Mathematicians Discover Pattern in Prime Numbers

[Collimatrix]

The terminal digit of consecutive prime numbers is not randomly distributed in the first hundred million prime numbers.

 

The comments at Bruce Schneier's blog took a look at this as well.  Anything having to do with patterns in prime numbers is potentially important to cryptography, since modern asymmetric encryption (the kind used for banking and other important stuff) relies on the difficulty of manipulating very large prime numbers.  If there are patterns that weren't recognized before, it might be easier to manipulate primes than was hitherto recognized, and that might mean that asymmetric encryption using prime numbers is less secure than previously thought.

[EnsignExpendable]

Once you go ECC you'll never... uh... Not do ECC?

[Collimatrix]

Once you go ECC you'll never... uh... Not do ECC?

 

That's pretty much been the retort whenever someone has proposed that there might be systematic weaknesses in integer factorization, or that the NSA has known one for years and kept it to themselves, &c.  I didn't mean to imply that an efficient way to factor primes would change the world, just a lot of people would have to change their encryption software in a very big hurry.  I admit to considerable ignorance on the specifics though; aren't discrete logarithms and elliptical curve schemes slower?

[EnsignExpendable]

Asymmetric encryption is slower than symmetric, so? In practice all you'll be doing is exchanging a session key anyway, so it doesn't really matter for real performance if you use prime numbers or ECC.

[Collimatrix]

Aha, makes sense.  Thanks.