From 26806655936224d4cd97ffe2745489bc7dc3a2c3 Mon Sep 17 00:00:00 2001
From: Hans Svensson <hanssv@gmail.com>
Date: Mon, 17 Jan 2022 12:20:58 +0100
Subject: [PATCH] Improve pow by using crypto:mod_pow

---
 src/ecu_misc.erl      | 13 ++++++++++++-
 src/ecu_secp256k1.erl | 11 ++---------
 2 files changed, 14 insertions(+), 10 deletions(-)

diff --git a/src/ecu_misc.erl b/src/ecu_misc.erl
index 41565e6..9f9dc3a 100644
--- a/src/ecu_misc.erl
+++ b/src/ecu_misc.erl
@@ -4,10 +4,21 @@
 %%% Created     : 13 Jan 2022 by Hans Svensson
 -module(ecu_misc).
 
--export([eea/2,
+-export([eea/2, exp_mod/3,
          hex_to_bin/1, bin_to_hex/1,
          pcomp/1]).
 
+%% A^B mod P
+exp_mod(_A, 0, _P) -> 1;
+exp_mod(A, B, P) when A > 0 ->
+  binary:decode_unsigned(crypto:mod_pow(A, B, P));
+exp_mod(A, B, P) ->
+  X = exp_mod(-A, B, P),
+  case B rem 2 == 0 orelse X == 0 of
+    true  -> X;
+    false -> P - X
+  end.
+
 %% Extended Euclidean Algorithm
 eea(A, B) when ((A < 1) or (B < 1)) ->
     undefined;
diff --git a/src/ecu_secp256k1.erl b/src/ecu_secp256k1.erl
index 034f33e..28267bb 100644
--- a/src/ecu_secp256k1.erl
+++ b/src/ecu_secp256k1.erl
@@ -79,13 +79,7 @@ p_add({X1, Y1}, {X2, Y2}) ->
   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)).
+pow(A, B) -> ecu_misc:exp_mod(A, B, ?P).
 
 %% Arithmetics in prime field P
 f_add(A, B) -> (A + B) rem ?P.
@@ -94,8 +88,7 @@ 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.
+  pow(A, ?P - 2).
 
 %% Arithmetics in curve group order N
 s_add(A, B) -> (A + B) rem ?N.