add curve25519 and toy

try/bin/curve.hoon

@@ -0,0 +1,34 @@
+::
+::  /=main=/bin/curve/hoon
+::
+=>  %=    .
+        +
+      =>  +
+      ^/===/lib/cryo
+    ==
+|=  [est=time eny=@uw]
+|=  ~
+^-  bowl
+:_  ~  :_  ~
+:-  %$
+!>
+=+  pk=48.084.050.389.777.770.101.701.157.326.923.977.117.
+       307.187.144.965.043.058.462.938.058.489.685.090.437
+=+  sk=(cla:curv 19.076.158.533.740.022.697.853.188.432.810.
+                 029.468.508.100.820.210.985.396.154.491.514.718.125.885.303)
+=+  ska=(gen:curv eny)
+=+  sky=(gen:curv (shax eny))
+:*
+  %public-test
+  :+
+    [%reference-public pk]
+    [%calculate-public (curve:curv sk 9)]
+    [%equals =((curve:curv sk 9) pk)]
+  %diffie-hellman
+  [%alice-secret ska]
+  [%bob-secret sky]
+  [%alice-calcs (curve:curv sky (curve:curv ska 9))]
+  [%bobp-calcs (curve:curv ska (curve:curv sky 9))]
+  %equals
+  =((curve:curv sky (curve:curv ska 9)) (curve:curv ska (curve:curv sky 9)))
+==

try/lib/cryo.hoon

@@ -337,4 +337,62 @@
     =((scam bb ss) (ward u.rr (scam u.aa h)))
   ::
   --
+++  curv
+  =+  pol=486.662
+  |%
+    ++  gen
+      |=  ent=@
+      (cla (shaw 0 256 ent))
+    ::
+    ++  cla
+      |=  raw=@
+      =+  low=(dis 248 (cut 3 [0 1] raw))
+      =+  hih=(con 64 (dis 127 (cut 3 [31 1] raw)))
+      =+  mid=(cut 3 [1 30] raw)
+      (can 3 [[1 low] [30 mid] [1 hih] ~])
+    ::
+    ++  sqr  |=  in=@  (mul in in)
+    ::
+    ++  pri  (sub (bex 255) 19)
+    ::
+    ++  inv
+      |=  in=@
+      (~(exp fo pri) (sub pri 2) in)
+    ::
+    ++  cad
+      |=  [n=[x=@ z=@] m=[x=@ z=@] d=[x=@ z=@]]
+      =+  ^=  xx
+          ;:  mul  4   z.d
+          (sqr (abs:si (dif:si (sun:si (mul x.m x.n)) (sun:si (mul z.m z.n)))))
+          ==
+      =+  ^=  zz
+          ;:  mul   4   x.d
+          (sqr (abs:si (dif:si (sun:si (mul x.m z.n)) (sun:si (mul z.m x.n)))))
+          ==
+      [(mod xx pri) (mod zz pri)]
+    ::
+    ++  cub
+      |=  [x=@ z=@]
+      =+  ^=  xx
+        (mul (sqr (abs:si (dif:si (sun:si x) (sun:si z)))) (sqr (add x z)))
+      =+  ^=  zz
+        :(mul 4 x z :(add (sqr x) :(mul pol x z) (sqr z)))
+      [(mod xx pri) (mod zz pri)]
+    ::
+    ++  curve
+      |=  [n=@ base=@]
+      =+  one=[base 1]
+      =+  two=(cub one)
+      =+  i=253
+      =+  q=one
+      =+  r=(cub one)
+      |-
+      ?:  =(i 0)
+        =+  x=(cub q)
+        (mod (mul -.x (inv +.x)) pri)
+      =+  m=(rsh 0 i n)
+      ?:  =(0 (mod m 2))
+         $(i (dec i), r (cad q r one), q (cub q))
+      $(i (dec i), q (cad q r one), r (cub r))
+  --
 --