From 3c64879ccf1212d2b33d5a764296f93b65563d26 Mon Sep 17 00:00:00 2001
From: Thorsten Sommer <service@sommer-engineering.com>
Date: Tue, 7 Jan 2020 00:21:29 +0100
Subject: [PATCH] Optimized ExpMod to operate without recursion

---
 Ed25519/Extensions.cs | 33 ++++++++++++++++++++++++---------
 1 file changed, 24 insertions(+), 9 deletions(-)

diff --git a/Ed25519/Extensions.cs b/Ed25519/Extensions.cs
index 20da4b0..39015af 100644
--- a/Ed25519/Extensions.cs
+++ b/Ed25519/Extensions.cs
@@ -54,20 +54,35 @@ namespace Ed25519
             return x;
         }
 
-        internal static BigInteger ExpMod(this BigInteger number, BigInteger exponent, BigInteger modulo)
+        public static BigInteger ExpMod(this BigInteger number, BigInteger exponent, BigInteger modulo)
         {
-            if (exponent.Equals(BigInteger.Zero))
+            var numberOperations = (int)Math.Ceiling(BigInteger.Log(exponent, 2)) + 1;
+            var series = new bool[numberOperations];
+            var previousNumber = exponent;
+            for (var n = 0; n < numberOperations; n++)
             {
-                return BigInteger.One;
+                if (n == 0)
+                {
+                    series[n] = !exponent.IsEven;
+                    continue;
+                }
+
+                var next = BigInteger.Divide(previousNumber, Constants.TWO);
+                series[n] = !next.IsEven;
+                previousNumber = next;
             }
 
-            var result = BigInteger.Pow(number.ExpMod(exponent / Constants.TWO, modulo), 2).Mod(modulo);
-            
-            if (exponent.IsEven)
-                return result;
+            var result = BigInteger.One;
+            for (var n = numberOperations - 2; n >= 0; n--)
+            {
+                result = BigInteger.Pow(result, 2).Mod(modulo);
+                if (series[n])
+                {
+                    result *= number;
+                    result = result.Mod(modulo);
+                }
+            }
 
-            result *= number;
-            result = result.Mod(modulo);
             return result;
         }