### Re: [Cryptography] A Likely Story!

On Sun, 8 Sep 2013, Peter Fairbrother wrote: On the one hand, if they continued to recommend that government people use 1024-bit RSA they could be accused of failing their mission to protect government communications. On the other hand, if they told ordinary people not to use 1024-bit RSA, they could be accused of failing their mission to spy on people. What to do? NIST recommends at least RSA-2048 for a long time, for example NIST Special Publication 800-57, back in August, 2005 said: [...] for Federal Government unclassified applications. A minimum of eighty bits of security shall be provided until 2010. Between 2011 and 2030, a minimum of 112 bits of security shall be provided. Thereafter, at least 128 bits of security shall be provided. Note that RSA-1024 ~ 80 bits of security; RSA-2048 ~ 112 bits; RSA-3072 ~ 128 bits So if anyone to blame for using 1024-bit RSA, it is not NIST. BTW, once you realize that 256 bits of security requires RSA with 15360 bits, you will believe conspiracy theories about ECC much less. Here exponentiation with 15360 bits takes 15^3=3375 times more CPU time than a 1024-bit exponentiation, thus using RSA for 256-bit security is impractical. You can use any one of trillions of different elliptic curves,which should be chosen partly at random and partly so they are the right size and so on; but you can also start with some randomly-chosen numbers then work out a curve from those numbers. and you can use those random numbers to break the session key setup. Can you elaborate on how knowing the seed for curve generation can be used to break the encryption? (BTW, the seeds for randomly generated curves are actually published.) -- Regards, ASK ___ The cryptography mailing list cryptography@metzdowd.com http://www.metzdowd.com/mailman/listinfo/cryptography

### Re: [Cryptography] A Likely Story!

On 09/09/13 12:53, Alexander Klimov wrote: On Sun, 8 Sep 2013, Peter Fairbrother wrote: You can use any one of trillions of different elliptic curves,which should be chosen partly at random and partly so they are the right size and so on; but you can also start with some randomly-chosen numbers then work out a curve from those numbers. and you can use those random numbers to break the session key setup. Can you elaborate on how knowing the seed for curve generation can be used to break the encryption? (BTW, the seeds for randomly generated curves are actually published.) Move along please, there is nothing to see here. This is just a wild and disturbing story. It may upset you to read it, so please stop reading now. You may have read a bit about the story in the papers or internet or elsewhere, but isn't actually true. Government Agencies do not try to break the internet's encryption, as used by Banks and Doctors and Commerce and Government Departments and even Government Agencies themselves - that wouldn't be sensible. Besides which, there is no such agency as the NSA. But .. Take FIPS P-256 as an example. The only seed which has been published is s= c49d3608 86e70493 6a6678e1 139d26b7 819f7e90 (the string they hashed and mashed in the process of deriving c). I don't think they could reverse the perhaps rather overly-complicated hashing/mashing process, but they could certainly cherry-pick the s until they found one which gave a c which they could use. c not being one of the usual parameters for an elliptic curve, I should explain that it was then used as c = a^3/b^2 mod p. However the choice of p, r, a and G was not seeded, and the methods by which those were chosen are opaque. I don't really know enough about ECC to say whether a perhaps cherry-picked c = a^3/b^2 mod p is enough that the resulting curve is secure against chosen curve attacks - but it does seem to me that there is a whole lot of legroom between a cherry-picked c and the final curve. And as I said, it's only a story. We don't know much about what the NSA knows about chosen curve attacks, although we do know that they are possible. Don't go believing it, it will just upset you. They wouldn't do that. -- Peter Fairbrother ___ The cryptography mailing list cryptography@metzdowd.com http://www.metzdowd.com/mailman/listinfo/cryptography