scholarly journals A general number field sieve implementation

1993 ◽  
pp. 103-126 ◽  
Author(s):  
Daniel J. Bernstein ◽  
A. K. Lenstra
Keyword(s):  
Number Field ◽  
Number Field Sieve ◽  
General Number

scholarly journals On polynomial selection for the general number field sieve

2006 ◽  
Vol 75 (256) ◽  
pp. 2037-2047 ◽  
Author(s):  
Thorsten Kleinjung
Keyword(s):  
Number Field ◽  
Number Field Sieve ◽  
General Number ◽  
Selection For

On General Number Field Sieve and its Polynomial Selection

2014 ◽  
Vol 519-520 ◽  
pp. 250-256
Author(s):  
Gang Zhou
Keyword(s):  
Number Field ◽  
Discrete Logarithm ◽  
Primality Testing ◽  
Number Field Sieve ◽  
General Number

This paper analyzes the algorithm of general number field sieve and suggesting some ofits solving in the problem of larger integers factorization. And a design of its implementation via thelibrary GMP for polynomial selection is discussed. Our work has the advantages of easy extensionsto various applications such as RSA, Discrete logarithm problems, Primality testing and so on.

The Quadratic Sieve Algorithm for Integer Factoring

2018 ◽  
pp. 241-252
Author(s):  
Kannan Balasubramanian ◽  
M. Rajakani
Keyword(s):  
Number Field ◽  
Number Field Sieve ◽  
General Number ◽  
Quadratic Sieve ◽  
Factoring Algorithm

At the time when RSA was invented in 1977, factoring integers with as few as 80 decimal digits was intractable. The first major breakthrough was quadratic sieve, a relatively simple factoring algorithm invented by Carl Pomerance in 1981, which can factor numbers up to 100 digits and more. It's still the best-known method for numbers under 110 digits or so; for larger numbers, the general number field sieve (GNFS) is now used. However, the general number field sieve is extremely complicated, for even the most basic implementation. However, GNFS is based on the same fundamental ideas as quadratic sieve. The fundamentals of the Quadratic Sieve algorithm are discussed in this chapter.

Integer Factoring Algorithms

2018 ◽  
pp. 228-240 ◽  
Author(s):  
Kannan Balasubramanian ◽  
Ahmed Mahmoud Abbas
Keyword(s):  
Number Field ◽  
Prime Numbers ◽  
Difficult Problem ◽  
Number Field Sieve ◽  
Large Numbers ◽  
General Number ◽  
Curve Method ◽  
Quadratic Sieve ◽  
Special Number ◽  
Elliptic Curve Method

Most cryptographic systems are based on an underlying difficult problem. The RSA cryptosystem and many other cryptosystems rely on the fact that factoring a large composite number into two prime numbers is a hard problem. The are many algorithms for factoring integers. This chapter presents some of the basic algorithms for integer factorization like the Trial Division, Fermat's Algorithm. Pollard's Rho Method, Pollard's p-1 method and the Elliptic Curve Method. The Number Field Sieve algorithm along with Special Number field Sieve and the General Number Field Sieve are also used in factoring large numbers. Other factoring algorithms discussed in this chapter are the Continued Fractions Algorithms and the Quadratic Sieve Algorithm.

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