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Let p be a prime number, let K be a field of characteristic not p, containing the p-th roots of unity, and let r >= 1 be an integer. We compute the essential dimension of Z/p(r) Z over K (Theorem 4.1). In particular, i) We have edℚ(ℤ/8ℤ)=4, a result which ...
In a paper of 2003, Kulshammer, Olsson and Robinson defined l-blocks for the symmetric groups, where l > 1 is an arbitrary integer. In this paper, we give a definition for the defect group of the principal l-block. We then check that, in the Abelian case, ...
We consider several "provably secure" hash functions that compute simple sums in a well chosen group (G,*). Security properties of such functions provably translate in a natural way to computational problems in G that are simple to define and possibly also ...
This paper reports on the factorization of the 768-bit number RSA-768 by the number field sieve factoring method and discusses some implications for RSA. ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2010
Similarly to the recently obtained result for two-terminal systems, we show that there are constraints on the full counting statistics for noninteracting fermions in multiterminal contacts. In contrast to the two-terminal result, however, there is no facto ...
In the synchronous periodic task model, a set \tau_1,...,\tau_n of tasks is given, each releasing jobs of running time c_i with relative deadline d_i, at each integer multiple of the period p_i. It is a classical result that Earliest Deadline First (EDF) i ...
In this paper, we demonstrate the advantage of the inherent algebraic structure of lattice codes, for the uplink channel of a cellular deployment. The out-of-cell interference is assumed to be symmetric, as in Wyner's model. We employ a new relaying techni ...
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2009
We take an approach toward Counting the number of integers n for which the curve (n),: y(2) = x(3) - n(2)x has 2-Selmer groups of a given size. This question was also discussed in a pair of papers by Roger Heath-Brown. In contrast to earlier work, our anal ...
We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number having more than 1024 bits, namely the Mersenne number 21039 -1. Although this factorization is orders of magnitude ...
In this paper we propose a new structure for multiplication using optimal normal bases of type 2. The multiplier uses an efficient linear transformation to convert the normal basis representations of elements of Fqn to suitable polynomials of deg ...
