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mpint: add a gcd function.

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This is another application of the existing mp_bezout_into, which
needed a tweak or two to cope with the numbers not necessarily being
coprime, plus a wrapper function to deal with shared factors of 2.

It reindents the entire second half of mp_bezout_into, so the patch is
best viewed with whitespace differences ignored.
This commit is contained in:
Simon Tatham
2020-02-18 18:55:57 +00:00
parent 957f14088f
commit 2debb352b0
4 changed files with 245 additions and 97 deletions
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42
test/cryptsuite.py
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@ -437,6 +437,48 @@ class mpint(MyTestBase):
int(monty_invert(mc, monty_import(mc, x))),
int(monty_import(mc, inv)))
def testGCD(self):
powerpairs = [(0,0), (1,0), (1,1), (2,1), (2,2), (75,3), (17,23)]
for a2, b2 in powerpairs:
for a3, b3 in powerpairs:
for a5, b5 in powerpairs:
a = 2**a2 * 3**a3 * 5**a5 * 17 * 19 * 23
b = 2**b2 * 3**b3 * 5**b5 * 65423
d = 2**min(a2, b2) * 3**min(a3, b3) * 5**min(a5, b5)
ma = mp_copy(a)
mb = mp_copy(b)
self.assertEqual(int(mp_gcd(ma, mb)), d)
md = mp_new(nbits(d))
mA = mp_new(nbits(b))
mB = mp_new(nbits(a))
mp_gcd_into(ma, mb, md, mA, mB)
self.assertEqual(int(md), d)
A = int(mA)
B = int(mB)
self.assertEqual(a*A - b*B, d)
self.assertTrue(0 <= A < b//d)
self.assertTrue(0 <= B < a//d)
self.assertEqual(mp_coprime(ma, mb), 1 if d==1 else 0)
# Make sure gcd_into can handle not getting some
# of its output pointers.
mp_clear(md)
mp_gcd_into(ma, mb, md, None, None)
self.assertEqual(int(md), d)
mp_clear(mA)
mp_gcd_into(ma, mb, None, mA, None)
self.assertEqual(int(mA), A)
mp_clear(mB)
mp_gcd_into(ma, mb, None, None, mB)
self.assertEqual(int(mB), B)
mp_gcd_into(ma, mb, None, None, None)
# No tests we can do after that last one - we just
# insist that it isn't allowed to have crashed!
def testMonty(self):
moduli = [5, 19, 2**16+1, 2**31-1, 2**128-159, 2**255-19,
293828847201107461142630006802421204703,