@inproceedings{0ce91d0b29ee4ea797c6a629e73b3922,
title = "The hidden number problem in extension fields and its applications",
abstract = "We present polynomial time algorithms for certain generalizations of the hidden number problem which has played an important role in gaining understanding of the security of commonly suggested one way functions. Namely, we consider an analogue of this problem for a certain class of polynomials over an extension of a finite field; recovering a hidden polynomial given the values of its trace at randomly selected points. Also, we give an algorithm for a variant of the problem in free finite dimensional modules. This result can be helpful for studying security of analogues of the RSA and Diffie–Hellman cryptosystems over such modules. The hidden number problem is also related to the so called black-box field model of computation. We show that simplified versions of the above recovery problems can be used to derive positive results on the computational power of this model.",
author = "Vasco, \{Mar{\'i}a Isabel Gonz{\'a}lez\} and Mats N{\"a}slund and Shparlinski, \{Igor E.\}",
year = "2002",
doi = "10.1007/3-540-45995-2\_14",
language = "English",
volume = "2286",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer, Springer Nature",
pages = "105--117",
editor = "Sergio Rajsbaum",
booktitle = "LATIN 2002",
address = "United States",
note = "5th Latin American Symposium on Theoretical Informatics (LATIN 2002) ; Conference date: 03-04-2002 Through 06-04-2002",
}