Improved Stage 2 to P±\pm1 Factoring Algorithms

International audienceSome implementations of stage 2 of the P-1 method of factorization use convolutions. We describe a space-efficient implementation, allowing convolution lengths around 2^23 and stage 2 limit around 10^16 while attempting to factor 230-digit numbers on modern PC's. We use the discrete cosine transform to multiply reciprocal polynomials. We present adjustments for the P+1 algorithm. We list some new findings

Root optimization of polynomials in the number field sieve

The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some algorithms for selecting polynomials with very good root properties.Comment: 16 pages, 18 reference

From quantum-codemaking to quantum code-breaking

This is a semi-popular overview of quantum entanglement as an important physical resource in the field of data security and quantum computing. After a brief outline of entanglement's key role in philosophical debates about the meaning of quantum mechanics I describe its current impact on both cryptography and cryptanalysis. The paper is based on the lecture given at the conference "Geometric Issues in the Foundations of Science" (Oxford, June 1996) in honor of Roger Penrose.Comment: 21 pages, LaTeX2e, psfig, multi3.cls, 1 eps figur