Add some EcDSA functionality

src/ecu_ecdsa.erl

@@ -0,0 +1,53 @@
+%%% File        : ecu_ecdsa.erl
+%%% Author      : Hans Svensson
+%%% Description : ecdsa functionality
+%%% Created     : 13 Jan 2022 by Hans Svensson
+-module(ecu_ecdsa).
+
+-export([sign/3, verify/4,
+         sign_secp256k1/2,
+         private_to_public/2]).
+
+private_to_public(secp256k1, <<PrivateKey:256>>) ->
+  ecu_secp256k1:compress(ecu_secp256k1:scalar_mul_base(PrivateKey)).
+
+sign(secp256k1, MsgHash = <<_:32/bytes>>, PrivateKey = <<_:32/bytes>>) ->
+  {Sig, _YVal} = sign_secp256k1(MsgHash, PrivateKey),
+  Sig.
+
+verify(secp256k1, MsgHash = <<_:32/bytes>>, PubKey = <<_:33/bytes>>, Sig = <<_:64/bytes>>) ->
+  verify(secp256k1, MsgHash, ecu_secp256k1:decompress(PubKey), Sig);
+verify(secp256k1, MsgHash = <<_:32/bytes>>, PubKey = {_, _}, Sig = <<_:64/bytes>>) ->
+  <<E:256>> = MsgHash,
+  <<R:256, S:256>> = Sig,
+  Z = E rem ecu_secp256k1:n(),
+  W = ecu_secp256k1:s_inv(S),
+  [P1, P2] = ecu_misc:pcomp(
+               [fun() -> ecu_secp256k1:scalar_mul_base(ecu_secp256k1:s_mul(Z, W)) end,
+                fun() -> ecu_secp256k1:scalar_mul(ecu_secp256k1:s_mul(R, W), PubKey) end]),
+  {X, _Y} = ecu_secp256k1:p_add(P1, P2),
+  R == (X rem ecu_secp256k1:n()).
+
+sign_secp256k1(MsgHash = <<_:32/bytes>>, PrivateKey = <<_:32/bytes>>) ->
+  <<E:256>> = MsgHash,
+  <<D:256>> = PrivateKey,
+  Z = E rem ecu_secp256k1:n(),
+  K = pick_k(secp256k1),
+  {X, Y} = ecu_secp256k1:scalar_mul_base(K),
+  R = X rem ecu_secp256k1:n(),
+  S = ecu_secp256k1:s_mul(ecu_secp256k1:s_inv(K),
+                          ecu_secp256k1:s_add(Z, ecu_secp256k1:s_mul(R, D))),
+  if R == 0 orelse S == 0 ->
+       sign(secp256k1, MsgHash, PrivateKey);
+     true ->
+       {<<R:256, S:256>>, Y}
+  end.
+
+%% --- internal functions
+
+pick_k(secp256k1) ->
+  <<K:256>> = crypto:strong_rand_bytes(32),
+  case K == 0 orelse K >= ecu_secp256k1:n() of
+    true  -> pick_k(secp256k1);
+    false -> K
+  end.

src/ecu_misc.erl

@@ -4,7 +4,7 @@
 %%% Created     : 13 Jan 2022 by Hans Svensson
 -module(ecu_misc).
 
--export([eea/2]).
+-export([eea/2, pcomp/1]).
 
 %% Extended Euclidean Algorithm
 eea(A, B) when ((A < 1) or (B < 1)) ->
@@ -18,4 +18,8 @@ eea(G0, S0, T0, G1, S1, T1) ->
     Q = G0 div G1,
     eea(G1, S1, T1, G0 - (Q * G1), S0 - (Q * S1), T0 - (Q * T1)).
 
-
+%% Very rudimentary parallel computation...
+pcomp(Fs) ->
+  Parent = self(),
+  Pids = [ spawn(fun() -> Parent ! {self(), F()} end) || F <- Fs ],
+  [ receive {Pid, X} -> X after 500 -> error(timeout) end || Pid <- Pids ].