On the Complexity of Computing Discrete Logarithms over Algebraic Tori

被引：0

作者：

Isobe, Shuji ^{[1
]}

Koizumi, Eisuke ^{[1
]}

Nishigaki, Yuji ^{[1
]}

Shizuya, Hiroki ^{[1
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Dept Math & Comp Sci, Sendai, Miyagi 9808576, Japan

来源：

IEICE TRANSACTIONS ON INFORMATION AND SYSTEMS | 2014年 / E97D卷 / 03期

关键词：

algebraic tori; order certified discrete logarithm; Turing reduction; CRYPTOGRAPHY; CRYPTOSYSTEMS; XTR;

D O I：

10.1587/transinf.E97.D.442

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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

引用

页码：442 / 447

页数：6

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