diff --git a/src/shamira/tests/test_fft.py b/src/shamira/tests/test_fft.py
new file mode 100644
--- /dev/null
+++ b/src/shamira/tests/test_fft.py
@@ -0,0 +1,56 @@
+# GNU GPLv3, see LICENSE
+
+import random
+import functools
+import operator
+from unittest import TestCase
+
+from .. import gf256
+from ..fft import *
+
+
+def batch_evaluate(coefs, xs):
+	return [gf256.evaluate(coefs, x) for x in xs]
+
+
+class TestFFT(TestCase):
+	def test_complex_dft(self):
+		self.assertEqual(complex_dft([0]), [0+0j])
+		self.assertEqual(complex_dft([1]), [1+0j])
+		self.assertEqual(complex_dft([2]), [2+0j])
+		all(self.assertAlmostEqual(a, b) for (a, b) in zip(complex_dft([3, 1]), [4+0j, 2+0j]))
+		all(self.assertAlmostEqual(a, b) for (a, b) in zip(complex_dft([3, 1, 4]), [8+0j, 0.5+2.59807621j, 0.5-2.59807621j]))
+		all(self.assertAlmostEqual(a, b) for (a, b) in zip(complex_dft([3, 1, 4, 1]), [9+0j, -1+0j, 5+0j, -1+0j]))
+		all(self.assertAlmostEqual(a, b) for (a, b) in zip(
+			complex_dft([3, 1, 4, 1, 5]),
+			[14+0j, 0.80901699+2.04087031j, -0.30901699+5.20431056j, -0.30901699-5.20431056j, 0.80901699-2.04087031j]
+		))
+
+	def test_complex_prime_fft(self):
+		random.seed(1918)
+		for divisors in [[3], [2, 3], [3, 5], [3, 5, 17], [2, 3, 5, 7, 11]]:
+			n = functools.reduce(operator.mul, divisors)
+			coefficients = [random.randint(-128, 127) for i in range(n)]
+			a = prime_fft(coefficients, divisors, complex_dft)
+			b = complex_dft(coefficients)
+			all(self.assertAlmostEqual(ai, bi) for (ai, bi) in zip(a, b))
+
+	def test_finite_dft(self):
+		random.seed(1918)
+		x = {i: precompute_x(i) for i in [3, 5, 15, 17]}  # all sets of xs
+
+		for n in [3, 5, 15, 17]:
+			coefficients = [random.randint(0, 255) for i in range(n)]
+			self.assertEqual(
+				dft(coefficients),
+				batch_evaluate(coefficients[::-1], x[n])
+			)
+
+	def test_finite_prime_fft(self):
+		random.seed(1918)
+		for divisors in [[3], [3, 5], [3, 17], [5, 17], [3, 5, 17]]:
+			n = functools.reduce(operator.mul, divisors)
+			coefficients = [random.randint(0, 255) for i in range(n)]
+			a = prime_fft(coefficients, divisors)
+			b = dft(coefficients)
+			all(self.assertAlmostEqual(ai, bi) for (ai, bi) in zip(a, b))