lab01

labs/01/lab1.ex

@@ -0,0 +1,36 @@
+defmodule Lab1 do
+  # Question 1 - Multiplicitive inverse of a module n
+  defp inverse_mod(r, t, newr, _) when newr == 0 do {r, t} end
+  defp inverse_mod(r, t, newr, newt) do
+    q = div(r, newr)
+    inverse_mod(
+      newr,
+      newt,
+      r - q * newr,
+      t - q * newt
+    )
+  end
+
+  def inverse_mod(a, n) do
+    case inverse_mod(n, 0, a, 1) do
+      {r, _} when r > 1 ->
+        :not_invertable
+
+      {_, t} when t < 0 ->
+        t + n
+
+      {_, t} ->
+        t
+    end
+  end
+
+  # Question 2 - Fast modular exponent
+  defp pow_mod(acc, _, m, _) when m == 0, do: acc
+  defp pow_mod(acc, a, m, n), do: pow_mod(
+    rem(acc * a, n), a, m - 1, n
+  )
+
+  def pow_mod(a, m, n) do
+    rem(pow_mod(1, a, m, n), n)
+  end
+end