Introduction to finite fields and their applications
Introduction to finite fields and their applications
A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Optimal normal bases in GF(pn)
Discrete Applied Mathematics
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Implementing elliptic curve cryptography
Implementing elliptic curve cryptography
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
Itoh-Tsujii Inversion in Standard Basis and Its Application in Cryptography and Codes
Designs, Codes and Cryptography
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
A Fast Software Implementation for Arithmetic Operations in GF(2n)
ASIACRYPT '96 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
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In this paper, we propose an efficient inversion algorithm for optimal normal bases type II. The efficiency of the arithmetic algorithms depends on the basis and many foregoing papers use either polynomial or optimal normal basis. An inversion algorithm based on reduced multiplication for optimal normal basis is studied. The combination of optimal normal basis and shifted form of the canonical basis is also employed. It is shown that the suggested inversion algorithm reduces the computation time to 45-60 % of the simple algorithm. The algorithm is very effective in composite numbers in which have optimal normal basis type II.