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
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
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
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This paper propose a new multiplicative inverse algorithm for Galois field GF(2n) whose elements are represented by 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. A normal basis element is always possible to rewrite canonical basis form. The proposed algorithm combines normal basis and canonical basis. It is shown that the suggested algorithm is suitable for implementation and reduces the computation time to 5-10 % of the normal basis algorithm.