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gh-37118: Fix random polynomial bias
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For a polynomial ring `R` say `GF(11)["x"]`, before `R.random_element`
is very far from random, now it is uniformly random.
    
URL: #37118
Reported by: grhkm21
Reviewer(s): grhkm21, Travis Scrimshaw
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Release Manager committed Mar 21, 2024
2 parents 9d73e3c + 9d1d0a1 commit 397fd3f
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Showing 5 changed files with 171 additions and 98 deletions.
24 changes: 12 additions & 12 deletions src/sage/crypto/lattice.py
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Original file line number Diff line number Diff line change
Expand Up @@ -112,10 +112,10 @@ def gen_lattice(type='modular', n=4, m=8, q=11, seed=None,
[ 0 11 0 0 0 0 0 0]
[ 0 0 11 0 0 0 0 0]
[ 0 0 0 11 0 0 0 0]
[-2 -3 -3 4 1 0 0 0]
[ 4 -2 -3 -3 0 1 0 0]
[-3 4 -2 -3 0 0 1 0]
[-3 -3 4 -2 0 0 0 1]
[-3 -3 -2 4 1 0 0 0]
[ 4 -3 -3 -2 0 1 0 0]
[-2 4 -3 -3 0 0 1 0]
[-3 -2 4 -3 0 0 0 1]
Ideal bases also work with polynomials::
Expand All @@ -125,10 +125,10 @@ def gen_lattice(type='modular', n=4, m=8, q=11, seed=None,
[ 0 11 0 0 0 0 0 0]
[ 0 0 11 0 0 0 0 0]
[ 0 0 0 11 0 0 0 0]
[ 1 4 -3 3 1 0 0 0]
[ 3 1 4 -3 0 1 0 0]
[-3 3 1 4 0 0 1 0]
[ 4 -3 3 1 0 0 0 1]
[-3 4 1 4 1 0 0 0]
[ 4 -3 4 1 0 1 0 0]
[ 1 4 -3 4 0 0 1 0]
[ 4 1 4 -3 0 0 0 1]
Cyclotomic bases with n=2^k are SWIFFT bases::
Expand All @@ -137,10 +137,10 @@ def gen_lattice(type='modular', n=4, m=8, q=11, seed=None,
[ 0 11 0 0 0 0 0 0]
[ 0 0 11 0 0 0 0 0]
[ 0 0 0 11 0 0 0 0]
[-2 -3 -3 4 1 0 0 0]
[-4 -2 -3 -3 0 1 0 0]
[ 3 -4 -2 -3 0 0 1 0]
[ 3 3 -4 -2 0 0 0 1]
[-3 -3 -2 4 1 0 0 0]
[-4 -3 -3 -2 0 1 0 0]
[ 2 -4 -3 -3 0 0 1 0]
[ 3 2 -4 -3 0 0 0 1]
Dual modular bases are related to Regev's famous public-key
encryption [Reg2005]_::
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4 changes: 2 additions & 2 deletions src/sage/crypto/lwe.py
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Original file line number Diff line number Diff line change
Expand Up @@ -670,7 +670,7 @@ def __init__(self, ringlwe):
sage: lwe = RingLWEConverter(RingLWE(16, 257, D, secret_dist='uniform'))
sage: set_random_seed(1337)
sage: lwe()
((32, 216, 3, 125, 58, 197, 171, 43), ...)
((171, 197, 58, 125, 3, 216, 32, 130), ...)
"""
self.ringlwe = ringlwe
self._i = 0
Expand All @@ -686,7 +686,7 @@ def __call__(self):
sage: lwe = RingLWEConverter(RingLWE(16, 257, D, secret_dist='uniform'))
sage: set_random_seed(1337)
sage: lwe()
((32, 216, 3, 125, 58, 197, 171, 43), ...)
((171, 197, 58, 125, 3, 216, 32, 130), ...)
"""
R_q = self.ringlwe.R_q

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28 changes: 14 additions & 14 deletions src/sage/misc/randstate.pyx
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Original file line number Diff line number Diff line change
Expand Up @@ -56,22 +56,22 @@ results of these random number generators reproducible. ::
sage: set_random_seed(0)
sage: print(rtest())
(303, -0.266166246380421, 1/6, (1,2), [ 0, 1, 1, 0, 0 ], 265625921, 79302, 0.2450652680687958)
(303, -0.266166246380421, 1/2*x^2 - 1/95*x - 1/2, (1,3), [ 1, 0, 0, 1, 1 ], 265625921, 5842, 0.9661911734708414)
sage: set_random_seed(1)
sage: print(rtest())
(978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
(978, 0.0557699430711638, -3*x^2 - 1/12, (1,2), [ 0, 0, 1, 1, 0 ], 807447831, 29982, 0.8335077654199736)
sage: set_random_seed(2)
sage: print(rtest())
(207, -0.0141049486533456, 0, (1,3)(4,5), [ 1, 0, 1, 1, 1 ], 1642898426, 16190, 0.9343331114872127)
(207, -0.0141049486533456, 4*x^2 + 1/2, (1,2)(4,5), [ 1, 0, 0, 1, 1 ], 1642898426, 41662, 0.19982565117278328)
sage: set_random_seed(0)
sage: print(rtest())
(303, -0.266166246380421, 1/6, (1,2), [ 0, 1, 1, 0, 0 ], 265625921, 79302, 0.2450652680687958)
(303, -0.266166246380421, 1/2*x^2 - 1/95*x - 1/2, (1,3), [ 1, 0, 0, 1, 1 ], 265625921, 5842, 0.9661911734708414)
sage: set_random_seed(1)
sage: print(rtest())
(978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
(978, 0.0557699430711638, -3*x^2 - 1/12, (1,2), [ 0, 0, 1, 1, 0 ], 807447831, 29982, 0.8335077654199736)
sage: set_random_seed(2)
sage: print(rtest())
(207, -0.0141049486533456, 0, (1,3)(4,5), [ 1, 0, 1, 1, 1 ], 1642898426, 16190, 0.9343331114872127)
(207, -0.0141049486533456, 4*x^2 + 1/2, (1,2)(4,5), [ 1, 0, 0, 1, 1 ], 1642898426, 41662, 0.19982565117278328)
Once we've set the random number seed, we can check what seed was used.
(This is not the current random number state; it does not change when
Expand All @@ -81,7 +81,7 @@ random numbers are generated.) ::
sage: initial_seed()
12345
sage: print(rtest())
(720, -0.612180244315804, 0, (1,3), [ 1, 0, 1, 1, 0 ], 1911581957, 65175, 0.8043027951758298)
(720, -0.612180244315804, x^2 - x, (1,2,3), [ 1, 0, 0, 0, 1 ], 1911581957, 27093, 0.9205331599518184)
sage: initial_seed()
12345
Expand Down Expand Up @@ -216,19 +216,19 @@ that you get without intervening ``with seed``. ::
sage: set_random_seed(0)
sage: r1 = rtest(); print(r1)
(303, -0.266166246380421, 1/6, (1,2), [ 0, 1, 1, 0, 0 ], 265625921, 79302, 0.2450652680687958)
(303, -0.266166246380421, 1/2*x^2 - 1/95*x - 1/2, (1,3), [ 1, 0, 0, 1, 1 ], 265625921, 5842, 0.9661911734708414)
sage: r2 = rtest(); print(r2)
(443, 0.185001351421963, -2, (1,3), [ 0, 0, 1, 1, 0 ], 53231108, 8171, 0.28363811590618193)
(105, 0.642309615982449, -x^2 - x - 6, (1,3)(4,5), [ 1, 0, 0, 0, 1 ], 53231108, 77132, 0.001767155077382232)
We get slightly different results with an intervening ``with seed``. ::
sage: set_random_seed(0)
sage: r1 == rtest()
True
sage: with seed(1): rtest()
(978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
(978, 0.0557699430711638, -3*x^2 - 1/12, (1,2), [ 0, 0, 1, 1, 0 ], 807447831, 29982, 0.8335077654199736)
sage: r2m = rtest(); r2m
(443, 0.185001351421963, -2, (1,3), [ 0, 0, 1, 1, 0 ], 53231108, 51295, 0.28363811590618193)
(105, 0.642309615982449, -x^2 - x - 6, (1,3)(4,5), [ 1, 0, 0, 0, 1 ], 53231108, 40267, 0.001767155077382232)
sage: r2m == r2
False
Expand All @@ -245,8 +245,8 @@ case, as we see in this example::
sage: with seed(1):
....: print(rtest())
....: print(rtest())
(978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
(181, 0.607995392046754, -x + 1/2, (2,3)(4,5), [ 1, 0, 0, 1, 1 ], 1010791326, 9693, 0.5691716786307407)
(978, 0.0557699430711638, -3*x^2 - 1/12, (1,2), [ 0, 0, 1, 1, 0 ], 807447831, 29982, 0.8335077654199736)
(138, -0.0404945051288503, 2*x - 24, (1,2,3), [ 1, 1, 0, 1, 1 ], 1010791326, 91360, 0.0033332230808060803)
sage: r2m == rtest()
True
Expand All @@ -258,7 +258,7 @@ NTL random numbers were generated inside the ``with seed``.
True
sage: with seed(1):
....: rtest()
(978, 0.0557699430711638, -1/8*x^2 - 1/2*x + 1/2, (1,2,3), [ 1, 0, 0, 0, 1 ], 807447831, 23865, 0.6170498912488264)
(978, 0.0557699430711638, -3*x^2 - 1/12, (1,2), [ 0, 0, 1, 1, 0 ], 807447831, 29982, 0.8335077654199736)
sage: r2m == rtest()
True
Expand Down
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