TY - GEN
T1 - Extractors for jacobians of binary genus-2 hyperelliptic curves
AU - Farashahi, Reza Rezaeian
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.
KW - Deterministic extractor
KW - Hyperelliptic curve
KW - Jacobian
UR - http://www.scopus.com/inward/record.url?scp=70349887605&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-70500-0-33
DO - 10.1007/978-3-540-70500-0-33
M3 - Conference proceeding contribution
AN - SCOPUS:70349887605
SN - 3540699716
SN - 9783540699712
VL - 5107 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 447
EP - 462
BT - Information Security and Privacy - 13th Australasian Conference, ACISP 2008, Proceedings
A2 - Mu, Yi
A2 - Susilo, Willy
A2 - Seberry, Jennifer
T2 - 13th Australasian Conference on Information Security and Privacy, ACISP 2008
Y2 - 7 July 2008 through 9 July 2008
ER -