Multiplicative complexity of polynomial multiplication over finite fields

A Lower Bound on the Complexity of Polynomial Multiplication Over Finite Fields

Efficient implementation of low time complexity and pipelined bit-parallel polynomial basis multiplier over binary finite fields

This paper presents two efficient implementations of fast and pipelined bit-parallel polynomial basis multipliers over GF (2m) by irreducible pentanomials and trinomials. The architecture of the first multiplier is based on a parallel and independent computation of powers of the polynomial variable. In the second structure only even powers of the polynomial variable are used. The par...

Private Multiplication over Finite Fields

The notion of privacy in the probing model, introduced by Ishai, Sahai, and Wagner in 2003, is nowadays frequently involved to assess the security of circuits manipulating sensitive information. However, provable security in this model still comes at the cost of a significant overhead both in terms of arithmetic complexity and randomness complexity. In this paper, we deal with this issue for ci...

Rings of Low Multiplicative Complexity and Fast Multiplication in Finite Fields

We survey the rings of low multiplicative complexity and the redundant representation of finite fields. The construction is originally due to Ito and Tsujii [3]. We give the important results of Silverman’s works in [1], [2]. Moreover, we note that the fields constructed with Silverman’s method are not suitable for elliptic curve cryptography while Silverman suggests those curves can be used in...

Multiplication of Polynomials over Finite Fields

We prove the 2.5n − o (n ) lower bound on the number of multiplications/divisions required to compute the coefficients of the product of two polynomials of degree n over a finite field by means of straight-line algorithms.