Open AccessOn the generalisation of special moduli for faster interleaved montgomery modular multiplication
Author(s) -
Akleylek Sedat,
Cenk Murat,
Özbudak Ferruh
Publication year - 2013
Publication title -
iet information security
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.308
H-Index - 34
eISSN - 1751-8717
pISSN - 1751-8709
DOI - 10.1049/iet-ifs.2010.0271
Subject(s) - moduli , elliptic curve cryptography , modular arithmetic , elliptic curve , multiplication (music) , mathematics , modular equation , integer (computer science) , arithmetic , cryptography , prime (order theory) , elliptic curve point multiplication , modular design , discrete mathematics , algebra over a field , computer science , algorithm , pure mathematics , public key cryptography , moduli of algebraic curves , moduli space , combinatorics , encryption , physics , quantum mechanics , programming language , operating system
In this study, the authors give a generalisation of special moduli for faster interleaved Montgomery modular multiplication algorithm with simplified pre‐computational phase for GF ( p n ), where p ≥ 2 is a prime number and n is a positive integer. The authors propose different sets of moduli that can be used in elliptic curve crytographic applications and pairing‐based cryptography. Moreover, this method also leads to efficient implementations for the elliptic curve parameters given in standards. It is shown that one can obtain efficient Montgomery modular multiplication architecture in view of the number of AND gates and XOR gates by choosing proposed sets of moduli. The authors eliminate final substraction step with proposed sets of moduli. These methods are easy to implement for hardware.