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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
- 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
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