454 research outputs found
A faster pseudo-primality test
We propose a pseudo-primality test using cyclic extensions of . For every positive integer , this test achieves the
security of Miller-Rabin tests at the cost of Miller-Rabin
tests.Comment: Published in Rendiconti del Circolo Matematico di Palermo Journal,
Springe
Homomorphic encryption and some black box attacks
This paper is a compressed summary of some principal definitions and concepts
in the approach to the black box algebra being developed by the authors. We
suggest that black box algebra could be useful in cryptanalysis of homomorphic
encryption schemes, and that homomorphic encryption is an area of research
where cryptography and black box algebra may benefit from exchange of ideas
Optimal Substring-Equality Queries with Applications to Sparse Text Indexing
We consider the problem of encoding a string of length from an integer
alphabet of size so that access and substring equality queries (that
is, determining the equality of any two substrings) can be answered
efficiently. Any uniquely-decodable encoding supporting access must take
bits. We describe a new data
structure matching this lower bound when while supporting
both queries in optimal time. Furthermore, we show that the string can
be overwritten in-place with this structure. The redundancy of
bits and the constant query time break exponentially a lower bound that is
known to hold in the read-only model. Using our new string representation, we
obtain the first in-place subquadratic (indeed, even sublinear in some cases)
algorithms for several string-processing problems in the restore model: the
input string is rewritable and must be restored before the computation
terminates. In particular, we describe the first in-place subquadratic Monte
Carlo solutions to the sparse suffix sorting, sparse LCP array construction,
and suffix selection problems. With the sole exception of suffix selection, our
algorithms are also the first running in sublinear time for small enough sets
of input suffixes. Combining these solutions, we obtain the first
sublinear-time Monte Carlo algorithm for building the sparse suffix tree in
compact space. We also show how to derandomize our algorithms using small
space. This leads to the first Las Vegas in-place algorithm computing the full
LCP array in time and to the first Las Vegas in-place algorithms
solving the sparse suffix sorting and sparse LCP array construction problems in
time. Running times of these Las Vegas
algorithms hold in the worst case with high probability.Comment: Refactored according to TALG's reviews. New w.h.p. bounds and Las
Vegas algorithm
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