Data commit

Task/Miller-Rabin-primality-test/Lua/miller-rabin-primality-test.lua

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+ function MRIsPrime(n, k)
+  -- If n is prime, returns true (without fail).
+  -- If n is not prime, then returns false with probability ≥ 4^(-k), true otherwise.
+  -- First, deal with 1 and multiples of 2.
+  if n == 1 then
+    return false
+  elseif n == 2 then
+    return true
+  elseif n%2 == 0 then
+    return false
+  end
+  -- Now n is odd and greater than 1.
+  -- Find the unique expression n = 1 + t*2^h for n, where t is odd and h≥1.
+  t = (n-1)/2
+  h = 1
+  while t%2 == 0 do
+    t = t/2
+    h = h + 1
+  end
+  for i = 1, k do
+    -- Generate a random integer between 1 and n-1 inclusive.
+    a = math.random(n-1)
+    -- Test whether a is an element of the set L, and return false if not.
+    if not IsInL(n, a, t, h) then
+      return false
+    end
+  end
+  -- All generated a were in the set L; thus with high probability, n is prime.
+  return true
+end
+
+function IsInL(n, a, t, h)
+  local b = PowerMod(a, t, n)
+  if b == 1 then
+    return true
+  end
+  for j = 0, h-1 do
+    if b == n-1 then
+      return true
+    elseif b == 1 then
+      return false
+    end
+    b = (b^2)%n
+  end
+  return false
+end
+
+function PowerMod(x, y, m)
+  -- Computes x^y mod m.
+  local z = 1
+  while y > 0 do
+    if y%2 == 0 then
+      x, y, z = (x^2)%m, y//2, z
+    else
+      x, y, z = (x^2)%m, y//2, (x*z)%m
+    end
+  end
+  return z
+end