Factoring Very Large Numbers Using a Massively Parallel ComputerFactorizationParallel ProcessingAlgorithmsArray ProcessorsThis paper discusses the Quadratic Sieve algorithms of factoring large numbers or parallel processors. 9 refs. (ERA citation 13:050321)Holdridge, D. B....
Factoring Large Numbers with the TWINKLE Device (extended abstract - Shamir - 1999 () Citation Context ...se of a quantum computer. Until such a computer has been developed, the NFS will remain the fastest usable algorithm for very large integers. 3.5.2 TWINKLE The Weizmann INstitute Key ...
The foundation of the most popular public-key cryptography algorithm in use today, RSA, rests on the difficulty of factoring large integers. When keys are generated, efficient algorithms are used to generate two very large prime numbers and multiply them together. The person who generated the ...
lost its advantage over trial division. However, that is because the regions involved are only two rows thick. For larger numbers, very many tries could still be required even in all but the very last stages, when Fermat factorization still retains its advantage over trial division. ...
The last two terms are due to DRAM storage, and have very small constants. Factoring Large Numbers with the TWIRL Device 9 Emitter Emitter Emitter Emitter Emitter Emitter Emitter Emitter Emitter Emitter Emitter Emitter Fig. 3. Schematic structure of a smallish station. at some single physical ...
Factoring also makes up an important part of most modern cryptographic algorithms used to secure communications over the internet. While you can see a small number can be easily factored, very large numbers may require a significantly larger amount of computer time for a factoring algorithm to run...
The quadratic sieve algorithm is currently the method of choice to factor very large composite numbers with no small factors. In the hands of the Sandia National Laboratories team of James Davis and Diane Holdridge, it has held the record for the largest hard number factore since mid-1983. As...
C# .NET implementation of the general number field sieve for factoring very large semi-prime numbers, which are used by the RSA public key encryption algorithm. The general number field sieve is an involved process, consisting of many steps: a polynomial creation, testing and selection process, ...
FACTORING POLYNOMIALSCONTINUED FRACTIONSFAST EXPONENTIATIONADDITION CHAINSFAST ALGORITHMGAUSS PERIODSGF(2MWe study exponentiation in finite fields with very special ... JVZ Gathen,M Nöcker - International Symposium on Symbolic & Algebraic Computation 被引量: 29发表: 1999年 Primes and Programming Miller'...
Computational methods for factoring large integers This paper presents a very readable account of some general purpose algorithms for factoring large random integers. Interest in this fascinating area of number theory has been greatly enhanced by the publication in 1978 (incorrectly quot... MC Wunderlic...