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On repeated squarings in binary fields. (English) Zbl 1267.94069
Jacobson, Michael J. jun. (ed.) et al., Selected areas in cryptography. 16th annual international workshop, SAC 2009, Calgary, Alberta, Canada, August 13–14, 2009. Revised selected papers. Berlin: Springer (ISBN 978-3-642-05443-3/pbk). Lecture Notes in Computer Science 5867, 331-349 (2009).
Summary: In this paper, we discuss the problem of computing repeated squarings (exponentiations to a power of 2) in finite fields with polynomial basis. Repeated squarings have importance, especially, in elliptic curve cryptography where they are used in computing inversions in the field and scalar multiplications on Koblitz curves. We explore the problem specifically from the perspective of efficient implementation using field-programmable gate arrays (FPGAs) where the look-up table (LUT) structure helps to reduce both area and delay overheads. In fact, we show that the optimum construction depends on the size of the LUTs. We propose several repeated squarer architectures and demonstrate their practicability for FPGA-based implementations. Finally, we show that the proposed repeated squarers can offer significant speedups and even improve resistivity against side-channel attacks.
For the entire collection see [Zbl 1177.94012].

94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
11Y99 Computational number theory
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