Abstract
We present a fast and compact hardware architecture of exponentiation in a finite field GF(2n) determined by a Gauss period of type (n,k) with k ≥ 2. Our construction is based on the ideas of Gao et al. and on the computational evidence that a Gauss period of type (n,k) over GF(2) is very often primitive when k ≥ 2. Also in the case of a Gauss period of type (n,1), i.e. a type I optimal normal element, we find a primitive element in GF(2n) which is a sparse polynomial of a type I optimal normal element and we propose a fast exponentiation algorithm which is applicable for both software and hardware purposes. We give an explicit hardware design using the algorithm.
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Kwon, S., Kim, C.H., Hong, C.P. (2003). Efficient Exponentiation for a Class of Finite Fields GF(2n) Determined by Gauss Periods. In: Walter, C.D., Koç, Ç.K., Paar, C. (eds) Cryptographic Hardware and Embedded Systems - CHES 2003. CHES 2003. Lecture Notes in Computer Science, vol 2779. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45238-6_19
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DOI: https://doi.org/10.1007/978-3-540-45238-6_19
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