From 226169a432a494953c1e344ecc22383745e928a9 Mon Sep 17 00:00:00 2001
From: Utkarsh Chaudhary <f2016303@pilani.bits-pilani.ac.in>
Date: Thu, 1 Oct 2020 23:27:32 +0530
Subject: [PATCH] Added Modular Binary Exponentiation (Recursive) (#337)

---
 Maths/ModularBinaryExponentiationRecursive.js | 31 +++++++++++++++++++
 1 file changed, 31 insertions(+)
 create mode 100644 Maths/ModularBinaryExponentiationRecursive.js

diff --git a/Maths/ModularBinaryExponentiationRecursive.js b/Maths/ModularBinaryExponentiationRecursive.js
new file mode 100644
index 000000000..c30ed5f2a
--- /dev/null
+++ b/Maths/ModularBinaryExponentiationRecursive.js
@@ -0,0 +1,31 @@
+/*
+  Modified from:
+    https://github.com/TheAlgorithms/Python/blob/master/maths/binary_exp_mod.py
+
+  Explaination:
+    https://en.wikipedia.org/wiki/Exponentiation_by_squaring
+*/
+
+const modularBinaryExponentiation = (a, n, m) => {
+  // input: a: int, n: int, m: int
+  // returns: (a^n) % m: int
+  if (n === 0) {
+    return 1
+  } else if (n % 2 === 1) {
+    return (modularBinaryExponentiation(a, n - 1, m) * a) % m
+  } else {
+    const b = modularBinaryExponentiation(a, n / 2, m)
+    return (b * b) % m
+  }
+}
+
+const main = () => {
+  // binary_exponentiation(2, 10, 17)
+  // > 4
+  console.log(modularBinaryExponentiation(2, 10, 17))
+  // binary_exponentiation(3, 9, 12)
+  // > 3
+  console.log(modularBinaryExponentiation(3, 9, 12))
+}
+
+main()