We propose to write Scheme code that unifies DSA and ECDSA which is sort of described in X9.63.
The input to the code is a computational Abelian group.
The 2014 Feb 8 version of <a href=http://en.wikipedia.org/wiki/Elliptic_Curve_DSA>this</a> is our inspiration.
Such a group is presented as (eq op I G inv n) where
<table>
<tr><td>eq<td>is the equality predicate for comparing two group<br>elements, in case representation is not canonical
<td>(eq a a)<br>(eq a b) → (eq b a)
<br>if (eq a b) then (if φ(a) then φ(b))
<tr><td>op<td>a function of type g×g→g
<br>where g is the set of group values<td>(eq (op a (op b c)) (op (op a b) c))<br>(eq (op a b) (op b a))
<tr><td>I<td>is the group identity<td>(eq (op I a) a)<br>(eq (op a I) a)
<tr><td>G<td>is some generator of the group
<tr><td>inv<td>is the inverse of the operation<td>(eq (op x (inv x)) I)
<tr><td>n<td>number of elements in group<td>nG = I</table>
I don’t know whether security or other logic depends on the group being commutative.
<p><tt>I</tt> could be computed as <tt>(((fileVal "expt") op #f #f) G n)</tt> or  <tt>(op G (inv G))</tt> but that seems unnecessary.
<br><tt>n</tt> could be computed as
<tt>(let c ((N 0)(g G)) (if (eq g I) N (+ 1 (c (op G g))))</tt> but then this would not qualify for the informal term “computational group”.
<hr><a href=http://en.wikipedia.org/wiki/ElGamal_signature_scheme>A good introduction</a> to the original signature idea.