Arjen Lenstra, a cryptology professor at the École Polytéchnique Fédérale de Lausanne in Switzerland, said the distributed computation project, conducted over 11 months, achieved the equivalent in difficulty of cracking a 700-bit RSA encryption key. Hence, transactions aren’t yet at risk, but "it is good advanced warning" of the coming dusk of 1024-bit RSA encryption, widely used now for Internet commerce, said Lenstra. The RSA encryption algorithm uses a system of public and private keys to encrypt and decrypt messages. The public key is calculated by multiplying two very large prime numbers. By identifying the two prime numbers used to create someone's public key, it's possible to calculate that person's private key and decrypt messages. But determining the prime numbers that make up a huge integer is nearly impossible without lots of computers and lots of time.
Using between 300 and 400 off-the-shelf laptop and desktop computers at EPFL, the University of Bonn and Nippon Telegraph and Telephone Corporation in Japan, researchers factored a 307-digit number into two prime numbers. Lenstra said they carefully selected a 307-digit number whose properties would make it easier to factor than other large numbers. Still, the calculations took 11 months, with the computers using special mathematical formulas created by researchers to calculate the prime numbers. The researchers would only be able to read a message encrypted with a key made from the 307-digit number they factored. But systems using the RSA encryption algorithm assign different keys to each user, and to break those keys, the process of calculating prime numbers would have to be repeated. The ability to calculate the prime number components of the current RSA 1024-bit public keys remains five to 10 years away, Lenstra said. Web sites should be looking toward stronger encryption than RSA 1024-bit.
News source: PC World
Using between 300 and 400 off-the-shelf laptop and desktop computers at EPFL, the University of Bonn and Nippon Telegraph and Telephone Corporation in Japan, researchers factored a 307-digit number into two prime numbers. Lenstra said they carefully selected a 307-digit number whose properties would make it easier to factor than other large numbers. Still, the calculations took 11 months, with the computers using special mathematical formulas created by researchers to calculate the prime numbers. The researchers would only be able to read a message encrypted with a key made from the 307-digit number they factored. But systems using the RSA encryption algorithm assign different keys to each user, and to break those keys, the process of calculating prime numbers would have to be repeated. The ability to calculate the prime number components of the current RSA 1024-bit public keys remains five to 10 years away, Lenstra said. Web sites should be looking toward stronger encryption than RSA 1024-bit.
News source: PC World
I know, off-the-shelf computers are used in this example. But a SuperComputer can most likely crack the system a touch faster.
And the quantum computer.
Long term however this will result in subspace warming and we will have to cut universal paradox emissions by 20% by 2090.
Long term however this will result in subspace warming and we will have to cut universal paradox emissions by 20% by 2090.
Lol, utilize paradoxes. Hahaha
Anyways they only factored a 307-digit number into two prime numbers, one 307-digit number which was carefully selected to be a easy one to factor. I guess those numbers are not used in RSA? So decrypting a 700-bit RSA encryption would probably take more than 11 months, even if they had better computers.
RSA 1024-bit encryption being at risk? Too optimistic I say.
And they are so stupid, lol I mean, if they had factored a 212-digit number RSA encryption (RSA-704), they would have received $30.000. Now why wouldn't they do that? Here is the link:
http://www.rsa.com/rsalabs/node.asp?id=2093
Or what about RSA-1024? Only 309 digtits, just two more than they used.. Prize: $100.000
RSA-640 has been decrypted, but that takes MUCH less time to decrypt. The computation took 5 months on 30 2.2 GHz AMD Opteron CPUs. Now that is a encryption that is risky to use.
As mentioned before, RSA-640 was decrypted by 30 opterons in 5 months. I believe some pro hackers can manage to get 30 opterons, and 5 months is not so much. But the time need to decrypt RSA-1024 is considerably higher than RSA-640, so it will be quite a while before that is not enough.
And the encryption can just increase as computers speed increases.
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