Optimal normal bases in GF(pn)
Discrete Applied Mathematics
Designs, Codes and Cryptography
Montgomery Multiplication in GF(2^k
Designs, Codes and Cryptography
Fast Multiplication in Finite Fields GF(2N)
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
Public-key cryptosystems with very small key lengths
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
An implementation of elliptic curve cryptosystems over F2155
IEEE Journal on Selected Areas in Communications
IEEE Transactions on Computers
A Redundant Representation of GF(q^n) for Designing Arithmetic Circuits
IEEE Transactions on Computers
Efficient multiplication over extension fields
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
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The complexity of the multiplication operation in finite fields is of interest for both theoretical and practical reasons. For example, an optimal normal basis for F"2"^"N has complexity 2N-1. A construction described in J. H. Silverman, (''Cryptographic Hardware and Embedded Systems,'' Lecture Notes in Computer Science, Vol. 1717, pp. 122-134, Springer-Verlag, Berlin, 1999.) allows multiplication of complexity N+1 to be performed in F"2"^"N by working in a larger ring R of dimension N+1 over F"2. In this paper we give a complete classification of all such rings and show that this construction is the only one which also has a certain useful permutability property.