REVIEW PAPER
APPLICATIONS OF L-FUNCTIONS IN CRYPTOLOGY
1
Uniwersytet Adama Mickiewicza w Poznaniu
Publication date: 2014-12-05
SBN 2014;6(2): 259-270
KEYWORDS
ABSTRACT
Security of asymmetric cryptological systems is based on the unproved hypothesis that one-way functions do exist. Some difficult computational problems in number
theory, such as factorization or a discrete logarithm problem in finite Abelian groups
may serve as a basis for constructing presumably one-way functions. The idea of using
L-functions (elements of the Selberg class) in this context goes back to M. Anshel and
D. Goldfeld (1997). Following them we describe an authentication protocol and an elliptic pseudo-random generator. The former uses Dirichlet L-functions, and the latter
Hasse-Weil L-functions of elliptic curves over Q. We conclude by proposing a protocol
of coin toss by phone based on the use of non-trivial zeros of L-functions.
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| ISSN: | 2082-2677 |
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