A public key cryptosystem and a signature scheme based on discrete logarithms
Proceedings of CRYPTO 84 on Advances in cryptology
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Proceedings on Advances in cryptology---CRYPTO '86
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Unbalanced Exponent Modular Reduction over Binary Field and Its Implementation
ICICIC '06 Proceedings of the First International Conference on Innovative Computing, Information and Control - Volume 1
An efficient RSA implementation without precomputation
Inscrypt'11 Proceedings of the 7th international conference on Information Security and Cryptology
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In this study we show how modular multiplication with Barrett and Montgomery reductions over certain finite fields of characteristic 2 can be implemented efficiently without using a pre-computational phase. We extend the set of moduli that is recommended by Standards for Efficient Cryptography (SEC) by defining two distinct sets for which either Barrett or Montgomery reduction is applicable. As the proposed algorithm is very suitable for a fast modular multiplication, we propose an architecture for the fast modular multiplier that can efficiently be used without pre-computing the inverse of the modulus.