From c58dbab47cf28ec8120dda808909bbeb91fd5f6e Mon Sep 17 00:00:00 2001
From: mhostetter <matthostetter@gmail.com>
Date: Tue, 30 Aug 2022 13:02:17 -0400
Subject: [PATCH] Add `seed` kwarg to `random_prime()`

Fixes #371
---
 src/galois/_prime.py | 22 +++++++++++++---------
 tests/test_primes.py |  9 +++++++++
 2 files changed, 22 insertions(+), 9 deletions(-)

diff --git a/src/galois/_prime.py b/src/galois/_prime.py
index 460204f86..8551ddbb3 100644
--- a/src/galois/_prime.py
+++ b/src/galois/_prime.py
@@ -237,7 +237,7 @@ def next_prime(n: int) -> int:
 
 
 @export
-def random_prime(bits: int) -> int:
+def random_prime(bits: int, seed: Optional[int] = None) -> int:
     r"""
     Returns a random prime :math:`p` with :math:`b` bits, such that :math:`2^b \le p < 2^{b+1}`.
 
@@ -250,6 +250,9 @@ def random_prime(bits: int) -> int:
     ----------
     bits
         The number of bits in the prime :math:`p`.
+    seed
+        Non-negative integer used to initialize the PRNG. The default is `None` which means that unpredictable
+        entropy will be pulled from the OS to be used as the seed.
 
     Returns
     -------
@@ -268,23 +271,24 @@ def random_prime(bits: int) -> int:
     --------
     Generate a random 1024-bit prime.
 
-    .. ipython::
+    .. ipython:: python
 
-        In [2]: p = galois.random_prime(1024); p
-        Out[2]: 236861787926957382206996886087214592029752524078026392358936844479667423570833116126506927878773110287700754280996224768092589904231910149528080012692722763539766058401127758399272786475279348968866620857161889678512852050561604969208679095086283103827661300743342847921567132587459205365243815835763830067933
+        p = galois.random_prime(1024, seed=1); p
+        galois.is_prime(p)
 
-        In [3]: galois.is_prime(p)
-        Out[3]: True
+    Verify that :math:`p` is prime using the OpenSSL library.
 
-    .. code-block::
+    .. code-block:: console
 
-        $ openssl prime 236861787926957382206996886087214592029752524078026392358936844479667423570833116126506927878773110287700754280996224768092589904231910149528080012692722763539766058401127758399272786475279348968866620857161889678512852050561604969208679095086283103827661300743342847921567132587459205365243815835763830067933
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is prime
+        $ openssl prime 327845897586213436751081882871255331286648902836386839087617368608439574698192016043769533823474001379935585889197488144338014865193967937011638431094821943416361149113909692569658970713864593781874423564706915495970135894084612689487074397782022398597547611189482697523681694691585678818112329605903872356773
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is prime
     """
     verify_isinstance(bits, int)
+    verify_isinstance(seed, int, optional=True)
     if not bits > 0:
         raise ValueError(f"Argument `bits` must be positive, not {bits}.")
 
+    random.seed(seed)
     while True:
         p = random.randint(2**bits, 2**(bits + 1) - 1)
         if is_prime(p):
diff --git a/tests/test_primes.py b/tests/test_primes.py
index 151194bfa..8f498e724 100644
--- a/tests/test_primes.py
+++ b/tests/test_primes.py
@@ -61,6 +61,8 @@ def test_next_prime(next_prime):
 def test_random_prime_exceptions():
     with pytest.raises(TypeError):
         galois.random_prime(10.0)
+    with pytest.raises(TypeError):
+        galois.random_prime(10, seed=1.0)
     with pytest.raises(ValueError):
         galois.random_prime(0)
     with pytest.raises(ValueError):
@@ -74,6 +76,13 @@ def test_random_prime():
         assert galois.is_prime(n) == True
 
 
+def test_random_prime_deterministic():
+    p1 = galois.random_prime(10, seed=1)
+    p2 = galois.random_prime(10, seed=1)
+    assert p1 == 1153
+    assert p2 == 1153
+
+
 def test_mersenne_exponents_exceptions():
     with pytest.raises(TypeError):
         galois.mersenne_exponents(10.0)