Summatory Functions of Digital Sums Occurring in Cryptography |
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Authors: | Thuswaldner Jörg M |
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Affiliation: | (1) Institut für Mathematik und Angewandte Geometrie Abteilung für Mathematik und Statistik, Montanuniversität Leoben, Franz-Josef-Strasse 18, A-8700 Leoben, Austria |
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Abstract: | Morain and Olivos gave two algorithms that allow fast exponentiation in elliptic curve cryptosystems. These algorithms are based on representations of integers in certain redundant binary number systems. In this paper we consider the weight and the sum of digits function of these representations. In particular, we give formulas for their summatory functions. In the proofs we use the Mellin-Perron formula. In order to apply this formula, we have to compute the analytic continuation of a class of Dirichlet series. |
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Keywords: | Digital sum Dirichlet series cryptosystem |
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