Factoring Large Numbers with the Twinkle Device (Extended Abstract)

The current record in factoring large RSA keys is the factorization of a 465 bit (140 digit) number achieved in February 1999 by running the Number Field Sieve on hundreds of workstations for several months. This paper describes a novel factoring apparatus which can accelerate known sieve-based factoring algorithms by several orders of magnitude. It is based on a very simple handheld optoelectronic device which can analyse 100,000,000 large integers, and determine in less than 10 milliseconds which ones factor completely over a prime base consisting of the first 200,000 prime numbers. The proposed apparatus can increase the size of factorable numbers by 100 to 200 bits, and in particular can make 512 bit RSA keys (which protect 95% of today’s E-commerce on the Internet) very vulnerable.