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Title: An RNS implementation of an Fp elliptic curve point multiplier
Authors: Michail, Harris 
Schinianakis, Dimitrios M.
Fournaris, Apostolos P.
Keywords: Computer arithmetic;Geometry;Algebra;Curves, Elliptic
Issue Date: 2009
Publisher: IEEE
Source: IEEE Transactions on Circuits and Systems I: Regular Papers, 2009, Volume 56, Issue 6, Pages 1202-1213
Abstract: Elliptic curve point multiplication is considered to be the most significant operation in all elliptic curve cryptography systems, as it forms the basis of the elliptic curve discrete logarithm problem. Designs for elliptic curve cryptography point multiplication are area demanding and time consuming. Thus, the efficient realization of point multiplication is of fundamental importance for the performance of an elliptic curve system. In this paper, a hardware architecture of an elliptic curve point multiplier is proposed that exploits the intrinsic parallelism of the residue number system (RNS), in order to speed up the elliptic curve point calculations and minimize the area complexity of the elliptic curve point multiplier. The architecture proves to be the fastest among all known design approaches, while complexity is less than half of that of previous efforts. This architecture also supports the required input (binary-to-RNS) and output (RNS-to-binary) conversions. Through a graph-oriented approach, the area of the elliptic curve point multiplier is minimized, by optimizing the point addition and doubling algorithms. Also, through this approach, the number of execution steps for point addition is matched to the number of execution steps for point doubling. Additionally, the impact of various RNS bases, in terms of number of moduli and their bit lengths, on the area and speed of the proposed implementation is analyzed, in an effort to define the potential for using RNS in elliptic curve cryptography.
ISSN: 10577122
DOI: 10.1109/TCSI.2008.2008507
Rights: © 2009 IEEE
Type: Article
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