Factoring large integers

Methods of Factoring Large Integers

Shor ’ s Algorithm for Factoring Large Integers ∗

This work is a tutorial on Shor's factoring algorithm by means of a worked out example. Some basic concepts of Quantum Mechanics and quantum circuits are reviewed. It is intended for non-specialists which have basic knowledge on undergraduate Linear Algebra.

Fast Factoring of Integers

An algorithm is given to factor an integer with N digits in lnN steps, with m approximately 4 or 5. Textbook quadratic sieve methods are exponentially slower. An improvement with the aid of an a particular function would provide a further exponential speedup. Factorization of large integers is important to many areas of pure mathematics and has practical applications in applied math including c...

Factoring Integers with Large-Prime Variations of the Quadratic Sieve

AMS Subject Classi cation: 11A51, 11Y05.

Factoring Integers Using SIMD Sieves

We describe our single-instruction multiple data (SIMD) implementation of the multiple polynomial quadratic sieve integer factoring algorithm. On a 16K MasPar massively parallel computer, our implementation can factor 100 digit integers in a few days. Its most notable success was the factorization of the 110-digit RSA-challenge number, which took about a month.