Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
Efficient Algorithms for Pairing-Based Cryptosystems
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Advances in Elliptic Curve Cryptography (London Mathematical Society Lecture Note Series)
Constructing Brezing-Weng Pairing-Friendly Elliptic Curves Using Elements in the Cyclotomic Field
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Exponentiation in Pairing-Friendly Groups Using Homomorphisms
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Endomorphisms for Faster Elliptic Curve Cryptography on a Large Class of Curves
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
Constructing pairing-friendly elliptic curves with embedding degree 10
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Pairing-Friendly elliptic curves of prime order
SAC'05 Proceedings of the 12th international conference on Selected Areas in Cryptography
IEEE Transactions on Information Theory
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
Handbook of Elliptic and Hyperelliptic Curve Cryptography, Second Edition
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Designing a code generator for pairing based cryptographic functions
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
A family of implementation-friendly BN elliptic curves
Journal of Systems and Software
Faster pairing computations on curves with high-degree twists
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
SAC'11 Proceedings of the 18th international conference on Selected Areas in Cryptography
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Pairings on elliptic curves usually take as input a point in a subgroup G 1 of an elliptic curve group $E({\mathbb{F}}_p)$ and a point in a subgroup G 2 of $E'({\mathbb{F}}_{p^d})$ for some twist E *** of E . In this paper we consider the problem of hashing to G 2 when the group G 2 has prime order. The naive approach requires multiplication in the group $E'({\mathbb{F}}_{p^d})$ by a large cofactor. Our main result is to describe a fast method to compute this cofactor multiplication; our method exploits an efficiently computable homomorphism.