A New Double Point Multiplication Algorithm and Its Application to Binary Elliptic Curves with Endomorphisms

We present a new double point multiplication algorithm based on differential addition chains. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We discuss deploying our scheme in a hardware implementation of single point mul...

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Bibliographic Details
Published in:IEEE transactions on computers Vol. 63; no. 10; pp. 2614 - 2619
Main Authors: Azarderakhsh, Reza, Karabina, Koray
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Algorithm design and analysis
Algorithms
Availability
Channels
Counting
differential addition chains
double point multiplication
Elliptic curve cryptography
Elliptic curve cryptosystems
Elliptic curves
endomorphism
Gain
Hardware
Multiplication
Multipliers
Resistance
ISSN:0018-9340, 1557-9956
Online Access:Get full text
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Summary:We present a new double point multiplication algorithm based on differential addition chains. Our proposed scheme has a uniform structure and has some degree of built-in resistance against side channel analysis attacks. We discuss deploying our scheme in a hardware implementation of single point multiplication on binary elliptic curves with efficiently computable endomorphisms. Based on operation counts, we expect to gain accelerations of 30% and 18% for computing single point multiplication with and without availability of parallel multipliers, respectively, and these results are verified in our implementations.
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ISSN:0018-9340
1557-9956
DOI:10.1109/TC.2013.112