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 NegreConnect in order to contact the contributor Submitted on : Friday, August 21, 2015 - 8:39:24 AM Last modification on : Tuesday, March 15, 2022 - 12:55:43 PM Long-term archiving on: : Wednesday, April 26, 2017 - 9:43:59 AM