Page "Integer factorization" Paragraph 1

When the numbers are very large, no efficient, non-quantum integer factorization algorithm is known ; an effort concluded in 2009 by several researchers factored a 232-digit number ( RSA-768 ), utilizing hundreds of machines over a span of 2 years.

The presumed difficulty of this problem is at the heart of widely used algorithms in cryptography such as RSA.

Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing.