8,313 research outputs found
Efficient algorithms for pairing-based cryptosystems
We describe fast new algorithms to implement recent cryptosystems based on the Tate pairing. In particular, our techniques improve pairing evaluation speed by a factor of about 55 compared to previously known methods in characteristic 3, and attain performance comparable
to that of RSA in larger characteristics.We also propose faster algorithms for scalar multiplication in characteristic 3 and square root extraction
over Fpm, the latter technique being also useful in contexts other than that of pairing-based cryptography
Quench protection analysis in accelerator magnets, a review of the tools
As accelerator magnets see the increase of their magnetic field and stored
energy, quench protection becomes a critical part of the magnet design. Due to
the complexity of the quench phenomenon interweaving magnetic, electrical and
thermal analysis, the use of numerical codes is a key component of the process.
In that respect, we propose here a review of several tools commonly used in the
magnet design community.Comment: 4 pages, Contribution to WAMSDO 2013: Workshop on Accelerator Magnet,
Superconductor, Design and Optimization; 15 - 16 Jan 2013, CERN, Geneva,
Switzerlan
Arithmetic circuits: the chasm at depth four gets wider
In their paper on the "chasm at depth four", Agrawal and Vinay have shown
that polynomials in m variables of degree O(m) which admit arithmetic circuits
of size 2^o(m) also admit arithmetic circuits of depth four and size 2^o(m).
This theorem shows that for problems such as arithmetic circuit lower bounds or
black-box derandomization of identity testing, the case of depth four circuits
is in a certain sense the general case. In this paper we show that smaller
depth four circuits can be obtained if we start from polynomial size arithmetic
circuits. For instance, we show that if the permanent of n*n matrices has
circuits of size polynomial in n, then it also has depth 4 circuits of size
n^O(sqrt(n)*log(n)). Our depth four circuits use integer constants of
polynomial size. These results have potential applications to lower bounds and
deterministic identity testing, in particular for sums of products of sparse
univariate polynomials. We also give an application to boolean circuit
complexity, and a simple (but suboptimal) reduction to polylogarithmic depth
for arithmetic circuits of polynomial size and polynomially bounded degree
Computing zeta functions of arithmetic schemes
We present new algorithms for computing zeta functions of algebraic varieties
over finite fields. In particular, let X be an arithmetic scheme (scheme of
finite type over Z), and for a prime p let zeta_{X_p}(s) be the local factor of
its zeta function. We present an algorithm that computes zeta_{X_p}(s) for a
single prime p in time p^(1/2+o(1)), and another algorithm that computes
zeta_{X_p}(s) for all primes p < N in time N (log N)^(3+o(1)). These generalise
previous results of the author from hyperelliptic curves to completely
arbitrary varieties.Comment: 23 pages, to appear in the Proceedings of the London Mathematical
Societ
Algorithms on Ideal over Complex Multiplication order
We show in this paper that the Gentry-Szydlo algorithm for cyclotomic orders,
previously revisited by Lenstra-Silverberg, can be extended to
complex-multiplication (CM) orders, and even to a more general structure. This
algorithm allows to test equality over the polarized ideal class group, and
finds a generator of the polarized ideal in polynomial time. Also, the
algorithm allows to solve the norm equation over CM orders and the recent
reduction of principal ideals to the real suborder can also be performed in
polynomial time. Furthermore, we can also compute in polynomial time a unit of
an order of any number field given a (not very precise) approximation of it.
Our description of the Gentry-Szydlo algorithm is different from the original
and Lenstra- Silverberg's variant and we hope the simplifications made will
allow a deeper understanding. Finally, we show that the well-known speed-up for
enumeration and sieve algorithms for ideal lattices over power of two
cyclotomics can be generalized to any number field with many roots of unity.Comment: Full version of a paper submitted to ANT
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