A computer is generally considered to be a universal computational device; ie, it is believed
able to simulate any physical computational device with a cost in computation time of at most …

Cryptography, in particular public-key cryptography, has emerged in the last 20 years as an
important discipline that is not only the subject of an enormous amount of research, but …

In this volume we have endeavored to provide a middle ground-hopefully even a bridge-
between" theory" and" experiment" in the matter of prime numbers. Of course, we speak of …

This introductory book emphasizes algorithms and applications, such as cryptography and
error correcting codes, and is accessible to a broad audience. The presentation alternates …

Elliptic curves have been intensively studied in algebraic geometry and number theory. In
recent years they have been used in devising efficient algorithms for factoring integers and …

The number field sieve is an algorithm for finding the prime factors of large integers. It
depends on algebraic number theory. Proposed by John Pollard in 1988, the method was …

Public key cryptography is a major interdisciplinary subject with many real-world
applications, such as digital signatures. A strong background in the mathematics underlying …

Cryptography is a key technology in electronic key systems. It is used to keep data secret,
digitally sign documents, access control, and so forth. Users therefore should not only know …

i& Page 1 i& Designs, Codes and Cryptography, 19, 101-128 (2000) •"'Il © 2000 Kluwer
Academic Publishers, Boston. Integer Factoring ARJEN K. LENSTRA arjen.lenstra@citicorp.com …

The number field sieve is an algorithm to factor integers of the form r, 4-s for small positive r
and s. This note is intended as a'report on work in progress' on this algorithm. We informally …