A low-complexity LUT-based squaring algorithm

Authors:
Te-Jen Chang;Chia-Long Wu;Der-Chyuan Lou;Ching-Yin Chen
Affiliations:
Department of Electrical Engineering, Chung Cheng Institute of Technology, National Defense University, Tahsi, Taoyuan 33509, Taiwan;Department of Aviation & Communication Electronics, Chinese Air Force Institute of Technology, Kaohsiung 82042, Taiwan;Department of Electrical Engineering, Chung Cheng Institute of Technology, National Defense University, Tahsi, Taoyuan 33509, Taiwan;Department of Electrical Engineering, Chung Cheng Institute of Technology, National Defense University, Tahsi, Taoyuan 33509, Taiwan
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

The computation of large modular multi-exponentiation is a time-consuming arithmetic operation used in cryptography. The standard squaring algorithm is well-known and the Guajardo-Paar algorithm fixes the improper carry handling bug produced by the standard squaring algorithm, but produces error-indexing bug. In this paper, a novel squaring algorithm is proposed, which stores base products in the Look-Up Table before the squaring computation and base size comparison method. The proposed algorithm can not only evaluate squaring efficiently but also avoid bugs produced in other proposed algorithms (the Guajardo-Paar algorithm and the Yang-Heih-Laih algorithm). The performance of the proposed algorithm is 1.615 times faster than the standard squaring algorithm and much faster than other algorithms.