How to Improve an Exponentiation Black-Box

Abstract. In this paper we present a method for improving the performance of RSA-type exponentiations. The scheme is based on the observation that replacing the exponent d by d = d + k(n) has no arithmetic impact but results in significant speed-ups when k is properly chosen. Statistical analysis, verified by extensive simulations, confirms a performance improvement of 9.3% for the square-and-multiply scheme and 4.3% for the signed binary digit algorithm. However, the most attractive feature of our method seems to be the fact that in most cases, existing exponentiation black-boxes can be accelerated by simple external one-time pre-computations without any internal code or hardware modifications.

• Type: Conference
• Year: 1998
• Where: EUROCRYPT
• Authors: Gérard D. Cohen, Antoine Lobstein, David Naccache, Gilles Zémor
• Keywords: Binary Digit Algorithm, Cryptology, EUROCRYPT 1998, External One-time Pre-computations, RSA-type Exponentiations