TY - GEN

T1 - Hashing into Hessian curves

AU - Farashahi, Reza Rezaeian

PY - 2011

Y1 - 2011

N2 - We describe a hashing function from the elements of the finite field double-struck 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 double-struck Fq with odd q and m = (q + i)/2 for some i = - 1,1,3.

AB - We describe a hashing function from the elements of the finite field double-struck 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 double-struck Fq with odd q and m = (q + i)/2 for some i = - 1,1,3.

KW - Elliptic curve cryptography

KW - hashing

KW - Hessian curve

UR - http://www.scopus.com/inward/record.url?scp=79960085090&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-21969-6_17

DO - 10.1007/978-3-642-21969-6_17

M3 - Conference proceeding contribution

AN - SCOPUS:79960085090

SN - 9783642219689

VL - 6737 LNCS

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 278

EP - 289

BT - Progress in Cryptology, AFRICACRYPT 2011 - 4th International Conference on Cryptology in Africa, Proceedings

A2 - Nitaj, Abderrahmane

A2 - Pointcheval, David

T2 - 4th International Conference on the Theory and Application of Cryptographic Techniques, AFRICACRYPT 2011

Y2 - 5 July 2011 through 7 July 2011

ER -