Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Timing Attacks on Implementations of Diffie-Hellman, RSA, DSS, and Other Systems
CRYPTO '96 Proceedings of the 16th Annual International Cryptology Conference on Advances in Cryptology
Power Analysis Breaks Elliptic Curve Cryptosystems even Secure against the Timing Attack
INDOCRYPT '00 Proceedings of the First International Conference on Progress in Cryptology
Exceptional Procedure Attackon Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
A Refined Power-Analysis Attack on Elliptic Curve Cryptosystems
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: 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
Protections against Differential Analysis for Elliptic Curve Cryptography
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
New Point Addition Formulae for ECC Applications
WAIFI '07 Proceedings of the 1st international workshop on Arithmetic of Finite Fields
Highly Regular Right-to-Left Algorithms for Scalar Multiplication
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Fast point multiplication on elliptic curves through isogenies
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Co-Z addition formulæ and binary ladders on elliptic curves
CHES'10 Proceedings of the 12th international conference on Cryptographic hardware and embedded systems
Memory-constrained implementations of elliptic curve cryptography in co-Z coordinate representation
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
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On smart-cards, Elliptic Curve Cryptosystems (ECC) can be vulnerable to Side Channel Attacks such as the Refined Power Analysis (RPA). This attack takes advantage of the apparition of special points of the form (0, y). In this paper, we propose a new countermeasure based on co-Z formulæ and an extension of the curve isomorphism countermeasure. It permits to transform the base point P=(x, y) into a base point P′=(0, y′), which, with −P′, are the only points with a zero X-coordinate. In such case, the RPA cannot be applied. Moreover, the cost of this countermeasure is very low compared to other countermeasures against RPA.