Advances in Applied Mathematics
Strong password-only authenticated key exchange
ACM SIGCOMM Computer Communication Review
Finite fields
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Hessian Elliptic Curves and Side-Channel Attacks
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The Hessian Form of an Elliptic Curve
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
How to Hash into Elliptic Curves
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
Provably secure password-authenticated key exchange using Diffie-Hellman
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
New formulae for efficient elliptic curve arithmetic
INDOCRYPT'07 Proceedings of the cryptology 8th international conference on Progress in cryptology
Faster group operations on elliptic curves
AISC '09 Proceedings of the Seventh Australasian Conference on Information Security - Volume 98
Efficient indifferentiable hashing into ordinary elliptic curves
CRYPTO'10 Proceedings of the 30th annual conference on Advances in cryptology
Estimating the size of the image of deterministic hash functions to elliptic curves
LATINCRYPT'10 Proceedings of the First international conference on Progress in cryptology: cryptology and information security in Latin America
Deterministic encoding and hashing to odd hyperelliptic curves
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Encoding points on hyperelliptic curves over finite fields in deterministic polynomial time
Pairing'10 Proceedings of the 4th international conference on Pairing-based cryptography
Construction of rational points on elliptic curves over finite fields
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Efficient arithmetic on hessian curves
PKC'10 Proceedings of the 13th international conference on Practice and Theory in Public Key Cryptography
Factorization of Trinomials over Galois Fields of Characteristic 2
Finite Fields and Their Applications
The geometry of flex tangents to a cubic curve and its parameterizations
Journal of Symbolic Computation
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
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We describe a hashing function from the elements of the finite field Fq into points on a Hessian curve. Our function features the uniform and smaller size for the cardinalities of almost all fibers compared with the other known hashing functions for elliptic curves. For ordinary Hessian curves, this function is 2 : 1 for almost all points. More precisely, for odd q, the cardinality of the image set of the function is exactly given by (q + i + 2)/2 for some i = -1, 1. Next, we present an injective hashing function from the elements of Zm into points on a Hessian curve over Fq with odd q and m = (q+i)/2 for some i = -1, 1, 3.