Abstract
In 2004, Bajard, Imbert and Plantard introduced a new system of representation to perform arithmetic modulo a prime integer p, the Adapted Modular Number System (AMNS). In this system, the elements are seen as polynomial of degree nāāā1 with the coefficients of size p 1/n. The best method for multiplication in AMNS works only for some specific moduli p. In this paper, we propose a novel algorithm to perform the modular multiplication in the AMNS. This method works for any AMNS, and does not use a special form of the modulo p. We also present a version of this algorithm in Lagrange Representation which performs the polynomial multiplication part of the first algorithm efficiently using Fast Fourier Transform.
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Negre, C., Plantard, T. (2008). Efficient Modular Arithmetic in Adapted Modular Number System Using Lagrange Representation. In: Mu, Y., Susilo, W., Seberry, J. (eds) Information Security and Privacy. ACISP 2008. Lecture Notes in Computer Science, vol 5107. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70500-0_34
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DOI: https://doi.org/10.1007/978-3-540-70500-0_34
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