In number theory, a branch of mathematics, the special number field sieve (SNFS) is a special-purpose integer factorization algorithm. The general… (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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2015

2015

- Taechan Kim
- IACR Cryptology ePrint Archive
- 2015

In this paper, we extend the tower number field sieve (TNFS) proposed by Barbulescu, Gaudry, and Kleinjung in Asaicrypt 2015. Our… (More)

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2015

2015

The general number sieve is the most efficient algorithm known integer factorization, it consists of polynomial selection… (More)

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2013

2013

- Antoine Joux, Cécile Pierrot
- Pairing
- 2013

In this paper, we study the discrete logarithm problem in finite fields related to pairing-based curves. We start with a precise… (More)

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2012

2012

- Greg Childers
- IACR Cryptology ePrint Archive
- 2012

I provide the details of the factorization of the Mersenne number 21061 − 1 by the Special Number Field Sieve. Although this… (More)

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Review

2012

Review

2012

- Emmanuel Thomé
- WAIFI
- 2012

We review several methods for the square root step of the Number Field Sieve, and present an original one, based on the Chinese… (More)

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Highly Cited

2008

Highly Cited

2008

- Gerhard Goos, Juris Hartmanis, +5 authors Kaoru Kurosawa
- 2008

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number… (More)

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2007

2007

- Kazumaro Aoki, Jens Franke, Thorsten Kleinjung, Arjen K. Lenstra, Dag Arne Osvik
- ASIACRYPT
- 2007

We describe how we reached a new factoring milestone by completing the first special number field sieve factorization of a number… (More)

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2006

2006

- Oliver Schirokauer
- Math. Comput.
- 2006

We define the weight of an integer N to be the smallest w such that N can be represented as ∑w i=1 i2 ci , with 1, . . . , w ∈ {1… (More)

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2002

2002

- Antoine Joux, Reynald Lercier
- ANTS
- 2002

In this paper, we describe improvements to the function field sieve (FFS) for the discrete logarithm problem in Fpn , when p is… (More)

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