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A Group Action on Z(p)(x) and the Generalized DLP with Auxiliary Inputs

Cited 5 time in Web of Science Cited 5 time in Scopus
Authors

Cheon, Jung Hee; Kim, Taechan; Song, Yong Soo

Issue Date
2014-05
Publisher
Springer Verlag
Citation
Lecture Notes in Computer Science, Vol.8282, pp.121-135
Abstract
The Discrete Logarithm Problem with Auxiliary Inputs (DLPwAI) is an important cryptographic hard problem to compute alpha is an element of Z(p) for given g, g(alpha),..., g(alpha d) where g is a generator of a group of order p. In this paper, we introduce a generalized version of this problem, so called the generalized DLPwAI (GDLPwAI) problem which is asked to compute a for given g, g(alpha e1), ..., g(alpha ed), and propose an efficient algorithm when K := {e(1), ..., e(d)} is a multiplicative subgroup of Z(p-1)(x) . Although the previous algorithms can only compute a when p +/- 1 has a small divisor d, our algorithm resolves the problem when neither p + 1 or p - 1 has an appropriate small divisor. Our method exploits a group action of K on Z(p)(x) to partition Z(p)(x) efficiently.
ISSN
0302-9743
URI
https://hdl.handle.net/10371/201215
DOI
https://doi.org/10.1007/978-3-662-43414-7_6
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  • College of Engineering
  • Dept. of Computer Science and Engineering
Research Area Cryptography, Privacy, Security

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