[curves] Implementation

[Michael Hamburg]

A new revision is online, which support SHA-512 and signatures.  It’s still experimental, of course.

On my Macbook air (Haswell, TurboBoost @ 3.3GHz):

keygen:       48.7µs (20.5k/s; 161kcy)
ecdh:        169.3µs (5.9k/s; 559kcy)
sign:         51.8µs (19.3k/s; 171kcy)
verify:      187.9µs (5.3k/s; 621kcy)

I agree that Karatsuba should be about right for speed comparisons, meaning (ratio of conjectured security bit strengths)^2.6.

Cheers,
— Mike

On Mar 1, 2014, at 10:47 PM, Trevor Perrin <trevp at trevp.net> wrote:

> 
> On Fri, Feb 21, 2014 at 2:58 PM, Michael Hamburg <mike at shiftleft.org> wrote:
> 
> https://sourceforge.net/p/ed448goldilocks/code/ci/master/tree/
> 
> 
> Cool.  It would be nice to see this on eBACS, but its performance looks good on my Macbook Air -
> 
> Scalar mults per second:
> ----
> OpenSSL P-256    ~2800
> OpenSSL P-384    ~1400
> OpenSSL P-521    ~670
> Curve25519-donna-c64 ~14300
> Goldilocks-448   ~5900
> (
>   OpenSSL 1.0.2-beta1
>   https://github.com/agl/curve25519-donna
>   http://sourceforge.net/p/ed448goldilocks/
>   2013 Macbook Air, 1.7 GHz Core i7
> )
> 
> How do we compare the efficiency of different-size curves?  Is it reasonable to assume performance scales as O(n) due to scalar size and O(n^1.6) due to Karatsuba, or O(n^2.6) overall, where n is the security level - i.e. the sqrt of the order of the base point?
> 
> For example, curve25519 has a security level of ~126 bits, so would we expect a comparably efficient curve of Goldilocks size (~223-bits security) to be ~4.4x slower = (223/126)^2.6 ?
> 
> 
> Trevor
> 

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