Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Efficient Arithmetic on Koblitz Curves
Designs, Codes and Cryptography - Special issue on towards a quarter-century of public key cryptography
Elliptic curves in cryptography
Elliptic curves in cryptography
A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
A New Elliptic Curve Scalar Multiplication Algorithm to Resist Simple Power Analysis
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
ACISP '02 Proceedings of the 7th Australian Conference on Information Security and Privacy
Efficient elliptic curve exponentiation
ICICS '97 Proceedings of the First International Conference on Information and Communication Security
ICISC '01 Proceedings of the 4th International Conference Seoul on Information Security and Cryptology
Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Securing Elliptic Curve Point Multiplication against Side-Channel Attacks
ISC '01 Proceedings of the 4th International Conference on Information Security
ISC '02 Proceedings of the 5th International Conference on Information Security
A Second-Order DPA Attack Breaks a Window-Method Based Countermeasure against Side Channel Attacks
ISC '02 Proceedings of the 5th International Conference on Information Security
A Fast Parallel Elliptic Curve Multiplication Resistant against Side Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Weierstraß Elliptic Curves and Side-Channel Attacks
PKC '02 Proceedings of the 5th International Workshop on Practice and Theory in Public Key Cryptosystems: Public Key Cryptography
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Enhancing Simple Power-Analysis Attacks on Elliptic Curve Cryptosystems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Some Security Aspects of the M IST Randomized Exponentiation Algorithm
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Address-Bit Differential Power Analysis of Cryptographic Schemes OK-ECDH and OK-ECDSA
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
DPA Countermeasures by Improving the Window Method
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Breaking the liardet-smart randomized exponentiation algorithm
CARDIS'02 Proceedings of the 5th conference on Smart Card Research and Advanced Application Conference - Volume 5
An efficient group key establishment in location-aided mobile ad hoc networks
PE-WASUN '05 Proceedings of the 2nd ACM international workshop on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks
A-Codes from Rational Functions over Galois Rings
Designs, Codes and Cryptography
Refinements of Miller's algorithm for computing the Weil/Tate pairing
Journal of Algorithms
Highly Regular Right-to-Left Algorithms for Scalar Multiplication
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Twisted Edwards Curves Revisited
ASIACRYPT '08 Proceedings of the 14th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Generalized Scalar Multiplication Secure against SPA, DPA, and RPA
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Jacobi Quartic Curves Revisited
ACISP '09 Proceedings of the 14th Australasian Conference on Information Security and Privacy
Refinements of Miller's algorithm for computing the Weil/Tate pairing
Journal of Algorithms
Encapsulated scalar multiplications and line functions in the computation of Tate pairing
TAMC'07 Proceedings of the 4th international conference on Theory and applications of models of computation
Affine precomputation with sole inversion in elliptic curve cryptography
ACISP'07 Proceedings of the 12th Australasian conference on Information security and privacy
Generalized MMM-algorithm secure against SPA, DPA, and RPA
ICISC'07 Proceedings of the 10th international conference on Information security and cryptology
SAC'07 Proceedings of the 14th international conference on Selected areas in cryptography
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Efficient and secure elliptic curve point multiplication using double-base chains
ASIACRYPT'05 Proceedings of the 11th international conference on Theory and Application of Cryptology and Information Security
A remark on implementing the weil pairing
CISC'05 Proceedings of the First SKLOIS conference on Information Security and Cryptology
Fast bilinear maps from the tate-lichtenbaum pairing on hyperelliptic curves
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Efficient computation of tate pairing in projective coordinate over general characteristic fields
ICISC'04 Proceedings of the 7th international conference on Information Security and Cryptology
A method for efficient parallel computation of Tate pairing
International Journal of Grid and Utility Computing
Group law computations on jacobians of hyperelliptic curves
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
Fast point quadrupling on elliptic curves
Proceedings of the Third Symposium on Information and Communication Technology
Implementing cryptographic pairings
Pairing'07 Proceedings of the First international conference on Pairing-Based Cryptography
Information Sciences: an International Journal
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The side channel attack (SCA) is a serious attack on wearable devices that have scarce computational resources. Cryptographic algorithms on them should be efficient using small memory -- we have to make efforts to optimize the trade-off between efficiency and memory. In this paper we present efficient SCA-resistant scalar multiplications based on window method. Möller proposed an SPA-resistant window method based on 2w-ary window method, which replaces w-consecutive zeros to 1 plus w-consecutive 1 and it requires 2w points of table (or 2w-1 +1 points if the signed 2w-ary is used). The most efficient window method with small memory is the width-w NAF, which requires 2w-2 points of table. In this paper we convert the width-w NAF to an SPA-resistant addition chain. Indeed we generate a scalar sequence with the fixed pattern, e.g. |0..0x|0..0x|...|0..0x|, where x is positive odd points w. Thus the size of the table is 2w-1, which is optimal in the construction of the SPA-resistant chain based on width-w NAF. The table sizes of the proposed scheme are 6% to 50% smaller than those of Möller's scheme for w = 2, 3, 4, 5, which are relevant choices in the sense of efficiency for 160-bit ECC.