Rotations and Translations of Number Field Sieve Polynomials
نویسنده
چکیده
We present an algorithm that finds polynomials with many roots modulo many primes by rotating candidate Number Field Sieve polynomials using the Chinese Remainder Theorem. We also present an algorithm that finds a polynomial with small coefficients among all integral translations of X of a given polynomial in ZZ[X]. These algorithms can be used to produce promising candidate Number Field Sieve poly-
منابع مشابه
Size Optimization of Sextic Polynomials in the Number Field Sieve
The general number field sieve (GNFS) is the most efficient algorithm known for factoring large integers. It consists of several stages, the first one being polynomial selection. The quality of the chosen polynomials in polynomial selection can be modelled in terms of size and root properties. In this paper, we describe some methods to optimize the size property of sextic polynomials.
متن کاملNon-linear polynomial selection for the number field sieve
We present an algorithm to find two non-linear polynomials for the Number Field Sieve integer factorization method. This algorithm extends Montgomery’s “two quadratics” method; for degree 3, it gives two skewed polynomials with resultant O(N5/4), which improves on Williams O(N4/3) result [12].
متن کاملOn Quadratic Polynomials for the Number Field Sieve
The newest, and asymptotically the fastest known integer factorisation algorithm is the number eld sieve. The area in which the number eld sieve has the greatest capacity for improvement is polynomial selection. The best known polynomial selection method nds quadratic polynomials. In this paper we examine the smoothness properties of integer values taken by these polynomials. Given a quadratic ...
متن کاملCollecting relations for the Number Field Sieve in GF(p6)
In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in Fp6 with the Number Field Sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strate...
متن کاملCollecting relations for the Number Field Sieve in GF ppq
In order to assess the security of cryptosystems based on the discrete logarithm problem in non-prime finite fields, as are the torus-based or pairing-based ones, we investigate thoroughly the case in Fp6 with the Number Field Sieve. We provide new insights, improvements, and comparisons between different methods to select polynomials intended for a sieve in dimension 3 using a special-q strate...
متن کامل