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Fix random polynomial bias #37118

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merged 23 commits into from
Mar 25, 2024
Merged

Fix random polynomial bias #37118

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dfaf9bb
Fix random polynomial bias
grhkm21 Jan 20, 2024
d67cf84
Allow `degree=-1` together with `monic=True`
grhkm21 Jan 20, 2024
e481786
Fix buggy sampling
grhkm21 Jan 21, 2024
9e037d4
Merge branch 'develop' into grhkm/uniform-polynomial-ring
grhkm21 Jan 24, 2024
f4b72cd
apply review changes 📖
grhkm21 Jan 24, 2024
388849c
apply review changes 📖
grhkm21 Jan 24, 2024
efac3ca
apply review changes 📖
grhkm21 Jan 25, 2024
2495622
fix docstring fullstops
grhkm21 Jan 25, 2024
7d4ece6
fix styling
grhkm21 Jan 25, 2024
a879ac5
apply review changes 📖
grhkm21 Jan 30, 2024
969c37d
apply review changes 📖
grhkm21 Feb 8, 2024
4d515d8
Merge branch 'develop' into grhkm/uniform-polynomial-ring
grhkm21 Feb 9, 2024
ccfdd93
refactor `.random_element` 📖
grhkm21 Feb 9, 2024
1b09de0
fix input docs format
grhkm21 Feb 9, 2024
4e1378f
I don't know what the code is trying to do here
grhkm21 Feb 9, 2024
97ad0a5
fix remaining doctests
grhkm21 Feb 9, 2024
d5215d4
fix docs wording + uniformity test 📖
grhkm21 Feb 10, 2024
786d7f0
Fix doctests
grhkm21 Feb 10, 2024
6beda49
long time doctests
grhkm21 Feb 13, 2024
b0c6057
Merge branch 'develop' into grhkm/uniform-polynomial-ring
grhkm21 Feb 22, 2024
0ea04b1
Small wording change
grhkm21 Feb 22, 2024
a0d5d4a
wrap some lines fix some indentation
grhkm21 Feb 23, 2024
9d1d0a1
wrap at 80
grhkm21 Feb 23, 2024
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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]_::
Expand Down
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

Expand Down
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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