2009/6/6 David Schwartz <dav...@webmaster.com>: > >> hello, >> when i read some books about cryptography, it always go that the >> cryptography is based on the difficult math problem, for example big >> integer decomposition, >> i don't understand it, for if we know that n = p*q , p, q are prime , >> why it's difficult to get p and q ? i think ,if we know the big >> integer and it is mul of two prime number. we can get prime number >> and test whether p*q == n, why people say it 's a difficult problem? >> may be my understanding is not right? someone who knows please tell me >> , thank you very much > > Okay, let's look at 'n' for a second. Both 'p' and 'q' are roughly of the > order of magnitude of the square root of 'n'. A typical 'n' might be 600 > digits, so 'p' and 'q' are roughly 300 digits long each (express in base how he find the prime number p and q? i think we should not test all the 300 bits number, we just find the prime, many prime has already find , hasn't ? we just choose the suitable prime number from the table .
> 10). Let's assume you could test, say, a hundred billion 'p'/'p' values in a > second. Well, you do the math and you get over 10^100 billion years expected > time to find the answer. may be i do not express my idea clearly, we know that p and q are prime . And we also know that the > > This is a simple and naive analysis, and doubtless there are faster > algorithms than trying every value. But even if you assume some brilliant > algorithm makes the process 100 billion billion times faster, it's still > over 10^100 billion years. > > This is hardly anything remotely resembling a formal proof, of course. But > it should give you the basic idea -- it's a difficult problem because the > numbers are big. > > DS > > > ______________________________________________________________________ > OpenSSL Project http://www.openssl.org > User Support Mailing List openssl-us...@openssl.org > Automated List Manager majord...@openssl.org > ______________________________________________________________________ OpenSSL Project http://www.openssl.org User Support Mailing List openssl-users@openssl.org Automated List Manager majord...@openssl.org
