Achieving efficient polynomial multiplication in fermat fields using the fast Fourier transform

We introduce an efficient way of performing polynomial multiplication in a class of finite fields GF(pm ) in the frequency domain. The Fast Fourier Transform (FFT) based frequency domain multiplication technique, originally proposed for integer multiplication, provides an extremely efficient method for multiplication with the best known asymptotic complexity, i.e. O(n log n log log n). Unfortunately, the original FFT method bears significant overhead due to the conversions between the time and the frequency domains, which makes it impractical to perform multiplication of relatively short (160 - 1024 bits) integer operands as used in many applications. In this work, we introduce an efficient way of performing polynomial multiplication in finite fields using the FFT. We show that, with careful selection of parameters, all the multiplications required for the FFT computations can be avoided and polynomial multiplication in finite fields can be achieved with only O(m) multiplications in a...

• Type: Conference
• Year: 2006
• Where: ACMSE
• Authors: Selçuk Baktir, Berk Sunar
• Keywords: ACMSE 2006, Finite Fields, Frequency Domains, Polynomial Multiplication, Theoretical Computer Science