Fast polynomial factorization over high algebraic extensions of finite fields
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Fast rectangular matrix multiplication and applications
Journal of Complexity
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
Polynomial Factorization 1987-1991
LATIN '92 Proceedings of the 1st Latin American Symposium on Theoretical Informatics
Efficient Finite Field Basis Conversion Involving Dual Bases
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
Constructing Composite Field Representations for Efficient Conversion
IEEE Transactions on Computers
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Hi-index | 14.98 |
We describe an efficient method for constructing the basis conversion matrix between two given finite field representations where one is composite. We are motivated by the fact that using certain representations, e.g., low-Hamming weight polynomial or composite field representations, permits arithmetic operations such as multiplication and inversion to be computed more efficiently. An earlier work by Paar defines the conversion problem and outlines an exponential time algorithm that requires an exhaustive search in the field. Another algorithm by Sunar et al. provides a polynomial time algorithm for the limited case where the second representation is constructed (rather than initially given). The algorithm we present facilitates existing factorization algorithms and provides a randomized polynomial time algorithm to solve the basis conversion problem where the two representations are initially given. We also adapt a fast trace-based factorization algorithm to work in the composite field setting which yields a subcubic complexity algorithm for the construction of the basis conversion matrix.