منابع مشابه
Root optimization of 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 algorithms for selecting polynomials with very good root properties. 1...
متن کاملSize 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 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 کاملRotations and Translations of Number Field Sieve Polynomials
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 ...
متن کاملSquare Root Algorithms for the Number Field Sieve
We review several methods for the square root step of the Number Field Sieve, and present an original one, based on the Chinese Remainder Theorem. We consider in this article the final step of the Number Field Sieve (NFS) factoring algorithm [3], namely the algebraic square root computation. This problem is stated as follows. Let K = Q(α) be a number field, where α is defined as a root of the i...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 2015
ISSN: 0025-5718,1088-6842
DOI: 10.1090/s0025-5718-2015-02926-3