Efficient bit-parallel systolic multiplier over GF (2<sup>m</sup>)

Mozhi, S. Arul; Ramya, Puppala

doi:10.1109/iceeot.2016.7755652

Cited by 2 publications

(2 citation statements)

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“…Hence, it is not possible to determine the representative based on the bound (9). The representative q = −2 − 2i follows from (10), as |q| ≈ 2.8284 < |q | = 3.…”

Section: Montgomery Reduction For Gaussian Integersmentioning

confidence: 99%

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Montgomery Reduction for Gaussian Integers

Safieh

Freudenberger

2021

Cryptography

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Modular arithmetic over integers is required for many cryptography systems. Montgomery reduction is an efficient algorithm for the modulo reduction after a multiplication. Typically, Montgomery reduction is used for rings of ordinary integers. In contrast, we investigate the modular reduction over rings of Gaussian integers. Gaussian integers are complex numbers where the real and imaginary parts are integers. Rings over Gaussian integers are isomorphic to ordinary integer rings. In this work, we show that Montgomery reduction can be applied to Gaussian integer rings. Two algorithms for the precision reduction are presented. We demonstrate that the proposed Montgomery reduction enables an efficient Gaussian integer arithmetic that is suitable for elliptic curve cryptography. In particular, we consider the elliptic curve point multiplication according to the randomized initial point method which is protected against side-channel attacks. The implementation of this protected point multiplication is significantly faster than comparable algorithms over ordinary prime fields.

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“…Hence, it is not possible to determine the representative based on the bound (9). The representative q = −2 − 2i follows from (10), as |q| ≈ 2.8284 < |q | = 3.…”

Section: Montgomery Reduction For Gaussian Integersmentioning

confidence: 99%

“…Public-key cryptography based on the Rivest-Shamir-Adleman (RSA) system benefits from the efficient Montgomery modulo reduction [2,3]. Similarly, elliptic curve cryptography (ECC) systems over prime fields apply Montgomery reduction to support arbitrary prime curves [4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%