[EMAIL PROTECTED] wrote: > > On 26 Feb 2002, at 19:46, Henk Stokhorst wrote: > > > http://slashdot.org > > > > factoring breakthrough? > > > Doesn't look like a breakthrough, although there may be a very > significant reduction in the amount of work required to factor > "awkward" numbers. > > The implications in terms of public key cryptography look as > though they could be significant - those "secure" 128-bit cyphers in > widespread use for e-commerce are starting to look pretty > transparent, but doubling the number of bits in the key is more than > sufficient to "defeat" this latest advance.
The 128 bits refer to the symmetric part of the protocol. Asymmetric ciphers are much slower than symmetric, so in practice one generates a session key for a symmetric cipher, encrypts that asymetrically and sends it to the other guy, and encrypts the actual communication with the symmetric key that both now have. For example, the Web Email service of the LRZ M�nchen uses 128 bit RC-4 for the symmetric part, and a 2048-bit RSA key for the asymmetric part, according to Opera. The symmetric ciphers are totally unaffected by advancements in integer factoring, but the asymmetric are not. Many public-key systems rely on the difficulty of factoring integers (i.e. RSA) or of computing discrete logarithms (ElGamal) and the ideas in Bernstein's paper can supposedly speed up both. Bernstein's point is that custom built hardware can reduce the asymptotic complexity of NFS factoring rather than offering just a linear speedup. He claims that with the same hardware cost, custom built hardware can factor numbers in the same time that a general purpose machines needs to factor numbers of a third the size. If that should prove true, it would be well deserving of the word "breakthrough". It remains to be seen whether the ideas work with numbers of "interesting" size (150-300 decimals, say) and whether the proposed circuits can be practically realised. > Regards > Brian Beesley Alex _________________________________________________________________________ Unsubscribe & list info -- http://www.ndatech.com/mersenne/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
