the irreducible trinomial f = u + u + 1 over GF (2): they are always less than those of the current fastest parallel multipliers – quadratic multipliers, i.e., n AND gates and n− 1 XOR gates. Our experimental res...