# Factoring Integers with the Self-Initializing Quadratic Sieve

@inproceedings{Contini1997FactoringIW, title={Factoring Integers with the Self-Initializing Quadratic Sieve}, author={Scott Contini}, year={1997} }

In 1996, we used the self initializing quadratic sieve (siqs) to set the general purpose integer factorization record for the Cunningham project. Here, we show that this algorithm is about twice as fast as the ordinary multiple polynomial quadratic sieve (mpqs). We give running times of both algorithms for 60, 70, and 80 digit numbers. These tables show the best timings we were able to get using various parameters for each of algorithms. In all cases, the best siqs times are about twice as fast…

## 18 Citations

### Integer Factorization and Computing Discrete Logarithms in Maple

- Computer Science, Mathematics
- 2006

A quadratic sieve algorithm for integer factorization in Maple is implemented to replace Maple’s implementation of the MorrisonBrillhart continued fraction algorithm, and an indexed calculus algorithm for discrete logarithms in GF(q) is implementedto replace Maple's implementation of Shanks’ baby-step giant-step algorithm.

### Speeding up Integer Multiplication and Factorization

- Computer Science, Mathematics
- 2010

Improvements to well-known algorithms for integer multiplication and factorization are explored, showing how parameters for these algorithms can be chosen accurately, taking into account the distribution of prime factors in integers produced by NFS to obtain an accurate estimate of finding a prime factor with given parameters.

### On the number field sieve: polynomial selection and smooth elements in number fields

- Computer Science
- 2012

The number field sieve is the asymptotically fastest known algorithm for factoring large integers that are free of small prime factors. Two aspects of the algorithm are considered in this thesis:…

### Impact of Optimization and Parallelism on Factorization Speed of SIQS

- Computer Science
- 2016

The goal of this paper is to show how it is possible to take advantage of parallelism in SIQS as well as reach a large speedup thanks to detailed source code analysis with optimization.

### Computing discrete logarithms in the Jacobian of high-genus hyperelliptic curves over even characteristic finite fields

- Computer Science, MathematicsMath. Comput.
- 2011

Improved versions of index-calculus algorithms for solving discrete logarithm problems in Jacobians of high-genus hyperelliptic curves are described, allowing them to predict accurately the number of random walk steps required to all relations, and to select optimal degree bounds for the factor base.

### HOW TO FIND SMALL FACTORS OF INTEGERS

- Mathematics, Computer Science
- 2000

The new algorithm is useful in congruence-combination methods to compute large factors, discrete logarithms, class groups, etc.

### Factoring Small to Medium Size Integers: An Experimental Comparison

- Computer Science
- 2010

Several general-purpose factoring algorithms suited for smaller numbers are implemented, from Shanks's square form factorization method to the self-initializing quadratic sieve, and the continued fraction algorithm is revisited in light of recent advances in smoothness detection batch methods.

### Factoring Small Integers: An Experimental Comparison

- Computer Science
- 2007

In this data-based paper we report on our experiments in factoring integers from 50 to 200 bits with the postsieving phase of NFS as a potential application. We implemented and compared several…

### Implementing the Hypercube Quadriatic Sieve with Two Large Primes

- Computer Science, Mathematics
- 2002

This paper describes what it believes is the rst implementation of the Hypercube Multiple Polynomial Quadratic Sieve with two large primes, and uses this program to factor many integers with up to 116 digits.

### Infrastructure, arithmetic, and class number computations in purely cubic function fields of characteristic at least 5

- Mathematics
- 2009

One of the more difficult and central problems in computational algebraic number theory is the computation of certain invariants of a field and its maximal order. In this thesis, we consider this…

## References

SHOWING 1-10 OF 54 REFERENCES

### Factoring by Electronic Mail

- Computer ScienceEUROCRYPT
- 1989

The distributed implementation of two factoring algorithms, the elliptic curve method (ecm) and the multiple polynomial quadratic sieve algorithm (mpqs), shows that the enormous computational task of factoring 100 digit integers with the current algoritluns can be completed almost for free.

### The Quadratic Sieve Factoring Algorithm

- MathematicsEUROCRYPT
- 1984

The quadratic sieve algorithm is currently the method of choice to factor very large composite numbers with no small factors, and some of the improvements suggested for it are described.

### A World Wide Number Field Sieve Factoring Record: On to 512 Bits

- Computer Science, MathematicsASIACRYPT
- 1996

A conservative extrapolation to estimate the difficulty of factoring 512-bit numbers is presented and a World Wide Web interface to the sieving program that is developed is discussed to facilitate contributing toThe sieving stage of future large scale factoring efforts.

### The multiple polynomial quadratic sieve

- Computer Science
- 1987

A modification, due to Peter Montgomery, of Pomerance's Quadratic Sieve for factoring large integers is discussed along with its implementation, which enables one to factor numbers in the 60-digit range in about a day, using a large minicomputer.

### Solving homogeneous linear equations over GF (2) via block Wiedemann algorithm

- Computer Science
- 1994

A method of solving large sparse systems of homogeneous linear equations over G F ( 2 ) , the field with two elements, is proposed and an algorithm due to Wiedemann is modified, which is competitive with structured Gaussian elimination in terms of time and has much lower space requirements.

### A Block Lanczos Algorithm for Finding Dependencies Over GF(2)

- Computer Science, MathematicsEUROCRYPT
- 1995

The Lanczos algorithm is modified to produce a sequence of orthogonal subspaces of GF(2)n, each having dimension almost N, by applying the given matrix and its transpose to N binary vectors at once.

### The Magic Words are Squeamish Ossifrage

- MathematicsASIACRYPT
- 1994

It is concluded that commonly-used 512-bit RSA moduli are vulnerable to any organization prepared to spend a few million dollars and to wait a few months.

### NFS with Four Large Primes: An Explosive Experiment

- Computer ScienceCRYPTO
- 1995

The results obtained while experimenting with the multi-large prime variation of the general number field sieve integer factoring algorithm NFS imply that factoring is somewhat easier than the authors thought.

### Factorization Using the Quadratic Sieve Algorithm

- Computer Science, MathematicsCRYPTO
- 1983

Since the cryptosecurity of the RSA two key cryptoalgorithm is no greater than the difficulty of factoring the modulus, a code that implements the Quadratic Sieve factorization algorithm on the CRAY I computer has been developed to determine as sharply as possible the current state-of-the-art in factoring.