[Cfrg] Review of ECC topics

[Robert Ransom <[e-mail]>]

See attached for a document reviewing the background in abstract
algebra, number theory, and elliptic curves that I consider necessary
to properly explain the specific design and implementation details of
Montgomery and Edwards curves (including conditions for twist
security, conversion between Montgomery and Edwards forms, conditions
for completeness of the Edwards-form addition law, use of Edwards
forms with a=-1 in fields where -1 is a non-square, and implementation
of simple point formats).

My main goal is to convey the intuition behind a few critical
mathematical concepts; I'm not trying to teach readers to implement
computations involving e.g. algebraic extension fields or Weierstrass
curves.  (Except for the sections on non-squares and square-root
computations, where I can only provide insight without a long
digression for fields in which -1 is a non-square.)


I would greatly appreciate any comments, especially from non-experts.
I am particularly interested in whether the sections on polynomial
rings, algebraic extension fields, and maps between curves (and
elliptic curves) are easy to understand.


Robert Ransom