A rigorous time bound for factoring integers

An algorithm for factoring integers

We propose an algorithm for factoring a composite number. The method seems new.

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...

Methods of Factoring Large Integers

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.

Factoring Integers by CVP Algorithms

We use pruned enumeration algorithms to find lattice vectors close to a specific target vector for the prime number lattice. These algorithms generate multiplicative prime number relations modulo N that factorize a given integer N . The algorithm New Enum performs the stages of exhaustive enumeration of close lattice vectors in order of decreasing success rate. For example an integer N ≈ 10 can...