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
IEEE Transactions on Computers
SAC '02 Revised Papers from the 9th Annual International Workshop on Selected Areas in Cryptography
CRYPTO '99 Proceedings of the 19th Annual International Cryptology Conference on Advances in Cryptology
Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
An Improved Algorithm for Arithmetic on a Family of Elliptic Curves
CRYPTO '97 Proceedings of the 17th 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
Two Efficient Algorithms for Arithmetic of Elliptic Curves Using Frobenius Map
PKC '98 Proceedings of the First International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
An Alternate Decomposition of an Integer for Faster Point Multiplication on Certain Elliptic Curves
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
Preventing SPA/DPA in ECC Systems Using the Jacobi Form
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Hessian Elliptic Curves and Side-Channel 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
Preventing Differential Analysis in GLV Elliptic Curve Scalar Multiplication
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
EUROCRYPT'99 Proceedings of the 17th international conference on Theory and application of cryptographic techniques
New Frobenius expansions for elliptic curves with efficient endomorphisms
ICISC'02 Proceedings of the 5th international conference on Information security and cryptology
Improved algorithms for efficient arithmetic on elliptic curves using fast endomorphisms
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
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There have been various methods to prevent DPA (Differential Power Analysis) on elliptic curve cryptosystems. As for the curves with efficient endomorphisms, Hasan suggested several countermeasures on anomalous binary curves, and Ciet, Quisquater and Sica proposed a countermeasure on GLV curves. Ciet et al.'s method is based on random decomposition of a scalar, and it is a two-dimensional generalization of Coron's method. Hasan's and Ciet et al.'s countermeasures are applied only to a small class of elliptic curves. In this paper, we enlarge the class of DPA-resistant curves by proposing a DPA countermeasure applicable to any curve where the Frobenius expansion method can be used. Our analysis shows that our countermeasure can produce a probability of collision around O (2−20) with only 15.4–34.0% extra computation for scalar multiplications on various practical settings.