The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Bit-Parallel Finite Field Multiplier and Squarer Using Polynomial Basis
IEEE Transactions on Computers
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Hardware Implementation of Finite Fields of Characteristic Three
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Efficient pth root computations in finite fields of characteristic p
Designs, Codes and Cryptography
The combinatorics of associated Hermite polynomials
European Journal of Combinatorics
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
IEEE Transactions on Computers
Low Complexity Cubing and Cube Root Computation over $\F_{3^m}$ in Polynomial Basis
IEEE Transactions on Computers
Elliptic periods for finite fields
Finite Fields and Their Applications
Finding optimal formulae for bilinear maps
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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In this paper, the Hermite polynomial representation is adapted as a new way to represent certain finite fields of characteristic three. We give the multiplication method to multiply two elements of F"3"^"n in the Hermite polynomial representation with subquadratic computational complexity by using a divide-and-conquer idea. We show that in some cases there is a set of irreducible binomials in the Hermite polynomial representation to obtain modular reduction with a lower addition complexity than the standard polynomial representation. We also investigate the matrix vector product method for the multiplication of the field elements represented by Hermite polynomials.