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

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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.
Publisher
SPRINGER
Issue Date
2018-01
Language
English
Article Type
Article
Keywords

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Citation

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, v.29, no.1, pp.41 - 57

ISSN
0938-1279
DOI
10.1007/s00200-017-0321-3
URI
http://hdl.handle.net/10203/240094
Appears in Collection
MA-Journal Papers(저널논문)
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