#### Presentation Title

Applying Polynomial Multiplication Algorithms to Cryptography

#### Abstract

Recent research has shown that creatively using the Toom-Cook algorithm can result in multiplying large polynomials quickly for NTRUencrypt. We formally describe the conditions in which the Toom-Cook algorithm can be used to multiply polynomials whose coefficients are elements of the ring of integers modulo a power of two. We apply these results to improve the speed of multiplication for different parameter sets for NTRUencrypt.

#### Primary Faculty Mentor Name

Christelle Vincent

#### Status

Graduate

#### Student College

College of Engineering and Mathematical Sciences

#### Program/Major

Mathematics

#### Primary Research Category

Engineering & Physical Sciences

Applying Polynomial Multiplication Algorithms to Cryptography

Recent research has shown that creatively using the Toom-Cook algorithm can result in multiplying large polynomials quickly for NTRUencrypt. We formally describe the conditions in which the Toom-Cook algorithm can be used to multiply polynomials whose coefficients are elements of the ring of integers modulo a power of two. We apply these results to improve the speed of multiplication for different parameter sets for NTRUencrypt.