International Association for Cryptologic Research

International Association
for Cryptologic Research

IACR News item: 30 June 2015

Nicolas Méloni, M. Anwar Hasan
ePrint Report ePrint Report
Modular exponentiation is core to today\'s main stream

public key cryptographic systems. In this article, we generalize the

classical fractional $w$NAF method for modular exponentiation -- the

classical method uses a digit set of the form $\\{1,3,\\dots,m\\}$

which is extended here to any set of odd integers of the form

$\\{1,d_2,\\dots, d_n\\}$. We give a formula for the average density of

non-zero terms in this new representation and discuss its asymptotic

behavior when those digits are randomly chosen from a given set. We

also propose a specific method for the precomputation phase of the

exponentiation algorithm.

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