A new method for accelerating matrix multiplication asymptotically is presented, by using a basic trilinear form which is not a matrix product, and making novel use of the Salem-Spencer Theorem.Expand

It is shown how to find sufficiently small integer solutions to a polynomial in a single variable modulo N, and to a Poole's inequality in two variables over the integers.Expand

A tour that minimizes ∑n i=1 `(i), where `( i) is the latency of pi, defined to be the distance traveled before first visiting pi, is constructed.Expand

Some of the safeguards against differential cryptanalysis that were built into the DES system from the beginning are shown, with the result that more than 10 15 bytes of chosen plaintext are required for this attack to succeed.Expand

We define an approximate version of the Fourier transform on $2^L$ elements, which is computationally attractive in a certain setting, and which may find application to the problem of factoring… Expand

This paper deals with a combinatorial minimization problem arising from studies on multimodule memory organizations with a particular solution proposed and it is demonstrated that it is close to optimum.Expand

We show how to solve a polynomial equation (mod N) of degree k in a single variable x, as long as there is a solution smaller than N1/k. We give two applications to RSA encryption with exponent 3.… Expand

A new construction of a pseudorandom generator based on a simple combination of two LFSRs is presented, suitable for practical implementation of efficient stream cipher cryptosystems.Expand

The ideas give a dramatic improvement even for moderate-sized fields such as GF (2^{127}) , and make (barely) possible computations in fields of size around 2^{400} .Expand

A consequence of these results is that ω, the exponent for matrix multiplication, is a limit point, that is, cannot be realized by any single algorithm.Expand