63 research outputs found
Generalized Riemann hypotheses: sufficient and equivalent criteria
This paper presents new sufficient and equivalent conditions for the
generalized version of the Riemann Hypothesis. The paper derives also
statements and remarks concerning zero-free regions, modified Hadamard-product
formulas and the behaviour of .Comment: Few changes. Accepted for publication in JP Journal of Algebra,
Number Theory and Application
Zeros of the Hurwitz zeta function in the interval (0,1)
We first give a condition on the parameters under which the Hurwitz
zeta function has no zeros and is actually negative. As a
corollary we derive that it is nonzero for and and, as a
particular instance, the known result that the classical zeta function has no
zeros in .Comment: Some reformulation done. Accepted for publication in Journal of
Combinatorics and Number Theor
On Canonical Subfield Preserving Polynomials
Explicit monoid structure is provided for the class of canonical subfield
preserving polynomials over finite fields. Some classical results and
asymptotic estimates will follow as corollaries.Comment: (To appear in Acta Arithmetica
Coding Solutions for the Secure Biometric Storage Problem
The paper studies the problem of securely storing biometric passwords, such
as fingerprints and irises. With the help of coding theory Juels and Wattenberg
derived in 1999 a scheme where similar input strings will be accepted as the
same biometric. In the same time nothing could be learned from the stored data.
They called their scheme a "fuzzy commitment scheme". In this paper we will
revisit the solution of Juels and Wattenberg and we will provide answers to two
important questions: What type of error-correcting codes should be used and
what happens if biometric templates are not uniformly distributed, i.e. the
biometric data come with redundancy. Answering the first question will lead us
to the search for low-rate large-minimum distance error-correcting codes which
come with efficient decoding algorithms up to the designed distance. In order
to answer the second question we relate the rate required with a quantity
connected to the "entropy" of the string, trying to estimate a sort of
"capacity", if we want to see a flavor of the converse of Shannon's noisy
coding theorem. Finally we deal with side-problems arising in a practical
implementation and we propose a possible solution to the main one that seems to
have so far prevented real life applications of the fuzzy scheme, as far as we
know.Comment: the final version appeared in Proceedings Information Theory Workshop
(ITW) 2010, IEEE copyrigh
Efficient evaluation of polynomials over finite fields
A method is described which allows to evaluate efficiently a polynomial in a
(possibly trivial) extension of the finite field of its coefficients. Its
complexity is shown to be lower than that of standard techniques when the
degree of the polynomial is large with respect to the base field. Applications
to the syndrome computation in the decoding of cyclic codes, Reed-Solomon codes
in particular, are highlighted.Comment: presented at AusCTW 201
The Rabin cryptosystem revisited
The Rabin public-key cryptosystem is revisited with a focus on the problem of
identifying the encrypted message unambiguously for any pair of primes. In
particular, a deterministic scheme using quartic reciprocity is described that
works for primes congruent 5 modulo 8, a case that was still open. Both
theoretical and practical solutions are presented. The Rabin signature is also
reconsidered and a deterministic padding mechanism is proposed.Comment: minor review + introduction of a deterministic scheme using quartic
reciprocity that works for primes congruent 5 modulo
An Active Attack on a Multiparty Key Exchange Protocol
The multiparty key exchange introduced in Steiner et al.\@ and presented in
more general form by the authors is known to be secure against passive attacks.
In this paper, an active attack is presented assuming malicious control of the
communications of the last two users for the duration of only the key exchange
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