Multi-exponentiation algorithm based on binary GCD computation and its application to side-channel countermeasure

A series of algorithms for evaluation of multi-exponentiation are proposed based on the binary greatest common divisor algorithm. The proposed algorithms are inversion free and have the capability to evaluate double or multi-exponentiation with non-fixed base numbers and exponents. They can also be...

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Bibliographic Details
Published in:Journal of cryptographic engineering Vol. 2; no. 2; pp. 99 - 110
Main Authors: Yen, Sung-Ming, Chen, Chien-Ning, Moon, SangJae
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer-Verlag 01.09.2012
Subjects:
Circuits and Systems
Communications Engineering
Computer Communication Networks
Computer Science
Cryptology
Data Structures and Information Theory
Networks
Operating Systems
Regular Paper
Multi-exponentiation
Euclidean algorithm
Binary GCD algorithm
Greatest common divisor
Exponentiation
Public-key cryptography
Side-channel attack
ISSN:2190-8508, 2190-8516
Online Access:Get full text
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Summary:A series of algorithms for evaluation of multi-exponentiation are proposed based on the binary greatest common divisor algorithm. The proposed algorithms are inversion free and have the capability to evaluate double or multi-exponentiation with non-fixed base numbers and exponents. They can also be employed in developing side-channel countermeasures. For n -bit double and triple exponentiation, they achieve the average complexity of 1.53 n and 1.75 n multiplications (including squarings), respectively. The proposed algorithms can be very useful for the implementation of many public-key cryptosystems on small devices with limited memory space, e.g., smart cards.
ISSN:2190-8508
2190-8516
DOI:10.1007/s13389-012-0032-4