Add secp256k1

src/ec_utils.app.src

@@ -4,7 +4,7 @@
   {registered, []},
   {applications, [kernel, stdlib]},
   {env,[]},
-  {modules, []},
+  {modules, [ecu_secp256k1, ecu_misc]},
   {licenses, ["MIT"]},
   {links, []}
  ]}.

src/ecu_misc.erl

@@ -0,0 +1,21 @@
+%%% File        : ecu_misc.erl
+%%% Author      : Hans Svensson
+%%% Description : Misc. functionality
+%%% Created     : 13 Jan 2022 by Hans Svensson
+-module(ecu_misc).
+
+-export([eea/2]).
+
+%% Extended Euclidean Algorithm
+eea(A, B) when ((A < 1) or (B < 1)) ->
+    undefined;
+eea(A, B) ->
+    eea(A, 1, 0, B, 0, 1).
+
+eea(G, S, T, 0, _, _) ->
+    {G, S, T};
+eea(G0, S0, T0, G1, S1, T1) ->
+    Q = G0 div G1,
+    eea(G1, S1, T1, G0 - (Q * G1), S0 - (Q * S1), T0 - (Q * T1)).
+
+

src/ecu_secp256k1.erl

@@ -0,0 +1,117 @@
+%%% File        : ecu_secp256k1.erl
+%%% Author      : Hans Svensson
+%%% Description : Trying to whip together a pure Erlang secp256k1
+%%%               Just for usage when speed isn't crucial...
+%%% Created     : 22 Dec 2021 by Hans Svensson
+-module(ecu_secp256k1).
+
+-define(P, 16#FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F).
+-define(A, 16#00).
+-define(B, 16#07).
+-define(X, 16#79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798).
+-define(Y, 16#483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8).
+-define(N, 16#FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141).
+-define(E, 16#7AE96A2B657C07106E64479EAC3434E99CF0497512F58995C1396C28719501EE).
+
+-define(ADD(A, B), ((A + B) rem ?P)).
+-define(MUL(A, B), ((A * B) rem ?P)).
+-define(SUB(A, B), ((A - B + ?P) rem ?P)).
+-define(DIV(A, B), f_div(A, B)).
+
+-export([on_curve/1, p/0, n/0,
+         scalar_mul/2, scalar_mul_base/1, p_add/2, p_neg/1,
+         compress/1, decompress/1,
+         f_add/2, f_mul/2, f_sub/2, f_div/2, f_inv/1,
+         s_add/2, s_mul/2, s_sub/2, s_div/2, s_inv/1]).
+
+-ifdef(TEST).
+-compile([export_all, nowarn_export_all]).
+-endif.
+
+on_curve({X, Y}) ->
+  %% y^2 = x^3 + 7
+  X3 = ?MUL(?MUL(X, X), X),
+  Y2 = ?MUL(Y, Y),
+  Y2 == ?ADD(X3, ?B).
+
+p() -> ?P.
+
+n() -> ?N.
+
+scalar_mul_base(K) ->
+  scalar_mul(K, {?X, ?Y}).
+
+scalar_mul(0, _P) ->
+  {0, 0};
+scalar_mul(1, P) ->
+  P;
+scalar_mul(K, P) ->
+  case K rem 2 == 0 of
+    true  -> scalar_mul(K div 2, p_add(P, P));
+    false -> p_add(P, scalar_mul(K - 1, P))
+  end.
+
+compress({X, Y}) when Y rem 2 == 0 -> <<2:8, X:256>>;
+compress({X, _})                   -> <<3:8, X:256>>;
+compress(<<4:8, X:256, Y:256>>)    -> compress({X, Y}).
+
+decompress(<<N:8, X:256>>) ->
+  Y0 = ?B + ?MUL(X, ?MUL(X, X)),
+  Y1 = pow(Y0, (?P + 1) div 4),
+  case Y1 rem 2 == N rem 2 of
+    true  -> {X, Y1};
+    false -> {X, ?P - Y1}
+  end.
+
+p_neg({X, Y}) -> {X, ?P - Y}.
+
+p_add(P1, {0, 0}) -> P1;
+p_add({0, 0}, P2) -> P2;
+p_add({X, Y1}, {X, Y2}) when Y1 /= Y2 -> {0, 0};
+p_add(P = {X1, Y1}, P) ->
+  M  = ?DIV(?MUL(3, ?MUL(X1, X1)), ?MUL(2, Y1)),
+  X3 = ?SUB(?MUL(M, M), ?MUL(2, X1)),
+  Y3 = ?SUB(?MUL(M, ?SUB(X1, X3)), Y1),
+  {X3, Y3};
+p_add({X1, Y1}, {X2, Y2}) ->
+  M  = ?DIV(?SUB(Y2, Y1), ?SUB(X2, X1)),
+  X3 = ?SUB(?MUL(M, M), ?ADD(X1, X2)),
+  Y3 = ?SUB(?MUL(M, ?SUB(X1, X3)), Y1),
+  {X3, Y3}.
+
+pow(_, 0) -> 1;
+pow(A, 1) -> A;
+pow(A, B) -> pow(A, B, 1).
+
+pow(_, 0, R)                   -> R;
+pow(A, B, R) when B rem 2 == 0 -> pow(A * A, B bsr 1, R);
+pow(A, B, R)                   -> pow(?MUL(A, A), B bsr 1, ?MUL(R, A)).
+
+%% Arithmetics in prime field P
+f_add(A, B) -> (A + B) rem ?P.
+f_mul(A, B) -> (A * B) rem ?P.
+f_sub(A, B) -> (A - B + ?P) rem ?P.
+f_div(A, B) -> f_mul(A, f_inv(B)).
+
+f_inv(A) ->
+  {1, S, _T} = ecu_misc:eea(A, ?P),
+  (S + ?P) rem ?P.
+
+%% Arithmetics in curve group order N
+s_add(A, B) -> (A + B) rem ?N.
+s_mul(A, B) -> (A * B) rem ?N.
+s_sub(A, B) -> (A - B + ?N) rem ?N.
+s_div(A, B) -> s_mul(A, s_inv(B)).
+
+s_inv(A) ->
+  {1, S, _T} = ecu_misc:eea(A, ?N),
+  (S + ?N) rem ?N.
+
+%% curve() ->
+%%   #{ p => 16#FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F,
+%%      a => 16#00, b => 16#07,
+%%      x => 16#79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798,
+%%      y => 16#483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8,
+%%      n => 16#FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141,
+%%      e => 16#7AE96A2B657C07106E64479EAC3434E99CF0497512F58995C1396C28719501EE
+%%    }.