TY - GEN
T1 - Counting points on genus 2 curves with real multiplication
AU - Gaudry, Pierrick
AU - Kohel, David
AU - Smith, Benjamin
PY - 2011/12/12
Y1 - 2011/12/12
N2 - We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite field Fqof large characteristic from Õ(log 8 q) to Õ (log5 q). Using our algorithm we compute a 256-bit prime-order Jacobian, suitable for cryptographic applications, and also the order of a 1024-bit Jacobian.
AB - We present an accelerated Schoof-type point-counting algorithm for curves of genus 2 equipped with an efficiently computable real multiplication endomorphism. Our new algorithm reduces the complexity of genus 2 point counting over a finite field Fqof large characteristic from Õ(log 8 q) to Õ (log5 q). Using our algorithm we compute a 256-bit prime-order Jacobian, suitable for cryptographic applications, and also the order of a 1024-bit Jacobian.
U2 - 10.1007/978-3-642-25385-0_27
DO - 10.1007/978-3-642-25385-0_27
M3 - Conference contribution
AN - SCOPUS:82955177074
SN - 9783642253843
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 504
EP - 519
BT - Advances in Cryptology, ASIACRYPT 2011 - 17th International Conference on the Theory and Application of Cryptology and Information Security, Proceedings
T2 - 17th International Conference on the Theory and Application of Cryptology and Information Security, ASIACRYPT 2011
Y2 - 4 December 2011 through 8 December 2011
ER -