Abstract
We present an efficient exponentiation algorithm for a finite field GF(q n) 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.
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Kwon, S. (2005). Signed Digit Representation with NAF and Balanced Ternary Form and Efficient Exponentiation in GF(q n) Using a Gaussian Normal Basis of Type II. In: Lim, C.H., Yung, M. (eds) Information Security Applications. WISA 2004. Lecture Notes in Computer Science, vol 3325. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31815-6_27
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DOI: https://doi.org/10.1007/978-3-540-31815-6_27
Publisher Name: Springer, Berlin, Heidelberg
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