Theoretical Statistics and Mathematics Unit, ISI 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 $(m, q) = 1.$