847 research outputs found
Group theory in cryptography
This paper is a guide for the pure mathematician who would like to know more
about cryptography based on group theory. The paper gives a brief overview of
the subject, and provides pointers to good textbooks, key research papers and
recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor
typographical changes. To appear in Proceedings of Groups St Andrews 2009 in
Bath, U
Cryptanalysis of three matrix-based key establishment protocols
We cryptanalyse a matrix-based key transport protocol due to Baumslag, Camps,
Fine, Rosenberger and Xu from 2006. We also cryptanalyse two recently proposed
matrix-based key agreement protocols, due to Habeeb, Kahrobaei and Shpilrain,
and due to Romanczuk and Ustimenko.Comment: 9 page
The existence of k-radius sequences
Let and be positive integers, and let be an alphabet of size .
A sequence over of length is a \emph{-radius sequence} if any two
distinct elements of occur within distance of each other somewhere in
the sequence. These sequences were introduced by Jaromczyk and Lonc in 2004, in
order to produce an efficient caching strategy when computing certain functions
on large data sets such as medical images.
Let be the length of the shortest -ary -radius sequence. The
paper shows, using a probabilistic argument, that whenever is fixed and
The paper observes that the same argument generalises to the situation when
we require the following stronger property for some integer such that
: any distinct elements of must simultaneously occur
within a distance of each other somewhere in the sequence.Comment: 8 pages. More papers cited, and a minor reorganisation of the last
section, since last version. Typo corrected in the statement of Theorem
Counting Additive Decompositions of Quadratic Residues in Finite Fields
We say that a set is additively decomposed into two sets and if
. A. S\'ark\"ozy has recently conjectured that
the set of quadratic residues modulo a prime does not have nontrivial
decompositions. Although various partial results towards this conjecture have
been obtained, it is still open. Here we obtain a nontrivial upper bound on the
number of such decompositions
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