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.
https://hal.archives-ouvertes.fr/hal-01185249
Contributor : Christophe Negre
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Submitted on : Friday, August 21, 2015 - 8:39:24 AM
Last modification on : Saturday, February 16, 2019 - 9:34:27 AM
Document(s) archivé(s) le : Wednesday, April 26, 2017 - 9:43:59 AM
