The algorithm that factored RSA129 takes about exp(sqrt((log n)(log log n))) steps. Indeed 10^17 instructions is just about how much work was required to factor RSA129--. That formula gives about 10^29 for a 1024 bit number. If computers double in speed every 18 months then they will be only 32 times as fast when the patents expire.

If that rate of speedup held long term, and no significantly better factoring algorithms showed up, it would be 60 years until a 1024 bit number were as easy to factor as RSA129 was this year. -fnerd - - - - - - - - - - - - - - - and i dreamed i was flying high up above my eyes could clearly see the statue of liberty sailing away to sea --Paul Simon -----BEGIN PGP SIGNATURE----- Version: 2.3a aKxB8nktcBAeQHabQP/d7yhWgpGZBIoIqII8cY9nG55HYHgvt3niQCVAgUBLMs3K ui6XaCZmKH68fOWYYySKAzPkXyfYKnOlzsIjp2tPEot1Q5A3/n54PBKrUDN9tHVz 3Ch466q9EKUuDulTU6OLsilzmRvQJn0EJhzd4pht6hSnC1R3seYNhUYhoJViCcCG sRjLQs4iVVM= =9wqs -----END PGP SIGNATURE-----