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Title:
GF(2^n) redundant representation using matrix embedding
Authors: Yongjia Wang, Xi Xiong, Haining Fan
Abstract:By embedding a Toeplitz matrix-vector product (MVP) of dimension n into a circulant MVP of dimension N=2n+\delta -1, where \delta can be any nonnegative integer, we present a GF(2^n) multiplication algorithm. This algorithm leads to a new redundant representation, and it has two merits: 1. The flexible choices of \delta make it possible to select a proper N such that the multiplication operation in ring GF(2)[x]/(x^N+1) can be performed using some asymptotically faster algorithms, e.g. the Fast Fourier Transformation (FFT)-based multiplication algorithm; 2. The redundant degrees, which are defined as N/n, are smaller than those of most previous GF(2^n) redundant representations, and in fact they are approximately equal to 2 for all applicable cases.
ePrint: https://eprint.iacr.org/2011/556
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