A fast parallel elliptic curve multiplication resistant against side channel attacks

Tetsuya Izu, Tsuyoshi Takagi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

92 Citations (Scopus)

Abstract

This paper proposes a fast elliptic curve multiplication algorithm applicable for any types of curves over finite fields Fp (p a prime), based on [Mon87], together with criteria which make our algorithm resistant against the side channel attacks (SCA). The algorithm improves both on an addition chain and an addition formula in the scalar multiplication. Our addition chain requires no table look-up (or a very small number of pre-computed points) and a prominent property is that it can be implemented in parallel. The computing time for n-bit scalar multiplication is one ECDBL + (n −1) ECADDs in the parallel case and (n −1) ECDBLs + (n −1) ECADDs in the single case. We also propose faster addition formulas which only use the x-coordinates of the points. By combination of our addition chain and addition formulas, we establish a faster scalar multiplication resistant against the SCA in both single and parallel computation. The improvement of our scalar multiplications over the previous method is about 37% for two processors and 5.7% for a single processor. Our scalar multiplication is suitable for the implementation on smart cards.

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
EditorsDavid Naccache, Pascal Paillier
PublisherSpringer Verlag
Pages280-296
Number of pages17
ISBN (Print)3540431683, 9783540431688
DOIs
Publication statusPublished - Jan 1 2002
Event5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002 - Paris, France
Duration: Feb 12 2002Feb 14 2002

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2274
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002
CountryFrance
CityParis
Period2/12/022/14/02

Fingerprint

Scalar multiplication
Side Channel Attacks
Elliptic Curves
Addition Chains
Multiplication
Addition formula
Smart cards
Smart Card
Look-up Table
Parallel Computation
Galois field
Side channel attack
Curve
Computing

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Izu, T., & Takagi, T. (2002). A fast parallel elliptic curve multiplication resistant against side channel attacks. In D. Naccache, & P. Paillier (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 280-296). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2274). Springer Verlag. https://doi.org/10.1007/3-540-45664-3_20

A fast parallel elliptic curve multiplication resistant against side channel attacks. / Izu, Tetsuya; Takagi, Tsuyoshi.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / David Naccache; Pascal Paillier. Springer Verlag, 2002. p. 280-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2274).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Izu, T & Takagi, T 2002, A fast parallel elliptic curve multiplication resistant against side channel attacks. in D Naccache & P Paillier (eds), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2274, Springer Verlag, pp. 280-296, 5th International Workshop on Practice and Theory in Public Key Cryptosystems, PKC 2002, Paris, France, 2/12/02. https://doi.org/10.1007/3-540-45664-3_20
Izu T, Takagi T. A fast parallel elliptic curve multiplication resistant against side channel attacks. In Naccache D, Paillier P, editors, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2002. p. 280-296. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45664-3_20
Izu, Tetsuya ; Takagi, Tsuyoshi. / A fast parallel elliptic curve multiplication resistant against side channel attacks. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / David Naccache ; Pascal Paillier. Springer Verlag, 2002. pp. 280-296 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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