[Cryptography] What to put in a new cryptography course

[Ron Garret]

On Jul 8, 2016, at 3:16 PM, Ray Dillinger <bear at sonic.net> wrote:

> 
> 
> On 07/07/2016 02:45 PM, Ron Garret wrote:
>> 
>> On Jul 7, 2016, at 2:15 PM, Ray Dillinger <bear at sonic.net> wrote:
>> 
>>> I get the _mechanics_ of ECC as "geometry of lines tangent to curves in
>>> modular coordinate systems"  but what makes a particular curve secure or
>>> insecure in a particular modular coordinate system?
>> 
>> This seems like a good place to start:
>> 
>> https://safecurves.cr.yp.to/
>> 
> 
> 
> The site contains lots of assertions that curves with particular
> properties are more secure than curves that don't have those
> properties.  I've read it before. It is good practical advice
> for selecting among known curves, and it is greatly appreciated
> as a resource. However, it is yet another resource which
> resolutely ignores the basic question I would want out of a
> course on ECC and had intended to ask.
> 
> In fact evaluating the rationales given for most of the advice
> would require that basic question to be answered first.
> 
> Having reread the whole site, I still have not discovered an
> explanation of exactly how the mechanics of geometry on modular
> coordinate systems are transformed in some cases into a specific
> algebraic formula whose solution would require mathematical
> operations believed to be Hard.

It’s the elliptic curve discrete logarithm problem:

http://wstein.org/edu/2007/spring/ent/ent-html/node89.html

(I feel like I must be misunderstanding your question because surely you knew that already?)

rg