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We investigate a general approach for the numerical approximation of incompressible Navier-Stokes equations based on splitting the original problem into successive subproblems which are cheaper to solve. The splitting is obtained through an algebraic appro ...
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. ...
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We establish new results and introduce new methods in the theory of measurable orbit equivalence. Our rigidity statements hold for a wide (uncountable) class of negatively curved groups. Amongst our applications are (a) measurable Mostow-type rigidity theo ...
This paper describes carry-less arithmetic operations modulo an integer 2^M-1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implementa ...
In this thesis we address the numerical approximation of the incompressible Navier-Stokes equations evolving in a moving domain with the spectral element method and high order time integrators. First, we present the spectral element method and the basic to ...
D.J. Bernstein has proposed a circuit-based implementation of the matrix step of the number field sieve factorization algorithm (see "Circuits for integer factorization: a proposal", http://cr.yp.to/papers.html#nfscircuit, 2001). These circuits offer an as ...
This paper reports on the factorization of the 512 bit number RSA-155 by the number field Sieve factoring method (NFS) and discusses the implications for RSA ...
Using simple examples and informal discussions this article surveys the key ideas and major advances of the last quarter century in integer factorization. ...
A framework for the construction of stable spectral methods on arbitrary domains with unstructured grids is presented. Although most of the developments are of a general nature, an emphasis is placed on schemes for the solution of partial differential equa ...
This paper describes carry-less arithmetic operations modulo an integer 2^M − 1 in the thousand-bit range, targeted at single instruction multiple data platforms and applications where overall throughput is the main performance criterion. Using an implemen ...