The CRC Handbook of Finite Fields (hereafter referred to as the Handbook) is a reference
book for the theory and applications of finite fields. It is not intended to be an introductory …

Factoring Polynomials Over Finite Fields: A Survey Page 1 doi:10.1006/jsco.1999.1002
Available online at http://www.idealibrary.com on J. Symbolic Computation (2001) 31, 3–17 …

This book is mainly devoted to some computational and algorithmic problems in finite fields
such as, for example, polynomial factorization, finding irreducible and primitive polynomials …

In this paper we give an overview of some of the cryptographic applications which were
derived from the proposal of RJ McEliece to use error correcting codes for cryptographic …

The results of Strassen and Raz show that good enough tensor rank lower bounds have
implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and …

Galois field implementations are central to the design of many reliable and secure systems,
with many systems implementing them in software. The two most common Galois field …

We demonstrate the cryptographic usefulness of a small subgroup of Z_n^* of hidden order.
Cryptographic schemes for integer commitment and digital signatures have been suggested …

Let q be a prime power, F _q F q be the finite field of order q and F _q (x) F q (x) be the field
of rational functions over F _q F q. In this paper we classify and count all rational functions φ …

In modern as well as ancient ciphers of public key cryptography, substitution boxes find a
permanent seat. Generation and cryptanalysis of 4-bit as well as 8-bit crypto S-boxes is of …

Finite fields are widely used in constructing error-correcting codes and cryptographic
algorithms. In practice, error-correcting codes use small finite fields to achieve high …