A method for obtaining digital signatures and public-key cryptosystems
Communications of the ACM
Checking Before Output May Not Be Enough Against Fault-Based Cryptanalysis
IEEE Transactions on Computers
Distinguishing Exponent Digits by Observing Modular Subtractions
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
ElectroMagnetic Analysis (EMA): Measures and Counter-Measures for Smart Cards
E-SMART '01 Proceedings of the International Conference on Research in Smart Cards: Smart Card Programming and Security
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
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
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
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
On the Performance of Signature Schemes Based on Elliptic Curves
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Montgomery Exponentiation with no Final Subtractions: Improved Results
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
Universal Exponentiation Algorithm
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
An Implementation of DES and AES, Secure against Some Attacks
CHES '01 Proceedings of the Third 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
Electromagnetic Analysis: Concrete Results
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Low-Cost Solutions for Preventing Simple Side-Channel Analysis: Side-Channel Atomicity
IEEE Transactions on Computers
Power Analysis Attacks: Revealing the Secrets of Smart Cards (Advances in Information Security)
Power Analysis Attacks: Revealing the Secrets of Smart Cards (Advances in Information Security)
Exponent Recoding and Regular Exponentiation Algorithms
AFRICACRYPT '09 Proceedings of the 2nd International Conference on Cryptology in Africa: Progress in Cryptology
Faster addition and doubling on elliptic curves
ASIACRYPT'07 Proceedings of the Advances in Crypotology 13th international conference on Theory and application of cryptology and information security
Complete atomic blocks for elliptic curves in jacobian coordinates over prime fields
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Journal of Systems and Software
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In this paper we propose a multiplicative blinding scheme for protecting implementations of a scalar multiplication over elliptic curves. Specifically, this blinding method applies to elliptic curves in the short Weierstraß form over large prime fields. The described countermeasure is shown to be a generalization of the use of random curve isomorphisms to prevent side-channel analysis, and our best configuration of this countermeasure is shown to be equivalent to the use of random curve isomorphisms. Furthermore, we describe how this countermeasure, and therefore random curve isomorphisms, can be efficiently implemented using Montgomery multiplication.