TY - GEN

T1 - On the complexity of computing discrete logarithms over algebraic tori

AU - Isobe, Shuji

AU - Koizumi, Eisuke

AU - Nishigaki, Yuji

AU - Shizuya, Hiroki

PY - 2009/12/14

Y1 - 2009/12/14

N2 - This paper studies the complexity of computing discrete logarithms over algebraic tori. We show that the order certified version of the discrete logarithm over general finite fields (OCDL, in symbols) reduces to the discrete logarithm over algebraic tori (TDL, in symbols) with respect to the polynomial-time Turing reducibility. This reduction means that if the integer factorization can be computed in polynomial time, then TDL is equivalent to the discrete logarithm DL over general finite fields with respect to the Turing reducibility.

AB - This paper studies the complexity of computing discrete logarithms over algebraic tori. We show that the order certified version of the discrete logarithm over general finite fields (OCDL, in symbols) reduces to the discrete logarithm over algebraic tori (TDL, in symbols) with respect to the polynomial-time Turing reducibility. This reduction means that if the integer factorization can be computed in polynomial time, then TDL is equivalent to the discrete logarithm DL over general finite fields with respect to the Turing reducibility.

KW - Algebraic tori

KW - Order certified discrete logarithms

KW - Turing reduction

UR - http://www.scopus.com/inward/record.url?scp=71549149987&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=71549149987&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-10433-6_29

DO - 10.1007/978-3-642-10433-6_29

M3 - Conference contribution

AN - SCOPUS:71549149987

SN - 3642104320

SN - 9783642104329

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

SP - 433

EP - 442

BT - Cryptology and Network Security - 8th International Conference, CANS 2009, Proceedings

T2 - 8th International Conference on Cryptology and Network Security, CANS 2009

Y2 - 12 December 2009 through 14 December 2009

ER -