On orders of optimal normal basis generators
Mathematics of Computation
Efficient Exponentiation of a Primitive Root in GF(2m)
IEEE Transactions on Computers
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Gauss periods: orders and cryptographical applications
Mathematics of Computation
A survey of fast exponentiation methods
Journal of Algorithms
Normal bases via general Gauss periods
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Handbook of Applied Cryptography
Handbook of Applied Cryptography
Introduction to Coding Theory
Signed Digit Representations of Minimal Hamming Weight
IEEE Transactions on Computers
Orders of Gauss Periods in Finite Fields
ISAAC '95 Proceedings of the 6th International Symposium on Algorithms and Computation
Gauss Periods and Fast Exponentiation in Finite Fields (Extended Abstract)
LATIN '95 Proceedings of the Second Latin American Symposium on Theoretical Informatics
On Complexity of Polynomial Basis Squaring in F2m
SAC '00 Proceedings of the 7th Annual International Workshop on Selected Areas in Cryptography
More Flexible Exponentiation with Precomputation
CRYPTO '94 Proceedings of the 14th Annual International Cryptology Conference on Advances in Cryptology
Fast exponentiation with precomputation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
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We present an efficient exponentiation algorithm for a finite field GF(qn) with small characteristic determined by a Gaussian normal basis of type II using signed digit representation of the exponents. Our signed digit representation uses a nonadjacent form (NAF) for GF(2n) and the balanced ternary number system for GF(3n). It is generally believed that a signed digit representation is hard to use when a normal basis is given because the inversion of a normal element requires quite a computational delay. On the other hand, the method of a signed digit representation is easily applicable to the fields with polynomial bases. However our result shows that a special normal basis called a Gaussian normal basis of type II or an optimal normal basis (ONB) of type II has a nice property which admits an effective exponentiation using signed digit representations of the exponents.