[Unique Solution From 10/Pg] Took 30 2

You are required to submit your code (as demonstrated in the lab manual) and running results (with comments if necessary).

An Industrial-Grade RSA System.

The RSA Corporation put out a number of public challenges with monetary rewards to factor some very large RSA moduli. RSA no longer offers such challenges, but RSA-640 was the last of these challenges that they put out in 2001 to be factored. The factorization was announced in 2005 by a team of scientists and it took 30 2.2GHz-Opteron-CPU years (in over 5 months of calendar time).

RSA-640 has 193 decimal digits (640 bits)

RSA-640 = 310741824049004372135075003588856793003734602284272754572016194882320644051808 150455634682967172328678243791627283803341547107310850191954852900733772482278 3525742386454014691736602477652346609

In the following tasks, use hexadecimal format for all numbers in your code:

Find the two prime factors and verify that they are indeed the factors of RSA-640. (Use VirtualBox and Openssl and BIGNUM library).