[curves] Implementation

Trevor Perrin trevp at trevp.net
Sat Mar 1 22:47:26 PST 2014

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
  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 ?

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