Boneh and Venkatesan proposed a problem called the hidden number problem and they gave a polynomial time algorithm to solve it. And they showed that one can compute g(xy) from g(x) and g(y) if one has an oracle which computes roughly root log p most significant bits of g(xy) from given g(x) and g(y) in F(p) by using an algorithm for solving the hidden number problem. Later, Shparlinski showed that one can compute g(x2) if one can compute roughly root log p most significant bits of g(x2) from given g(x). In this paper we extend these results by using some improvements on the hidden number problem and the bound of exponential sums. We show that for given g, g(alpha),...g(alpha l) is an element of F(p)*, computing about root log p most significant bits of g(1/alpha) is as hard as computing g(1/alpha) itself, provided that the multiplicative order of g is prime and not too small. Furthermore, we show that we can do it when g has even much smaller multiplicative order in some special cases. (C) 2010 Elsevier B.V. All rights reserved.

- Publisher
- ELSEVIER SCIENCE BV

- Issue Date
- 2010-09

- Language
- English

- Article Type
- Article

- Citation
INFORMATION PROCESSING LETTERS, v.110, no.18-19, pp.799 - 802

- ISSN
- 0020-0190

- Appears in Collection
- MA-Journal Papers(저널논문)

- Files in This Item
- There are no files associated with this item.

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.