DreamMX Weblogs » Fun http://blog.dreammx.com Team Blog Sun, 22 Mar 2009 19:07:39 +0000 http://wordpress.org/?v=2.9.2 en hourly 1 An attack on RSA http://blog.dreammx.com/general/fun/an-attack-on-rsa.html http://blog.dreammx.com/general/fun/an-attack-on-rsa.html#comments Tue, 17 Mar 2009 02:05:12 +0000 fox http://blog.dreammx.com/fox/general/fun/an-attack-on-rsa/ A simple concept on cracking RSA

The security of RSA is based on a math problem. For 2 huge(1000 bits) prime numbers p and q. We have n = p * q. Agreement on that: knowing n, calculating p and q is impossible right now.

But if p and q are close together (close means |p-q| < 1,000,000,000), the we’ve got a change

n = p*q = (p+q / 2)^2 – (p-q / 2)^2

Denotes T = √(p+q / 2)^2 and S = √(p-q/ 2)^2

if p and q are close

then S is close to 0

and T is close to √n

now start look at the following numbers

⌈√n⌉,⌈√n⌉+1,⌈√n⌉+2,⌈√n⌉+3,…

stop when we find a n that make t^2 – n is a perfect square number

and we’ve got the value of p and q.

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