Abstract
We study scheme (hardware) and program (software) methods of multiplication of polynomials over fields of characteristic 7 in order to apply them to pairing-based cryptographic protocols on hyperelliptic curves of genus three. We consider hardware and software implementations of arithmetic in GF(7), GF(72), GF(7 n ), GF(77n ), and GF(714n ) and estimate the complexity of corresponding schemes and programs.
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