General number field sieve
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The security of pairing-based crypto-systems relies on the difficulty to compute discrete logarithms in finite fields Fpn where n… (More)
The general number field sieve (GNFS) is the asymptotically fastest algorithm for factoring large integers. Its runtime depends… (More)
In 1990, the ninth Fermat number was factored into primes by means of a new algorithm, the "number field sieve", which was… (More)
We describe the main ideas underlying integer factorization using the number field sieve.
RSA is a very popular public key cryptosystem. This algorithm is known to be secure, but this fact relies on the difficulty of… (More)
With the proliferation of computers into homes and businesses and the explosive growth rate of the Internet, the ability to… (More)
The diiculty in solving the discrete logarithm problem is of extreme cryptographic importance since it is widely used in… (More)
It was shown in 2] that under reasonable assumptions the general number eld sieve (GNFS) is the asymptotically fastest known… (More)
- SIAM J. Discrete Math.
Recently, several algorithms using number field sieves have been given to factor a number n in heuristic expected time Ln[1/3; c… (More)
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)