Add seed kwarg to random_prime()

Fixes #371

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
- 1514D68EDB7C650F1FF713531A1A43255A4BE6D66EE1FDBD96F4EB32757C1B1BAF16A5933E24D45FAD6C6A814F3C8C14F3CB98F24FEA74C43C349D6FA3AB76EB0156811A1FBAA64EB4AC525CCEF9278AF78886DC6DBF46C4463A34C0E53B0FA2F784BB2DC5FDF076BB6E145AA15AA6D616ACC1D5F95B8BE757670B9AAF53292DD (236861787926957382206996886087214592029752524078026392358936844479667423570833116126506927878773110287700754280996224768092589904231910149528080012692722763539766058401127758399272786475279348968866620857161889678512852050561604969208679095086283103827661300743342847921567132587459205365243815835763830067933) 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):

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)