In number theory, the general number field sieve (GNFS) is the most efficient classical algorithm known for factoring integers larger than 10100… (More)

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2015

2015

- Razvan Barbulescu, Pierrick Gaudry, Thorsten Kleinjung
- ASIACRYPT
- 2015

The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields Fpn where n… (More)

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2006

2006

- Thorsten Kleinjung
- Math. Comput.
- 2006

The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends… (More)

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Highly Cited

2005

Highly Cited

2005

- Carl Pomerance, Dan Bernstein, +5 authors Robert Rumely
- 2005

In 1990, the ninth Fermat number was factored into primes by means of a new algorithm, the "number field sieve", which was… (More)

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2005

2005

We describe the main ideas underlying integer factorization using the number field sieve.

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2003

2003

- Michael L. Case
- 2003

RSA is a very popular public key cryptosystem. This algorithm is known to be secure, but this fact relies on the difficulty of… (More)

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1998

1998

With the proliferation of computers into homes and businesses and the explosive growth rate of the Internet, the ability to… (More)

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1996

1996

- Damian Weber
- ANTS
- 1996

The diiculty in solving the discrete logarithm problem is of extreme cryptographic importance since it is widely used in… (More)

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1993

1993

- Johannes A. Buchmann, J. Loho, J. Zayer
- CRYPTO
- 1993

It was shown in 2] that under reasonable assumptions the general number eld sieve (GNFS) is the asymptotically fastest known… (More)

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Highly Cited

1993

Highly Cited

1993

- Daniel M. Gordon
- SIAM J. Discrete Math.
- 1993

Recently, several algorithms using number field sieves have been given to factor a number n in heuristic expected time Ln[1/3; c… (More)

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Highly Cited

1990

Highly Cited

1990

The number field sieve is an algorithm to factor integers of the form r e ± s for small positive r and s . This note is intended… (More)

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