Topic: why did bitcoin choose secp256k1 over secp256r1? - page 2. (Read 19374 times)

That thread is a _little_ misleading.  The author is writing about the traditional characteristic 2 koblitz curves (e.g. NIST k curves). SECP256k1 is a curve which is not part of the nist standard. It is a generalization of the koblitz but with a prime field that admits similar optimizations. The design freedom for it is this generalization is somewhat larger than than that available for characteristic 2 koblitz. ... but the design space still is substantially constrained, and I agree with the conclusion that it reduces the room for carefully selected values.

Since 2007 there is evidence that the supposedly random constants in secp256r1 may have been manipulated by the NSA to provide a backdoor.  See http://www.wired.com/politics/security/commentary/securitymatters/2007/11/securitymatters_1115.  Presumably Satoshi was aware of this.  The Koblitz curves cannot have been so "cooked"; see http://crypto.stackexchange.com/questions/10263/should-we-trust-the-nist-recommended-ecc-parameters/10273#10273.

Ed25519 is not curve25519. Ed25519 is the work of Daniel J. Bernstein, Niels Duif, Tanja Lange, Peter Schwabe, Bo-Yin Yang..

"frankenlicenses" on some code are irrelevant, as no one is married to a particular implementation... though the reference Ed25519 implementation is public domain.

Bitcoin can smoothly pick up new signature methods. We've even done a deployment of this with P2SH.  But the big speedup of Ed25519 is perhaps not the cost and risk which is why no one is proposing it at least now.

Everything he does is non-standard. He invented his own FHS and init implementation, just because. Integrating his software with any system vaguely unix-like is an enormous pain in the ass that people only ever tolerated because the alternatives to his software (Bind) sucked that much at the time.

i've always been a bit wary of djb crypto, despite the guy being a pretty big producer idea-wise. his algos are not nearly as well-studied as the standard ones and he has a tendency to assign "frankenlicenses" on his code.

i guess any change to bitcoin crypto would require a hard fork in the absence of plumbing that would facilitate smooth cipher changes.

Perhaps somebody should start selling some kind of PCI-Express slot dedicated ASIC coprocessor for such computations to mitigate that bottleneck ?

If Bitcoin becomes really popular, such needs may arise in the future - i can see a market for that then.

sipa was saying that he thinks it's possible to maybe double the speed of signature checking by using an implementation specifically created just for that curve (this is beyond the GLV optimizations). But we'll see.

Signature checking is, in fact, a major bottleneck. It didn't use to be but it is now. Sadly, Ed25519 didn't exist back then...

yeah, i had seen that it does offer some speed advantages. i don't believe signature checking speed is currently a bottleneck, but extra cpu cycles always help.

The random curves aren't really any more or less secure than the other curves, they are merely more conservative. Given some arbitrary constants with which to initialize the algorithms, choosing random numbers (or more specifically, nothing-up-my-sleeve numbers) is one way to build trust that there are no funny games being played with the specific choices.

However, the GLV method allows for much faster computations when these constants are not randomly chosen but rather chosen according to some criteria. It opens up the possibility that by selecting values in this way, some unknown weakness is introduced, but nobody has ever been able to show that the non-random curves actually are more insecure.

There have been no further discussions of this topic since the original thread you linked to.

something i find rather disconcerting about bitcoin is a lack of justification/explanation for some of the design decisions, in particular the choice of doing 256-bit ecdsa keypairs over secp256k1 vs secp256r1 (a.k.a. P-256) for wallets.

the best i could find on the forum is this thread from 2011 - https://bitcointalk.org/?topic=2699.0

NIST recommends use of secp256r1, and more generally prefers random curve parameters to the Koblitz ones. i can only speculate why this choice was made, here are a couple possible reasons:

* NIST sets standards for NSA / US govt crypto and is genuinely concerned about everyone's security. they have found that random curves are more secure than Koblitz ones.
* NIST has made an intentionally poor suggestion to use secp256r1, so it acts as a honeypot. they have found that Koblitz curves are actually more secure than the random ones.

with those reasons in mind i could see bitcoin having analogous justifications:

* Satoshi had information which led him/them to believe that secp256r1 was indeed a honeypot and that secp256k1 was the better choice for real security
* Satoshi knew that secp256k1 was weak and intentionally included it in bitcoin to make bitcoin into a honeypot

considering that the design decisions for both BTC and NIST ciphers are both entirely opaque, it is difficult to make a good guess as to their motivation. i have similar reservations about using base58 everywhere, but that is less a concern from a security perspective.

can anyone provide a justification for using secp256k1 over secp256r1 besides "that's just the way it is" or "so it was written in the great book"?