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Efficient Regular Modular Exponentiation Using Multiplicative Half-Size Splitting

Christophe Negre 1 Thomas Plantard 2
1 DALI - Digits, Architectures et Logiciels Informatiques
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier, UPVD - Université de Perpignan Via Domitia
Abstract : In this paper, we consider efficient RSA modular exponentiations x^K \mod N which are regular and constant time. We first review the multiplicative splitting of an integer x modulo N into two half-size integers. We then take advantage of this splitting to modify the square-and-multiply exponentiation as a regular sequence of squarings always followed by a multiplication by a half-size integer. The proposed method requires around 16% less word operations compared to Montgomery-ladder, square-always and square-and-multiply-always exponentiations. These theoretical results are validated by our implementation results which show an improvement by more than 12% compared approaches which are both regular and constant time.
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Submitted on : Friday, August 21, 2015 - 8:39:24 AM
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Christophe Negre, Thomas Plantard. Efficient Regular Modular Exponentiation Using Multiplicative Half-Size Splitting. Journal of Cryptographic Engineering, Springer, 2017, 7 (3), pp.245-253. ⟨10.1007/s13389-016-0134-5⟩. ⟨hal-01185249⟩



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