# Seminar at SMU Delhi

January 13, 2015 (Tuesday) , 3:30 PM at Webinar
Speaker: Alok Mishra, Indian Institute of Technology, Delhi
Title: On the normal bases over finite fields
Abstract of Talk
Efficient field arithmetic is required in various coding, cryptographic and signal processing techniques.Efficiency of field arithmetic operations presumably depends on how the elements are represented. One important factor that affects the finite field computation efficiency is choice of the basis. Normal bases with lowest possible complexities over finite fields are preferred over polynomial bases due to efficient exponentiation and multiplication. First, we discuss the bounds on the complexity of the normal basis generated by the trace of the dual element of a Type I optimal normal element and provide conditions under which our bounds are better than the known ones. Finally, we discuss the possibility for a product of two self-dual normal bases generators to be a self-dual normal basis generator and vice versa. In addition,We also discuss the possibility of a relation between the number of self-dual normal bases of $\mathbb{F}_{q^{n}}$ over $\mathbb{F}_q$ and those of $\mathbb{F}_{q^{m}}$ over $\mathbb{F}_q,$ where $n = p^{t} m$ with $(m, q) = 1.$