Security-57031.1.35.tar.gz

[apple/security.git] / Security / libsecurity_cryptkit / lib / Mathematica.FEE

diff --git a/Security/libsecurity_cryptkit/lib/Mathematica.FEE b/Security/libsecurity_cryptkit/lib/Mathematica.FEE
new file mode 100644 (file)
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+++ b/Security/libsecurity_cryptkit/lib/Mathematica.FEE
@@ -0,0 +1,57 @@
+(* Elliptic algebra functions: FEE format.
+
+   y^2 = x^3 + c x^2 + a x + b.
+
+   Montgomery: b = 0, a = 1;
+   Weierstrass: c = 0;
+   Atkin3: c = a = 0;
+   Atkin4: c = b = 0;
+
+   Parameters c, a, b, p must be global.
+ *)
+
+elleven[pt_] := Block[{x1 = pt[[1]], z1 = pt[[2]], e, f },
+       e = Mod[(x1^2 - a z1^2)^2 - 4 b (2 x1 + c z1) z1^3, p];
+       f = Mod[4 z1 (x1^3 + c x1^2 z1 + a x1 z1^2 + b z1^3), p];
+       Return[{e,f}]
+];
+
+ellodd[pt_, pu_, pv_] := Block[
+               {x1 = pt[[1]], z1 = pt[[2]],
+                x2 = pu[[1]], z2 = pu[[2]],
+                xx = pv[[1]], zz = pv[[2]], i, j},
+            i = Mod[zz ((x1 x2 - a z1 z2)^2 -
+                 4 b(x1 z2 + x2 z1 + c z1 z2) z1 z2), p];
+            j = Mod[xx (x1 z2 - x2 z1)^2, p];
+                Return[{i,j}]
+];
+
+bitList[k_] := Block[{li = {}, j = k},
+       While[j > 0,
+           li = Append[li, Mod[j,2]];
+           j = Floor[j/2];
+       ];
+       Return[Reverse[li]];
+       ];
+
+elliptic[pt_, k_] := Block[{porg, ps, pp, q},
+
+       If[k ==1, Return[pt]];
+       If[k ==2, Return[elleven[pt]]];
+       porg = pt;
+       ps = elleven[pt];
+       pp = pt;
+       bitlist = bitList[k];
+       Do[
+          If[bitlist[[q]] == 1,
+                  pp = ellodd[ps, pp, porg];
+                  ps = elleven[ps],
+                     ps = ellodd[pp, ps, porg];
+                     pp = elleven[pp]
+          ],
+          {q,2,Length[bitlist]}
+    ];
+    Return[Mod[pp,p]]
+];
+ellinv[n_] := PowerMod[n,-1,p];
+ex[pt_] := Mod[pt[[1]] * ellinv[pt[[2]]], p];