Abstract: | Many cryptographic applications use finite fields as basic components.
These applications require fast implementation of arithmetic in finite fields. One of the most used ways to represent the elements of finite fields involve polynomials; operations with elements of the finite fields are done by executing the respective operations on the polynomials. In order for this idea to work, irreducible polynomials are required.
In this talk we focus on irreducible polynomials over finite fields of interest when implementing arithmetic operations for cryptographic use, both in hardware and software. We survey several families of irreducible polynomials over finite fields proposed in the literature, and comment on the properties that these irreducible polynomials have. In addition, we briefly present some theoretical open problems related to irreducible polynomials and their potential use in cryptography. |
