The development of the number field sieve 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 used in 1990 to factor the ninth Fermat number a 155 digit integer. The algorithm is most suited to numbers of a special form but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve from both theoretical and practical perspectives. Pollards original manuscript is included. In addition there is an annotated bibliography of directly related literature