Title :
Selected RNS Bases for Modular Multiplication
Author :
Bajard, J.C. ; Kaihara, M. ; Plantard, T.
Author_Institution :
LIRMM, Univ. Montpellier 2, Montpellier, France
Abstract :
The selection of the elements of the bases in an RNS modular multiplication method is crucial and has a great impact in the overall performance.This work proposes specific sets of optimal RNS moduli with elements of Hamming weight three whose inverses used in the MRS reconstruction have very small Hamming weight. This property is exploited in RNS bases conversions, to completely remove and replace the products by few additions/subtractions and shifts, reducing the time complexity of modular multiplication.These bases are specially crafted to computation with operands of sizes 256 or more and are suitable for cryptographic applications such as the ECC protocols.
Keywords :
cryptography; residue number systems; Hamming weight; RNS; cryptographic applications; modular multiplication; residue number system; Application software; Australia; Costs; Cryptographic protocols; Digital arithmetic; Digital signal processing; Elliptic curve cryptography; Hamming weight; Public key cryptography; Signal processing algorithms; cryptography application; modular arithmetic; residue number systems;
Conference_Titel :
Computer Arithmetic, 2009. ARITH 2009. 19th IEEE Symposium on
Conference_Location :
Portland, OR
Print_ISBN :
978-0-7695-3670-5
DOI :
10.1109/ARITH.2009.20
