Concurrent Error Detection in Montgomery Multiplication over GF(2m)

Che-Wun CHIOU  Chiou-Yng LEE  An-Wen DENG  Jim-Min LIN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.2   pp.566-574
Publication Date: 2006/02/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.2.566
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Security
cryptography,  Montgomery multiplication,  finite field arithmetic,  fault-tolerant computing,  concurrent error detection,  

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Because fault-based attacks on cryptosystems have been proven effective, fault diagnosis and tolerance in cryptography have started a new surge of research and development activity in the field of applied cryptography. Without magnitude comparisons, the Montgomery multiplication algorithm is very attractive and popular for Elliptic Curve Cryptosystems. This paper will design a Montgomery multiplier array with a bit-parallel architecture in GF(2m) with concurrent error detection capability to protect it against fault-based attacks. The robust Montgomery multiplier array with concurrent error detection requires only about 0.2% extra space overhead (if m=512 is as an example) and requires four extra clock cycles compared to the original Montgomery multiplier array without concurrent error detection.