The l-th power Diffie-Hellman problem and the l-th root Diffie-Hellman problem

被引：0

作者：

Roh, Dongyoung ^{[1
]}

Kim, I-Yeol ^{[2
]}

Hahn, Sang Geun ^{[2
]}

机构：

[1] Natl Secur Res Inst, Daejeon, South Korea

[2] Korea Adv Inst Sci & Technol, Daejeon, South Korea

来源：

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING | 2018年 / 29卷 / 01期

关键词：

Discrete logarithm problem; Computational Diffie-Hellman problem; Square Diffie-Hellman problem; Square root Diffie-Hellman problem; l-th power Diffie-Hellman problem; l-th root Diffie-Hellman problem; SIGNATURE SCHEMES;

D O I：

10.1007/s00200-017-0321-3

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

There are many variants of the computational Diffie-Hellman problem that are necessary to provide security of many cryptographic schemes. Two of them are the square Diffie-Hellman problem and the square root Diffie-Hellman problem. Recently, the first and third authors proved that these two problems are polynomial-time equivalent under a certain condition (Roh and Hahn in Des Codes Cryptogr 62(2): 179-187, 2011). In this paper, we generalize this result. We introduce the l-th power Diffie-Hellman problem and the l-th root Diffie-Hellman problem and show that these two problems are polynomial-time equivalent for l = O(log p) under a condition similar to that of Roh and Hahn (2011), where p is the order of the underlying group.

引用

页码：41 / 57

页数：17

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