Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Optimal normal bases in GF(pn)
Discrete Applied Mathematics
Discrete Applied Mathematics
An Efficient Optimal Normal Basis Type II Multiplier
IEEE Transactions on Computers
A Modified Massey-Omura Parallel Multiplier for a Class of Finite Fields
IEEE Transactions on Computers
Efficient Software Implementation for Finite Field Multiplication in Normal Basis
ICICS '01 Proceedings of the Third International Conference on Information and Communications Security
Fast Multiplication in Finite Fields GF(2N)
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
New directions in cryptography
IEEE Transactions on Information Theory
Bit-serial Reed - Solomon encoders
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
Finite Fields and Their Applications
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Efficient multiplication in finite fields F"q"^"n requires F"q-bases of low density, i.e., such that the products of the basis elements have a sparse expression in the basis. In this paper we introduce a new family of bases: the quasi-normal bases. These bases generalize the notion of normal bases and provide simple exponentiation to the power q in F"q"^"n. For some extension fields F"q"^"n over F"q, we construct quasi-normal bases of low density.