IEICE TRANSACTIONS on Fundamentals
Fast Elliptic Curve Multiplications Resistant against Side Channel Attacks
Summary :
This paper proposes fast elliptic curve multiplication algorithms resistant against side channel attacks, based on the Montgomery-type scalar multiplication. The proposed scalar multiplications can be applied to all curves over prime fields, e.g., any standardized curves over finite fields with characteristic larger than 3. The method utilizes the addition formulas xECDBL and xECADD assembled by only x-coordinates of points, and is applicable for any types of curves over finite fields. Then, we encapsulate two addition formulas into one formula xECADDDBL, which accomplishes a faster computation because several auxiliary variables of two formulas can be shared. We also develop a novel addition chain for the new formula, with which we can compute scalar multiplications. The improvement of our scalar multiplications over previous Coron's dummy operation method is about 18% for a 160-bit scalar multiplication. Our method requires no table-up of precomputed points and it is suitable for the implementation on memory constraint computing architectures, e.g., smart cards. Moreover, we optimize the proposed algorithms for parallelized implementations with SIMD operations. Compared with the similar scheme proposed by Fischer et al., our scheme is about 16% faster.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.1 pp.161-171
- Publication Date
- 2005/01/01
- Publicized
- Online ISSN
- DOI
- 10.1093/ietfec/e88-a.1.161
- Type of Manuscript
- Special Section PAPER (Special Section on Cryptography and Information Security)
- Category
- Tamper-Resistance
Authors
Keyword
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Tetsuya IZU, Tsuyoshi TAKAGI, "Fast Elliptic Curve Multiplications Resistant against Side Channel Attacks" in IEICE TRANSACTIONS on Fundamentals,
vol. E88-A, no. 1, pp. 161-171, January 2005, doi: 10.1093/ietfec/e88-a.1.161.
Abstract: This paper proposes fast elliptic curve multiplication algorithms resistant against side channel attacks, based on the Montgomery-type scalar multiplication. The proposed scalar multiplications can be applied to all curves over prime fields, e.g., any standardized curves over finite fields with characteristic larger than 3. The method utilizes the addition formulas xECDBL and xECADD assembled by only x-coordinates of points, and is applicable for any types of curves over finite fields. Then, we encapsulate two addition formulas into one formula xECADDDBL, which accomplishes a faster computation because several auxiliary variables of two formulas can be shared. We also develop a novel addition chain for the new formula, with which we can compute scalar multiplications. The improvement of our scalar multiplications over previous Coron's dummy operation method is about 18% for a 160-bit scalar multiplication. Our method requires no table-up of precomputed points and it is suitable for the implementation on memory constraint computing architectures, e.g., smart cards. Moreover, we optimize the proposed algorithms for parallelized implementations with SIMD operations. Compared with the similar scheme proposed by Fischer et al., our scheme is about 16% faster.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.1.161/_p
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@ARTICLE{e88-a_1_161,
author={Tetsuya IZU, Tsuyoshi TAKAGI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Fast Elliptic Curve Multiplications Resistant against Side Channel Attacks},
year={2005},
volume={E88-A},
number={1},
pages={161-171},
abstract={This paper proposes fast elliptic curve multiplication algorithms resistant against side channel attacks, based on the Montgomery-type scalar multiplication. The proposed scalar multiplications can be applied to all curves over prime fields, e.g., any standardized curves over finite fields with characteristic larger than 3. The method utilizes the addition formulas xECDBL and xECADD assembled by only x-coordinates of points, and is applicable for any types of curves over finite fields. Then, we encapsulate two addition formulas into one formula xECADDDBL, which accomplishes a faster computation because several auxiliary variables of two formulas can be shared. We also develop a novel addition chain for the new formula, with which we can compute scalar multiplications. The improvement of our scalar multiplications over previous Coron's dummy operation method is about 18% for a 160-bit scalar multiplication. Our method requires no table-up of precomputed points and it is suitable for the implementation on memory constraint computing architectures, e.g., smart cards. Moreover, we optimize the proposed algorithms for parallelized implementations with SIMD operations. Compared with the similar scheme proposed by Fischer et al., our scheme is about 16% faster.},
keywords={},
doi={10.1093/ietfec/e88-a.1.161},
ISSN={},
month={January},}
Copy
TY - JOUR
TI - Fast Elliptic Curve Multiplications Resistant against Side Channel Attacks
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 161
EP - 171
AU - Tetsuya IZU
AU - Tsuyoshi TAKAGI
PY - 2005
DO - 10.1093/ietfec/e88-a.1.161
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2005
AB - This paper proposes fast elliptic curve multiplication algorithms resistant against side channel attacks, based on the Montgomery-type scalar multiplication. The proposed scalar multiplications can be applied to all curves over prime fields, e.g., any standardized curves over finite fields with characteristic larger than 3. The method utilizes the addition formulas xECDBL and xECADD assembled by only x-coordinates of points, and is applicable for any types of curves over finite fields. Then, we encapsulate two addition formulas into one formula xECADDDBL, which accomplishes a faster computation because several auxiliary variables of two formulas can be shared. We also develop a novel addition chain for the new formula, with which we can compute scalar multiplications. The improvement of our scalar multiplications over previous Coron's dummy operation method is about 18% for a 160-bit scalar multiplication. Our method requires no table-up of precomputed points and it is suitable for the implementation on memory constraint computing architectures, e.g., smart cards. Moreover, we optimize the proposed algorithms for parallelized implementations with SIMD operations. Compared with the similar scheme proposed by Fischer et al., our scheme is about 16% faster.
ER -
English
