Decoding Secret Credit Card Numbers & Phone Recharge Codes

[debayan]

how are the secret codes for recharging the credit of a phone or the secret credit card numbers gnerated? i hrd something with prime nos. any way to decode them?

 

[HallsofIvy]

I assume you are talking about "trap door" codes- where you can be told how to encode a messsage but that doesn't help you decode it. I don't know all the details but essentially it uses the fact that while it is relatively easy to multiply two large (prime) numbers together, it is almost impossible to factor the product without knowing the two factors to begin with. Yes, it is possible to decode them:
(1) Know the correct factors to begin with
(2) Use very, very powerful computer for a very, very long time.

 

[CompuChip]

Well, it can be cracked, but there's no smooth way to do it.
If there were, http://www.rsa.com/rsalabs/node.asp?id=2092 wouldn't give out $30,000 to the one who factors a number of "just" 212 decimal digits (and $200,000 for a 600+ digit number) :)

 

[Feldoh]

"RSA-640 is factored!

The factoring research team of F. Bahr, M. Boehm, J. Franke, T. Kleinjung continued its productivity with a successful factorization of the challenge number RSA-640, reported on November 2, 2005. The factors [verified by RSA Laboratories] are:

16347336458092538484431338838650908598417836700330
92312181110852389333100104508151212118167511579

and

1900871281664822113126851573935413975471896789968
515493666638539088027103802104498957191261465571

The effort took approximately 30 2.2GHz-Opteron-CPU years according to the submitters, over five months of calendar time. (This is about half the effort for RSA-200, the 663-bit number that the team factored in 2004.)
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Remember what HallsofIvy was just saying XD