Elliptic Curve Based Password Authenticated Key Exchange Protocols
ACISP '01 Proceedings of the 6th Australasian Conference on Information Security and Privacy
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Toward Hierarchical Identity-Based Encryption
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Short Signatures from the Weil Pairing
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
Hierarchical ID-Based Cryptography
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
ID-Based Blind Signature and Ring Signature from Pairings
ASIACRYPT '02 Proceedings of the 8th International Conference on the Theory and Application of Cryptology and Information Security: Advances in Cryptology
An Identity-Based Signature from Gap Diffie-Hellman Groups
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
PKC '03 Proceedings of the 6th International Workshop on Theory and Practice in Public Key Cryptography: Public Key Cryptography
On Exponential Sums and Group Generators for Elliptic Curves over Finite Fields
ANTS-IV Proceedings of the 4th International Symposium on Algorithmic Number Theory
The Weil and Tate Pairings as Building Blocks for Public Key Cryptosystems
ANTS-V Proceedings of the 5th International Symposium on Algorithmic Number Theory
Pairing-Friendly Hyperelliptic Curves with Ordinary Jacobians of Type y2 = x5 + ax
Pairing '08 Proceedings of the 2nd international conference on Pairing-Based Cryptography
Generating Genus Two Hyperelliptic Curves over Large Characteristic Finite Fields
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
How to Hash into Elliptic Curves
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Aggregate and verifiably encrypted signatures from bilinear maps
EUROCRYPT'03 Proceedings of the 22nd international conference on Theory and applications of cryptographic techniques
Efficient indifferentiable hashing into ordinary elliptic curves
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Construction of rational points on elliptic curves over finite fields
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
Verified indifferentiable hashing into elliptic curves
POST'12 Proceedings of the First international conference on Principles of Security and Trust
Indifferentiable hashing to barreto---naehrig curves
LATINCRYPT'12 Proceedings of the 2nd international conference on Cryptology and Information Security in Latin America
Elligator: elliptic-curve points indistinguishable from uniform random strings
Proceedings of the 2013 ACM SIGSAC conference on Computer & communications security
Verified indifferentiable hashing into elliptic curves
Journal of Computer Security - Security and Trust Principles
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In this paper we propose a very simple and efficient encoding function from Fq to points of a hyperelliptic curve over Fq of the form H: y2 = f(x) where f is an odd polynomial. Hyperelliptic curves of this type have been frequently considered in the literature to obtain Jacobians of good order and pairing-friendly curves. Our new encoding is nearly a bijection to the set of Fq-rational points on H. This makes it easy to construct well-behaved hash functions to the Jacobian J of H, as well as injective maps to J(Fq) which can be used to encode scalars for such applications as ElGamal encryption. The new encoding is already interesting in the genus 1 case, where it provides a well-behaved encoding to Joux's supersingular elliptic curves.