Factorization of RSA-140 Using the Number Field Sieve

@inproceedings{Cavallar1999FactorizationOR,
  title={Factorization of RSA-140 Using the Number Field Sieve},
  author={Stefania Cavallar and Bruce Dodson and Arjen K. Lenstra and Paul C. Leyland and Walter M. Lioen and Peter L. Montgomery and Brian Murphy and Herman J. J. te Riele and Paul Zimmermann},
  booktitle={ASIACRYPT},
  year={1999}
}
On February 2, 1999, we completed the factorization of the 140-digit number RSA-140 with the help of the Number Field Sieve factoring method (NFS. [] Key Result The implications of the new polynomial selection method for factoring a 512-bit RSA modulus are discussed and it is concluded that 512-bit (= 155-digit) RSA moduli are easily and realistically within reach of factoring efforts similar to the one presented here.
Reportrapport Factorization of a 512--bit Rsa Modulus Factorization of a 5122bit Rsa Modulus
TLDR
On August 22, 1999, the factorization of the 512{bit 155{digit number RSA{155 with the help of the Number Field Sieve factoring method (NFS) was completed, a new record for factoring general numbers.
Centrum voor Wiskunde en Informatica Factorization of a 512--bit RSA modulus
TLDR
This factorization of the bit digit number RSA with the help of the Number Field Sieve factoring method NFS is a new record for factoring general numbers.
History of integer factorization
The integer factorization problem is well known as the mathematical foundation of the public-key cryptosystem RSA. When RSA was introduced forty years ago, the largest number one could factor was
Polynomial Selection for the Number Field Sieve Integer Factorisation Algorithm
TLDR
The number field sieve, the newest and fastest known method for factorising integers used in public-key cryptosystems, is considered, and so-called polynomial selection methods for the numberField sieve are improved.
Improved Factoring of RSA Modulus
TLDR
Based on the open source GGNFS, the 512-bit RSA modulus can be factored within 3 days by the high-performance computing resource at National Taiwan University.
A New Deterministic RSA-Factoring Algorithm
TLDR
A new deterministic factoring algorithm, that factors RSA n = p * q, the algorithm running time relays on the number of digits of n rather than the value of n, which eliminates the storage problem and improves the running time and complexity of the algorithm.
On the Design of RSA With Short Secret Exponent
TLDR
It is shown that it is possible to use a short secret exponent which is below these bounds while not compromising with the security of RSA provided that p and q are differing in size and are large enough to combat factoring algorithms.
MPQS with Three Large Primes
TLDR
This work reports the factorization of a 135-digit integer by the triple-large-prime variation of the multiple polynomial quadratic sieve, and characterize the various types of cycles present, and gives a semi-quantitative description of their rather mysterious behaviour.
GNFS Factoring Statistics of RSA-100, 110, ..., 150
TLDR
This manuscript implemented GNFS and factored 100to 150-digits number on the same environment using lattice sieve and did not use line sieve, hoping that these results will help running time estimation of factoring a large integer.
Review of primality testing and integer factorization in public key cryptography by Song Y. Yan
TLDR
Although public key cryptography was discovered in the 1970s, it did not percolate through the mathematical community until much later, and it had some interesting side effects in mathematics.
...
...

References

SHOWING 1-10 OF 27 REFERENCES
A World Wide Number Field Sieve Factoring Record: On to 512 Bits
TLDR
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.
On the Factorization of RSA-120
TLDR
This work presents data concerning the factorization of the 120-digit number RSA-120, which was factored on July 9, 1993, using the quadratic sieve method, and discusses the issue of the crossover point between these two methods.
Factoring integers with the number field sieve
In 1990, the ninth Fermat number was factored into primes by means of a new algorithm, the “number field sieve”, which was proposed by John Pollard. The present paper is devoted to the description
Factoring Large Numbers with the Twinkle Device (Extended Abstract)
TLDR
This paper describes a novel factoring apparatus which can accelerate known sieve-based factoring algorithms by several orders of magnitude, and can make 512 bit RSA keys (which protect 95% of today’s E-commerce on the Internet) very vulnerable.
Modelling the Yield of Number Field Sieve Polynominals
TLDR
The yield of number field sieve polynomials, concentrating on those produced by Montgomery's selection algorithm, is examined, and a preliminary model is suggested to approximate the behaviour of these polynmials across the sieving region.
Factoring by Electronic Mail
TLDR
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.
Factoring With Two Large Primes
TLDR
This paper presents a new technique that proved to be extremely useful, not only to achieve a considerable speed-up of an older and widely studied factoring algorithm, but also, and more importantly, to make practical application of a new factoring algorithms feasible.
The Magic Words are Squeamish Ossifrage
TLDR
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.
An Implementation of the Number Field Sieve
TLDR
An implementation of the NFS is described, including the choice of two quadratic polynomials, both classical sieving and a special form of lattice sieving (line sieving), the block Lanczos method and a new square root algorithm.
Strategies in Filtering in the Number Field Sieve
TLDR
This paper discusses several possible filter strategies and their use in the recent record factorizations of RSA-140, R211 and RSA-155.
...
...