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 -