Implementation of the general number field sieve

An Introduction to the General Number Fi

An Introduction to the General Number Field Sieve

✍ Briggs M. 📂 Library 📅 1998 🌐 English ⚖ 850 KB

The General Number Field Sieve (GNFS) is the fastest known method for factoring "large" integers, where large is generally taken to mean over 110 digits. This makes it the best algorithm for attempting to unscramble keys in the RSA [2, Chapter 4] public-key cryptography system, one of the most preva

Development of the Number Field Sieve

✍ Lenstra H. W. 📂 Library 📅 1993 🌐 English ⚖ 611 KB

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 fo

Survey of the number field sieve

✍ Nakamula. 📂 Library 🌐 English ⚖ 81 KB

The Development of the Number Field Siev

The Development of the Number Field Sieve

✍ Arjen K. Lenstra, Hendrik W.Jr. Lenstra 📂 Library 📅 1993 🏛 Springer 🌐 English ⚖ 127 KB

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 fo

The development of the number field siev

The development of the number field sieve

✍ H. W. Lenstra Jr. (auth.), Arjen K. Lenstra, Hendrik W. Lenstra Jr. (eds.) 📂 Library 📅 1993 🏛 Springer 🌐 English ⚖ 1 MB

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 fo

Modifications to the Number Field Sieve

✍ Don Coppersmith 📂 Article 📅 1993 🏛 Springer 🌐 English ⚖ 469 KB

I-LLMP'I and Buhler et al. I'BLP], is a new routine for factoring integers. We present here a modification of that sieve. We use the fact that certain smoothness computations can be reused, and thereby reduce the asymptotic running time of the Number Field Sieve. We also give a way to precompute tab