TY - GEN
T1 - Extractors for Jacobians of binary genus-2 hyperelliptic curves
AU - Rezaeian Farashahi, R.
PY - 2008
Y1 - 2008
N2 - Extractors are an important ingredient in designing key exchange protocols and secure pseudorandom sequences in the standard model. Elliptic and hyperelliptic curves are gaining more and more interest due to their fast arithmetic and the fact that no subexponential attacks against the discrete logarithm problem are known.
In this paper we propose two simple and efficient deterministic extractors for , the Jacobian of a genus 2 hyperelliptic curve H defined over , where q¿=¿2 n , called the sum and product extractors.
For non-supersingular hyperelliptic curves having a Jacobian with group order 2m, where m is odd, we propose the modified sum and product extractors for the main subgroup of . We show that, if is chosen uniformly at random, the bits extracted from D are indistinguishable from a uniformly random bit-string of length n.
AB - Extractors are an important ingredient in designing key exchange protocols and secure pseudorandom sequences in the standard model. Elliptic and hyperelliptic curves are gaining more and more interest due to their fast arithmetic and the fact that no subexponential attacks against the discrete logarithm problem are known.
In this paper we propose two simple and efficient deterministic extractors for , the Jacobian of a genus 2 hyperelliptic curve H defined over , where q¿=¿2 n , called the sum and product extractors.
For non-supersingular hyperelliptic curves having a Jacobian with group order 2m, where m is odd, we propose the modified sum and product extractors for the main subgroup of . We show that, if is chosen uniformly at random, the bits extracted from D are indistinguishable from a uniformly random bit-string of length n.
U2 - 10.1007/978-3-540-70500-0_33
DO - 10.1007/978-3-540-70500-0_33
M3 - Conference contribution
SN - 978-3-540-69971-2
T3 - Lecture Notes in Computer Science
SP - 447
EP - 462
BT - Information Security and Privacy (13th Australasian Conference, ACISP 2008, Wollongong, Australia, July 7-9, 2008, Proceedings)
A2 - Mu, Y.
A2 - Susilo, W.
A2 - Seberry, J.
PB - Springer
CY - Berlin
ER -