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Improve utils and add Circulant extractor (#6)
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Co-authored-by: cforeman-cqc <[email protected]>
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@y-richie-y @cforeman-cqc
y-richie-y and cforeman-cqc authored Jan 13, 2024
1 parent 43de732 commit 39f9069
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130 changes: 130 additions & 0 deletions cryptomite/circulant.py
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"""
Circulant is a seeded extractor that takes an input of
n - 1 bits and a seed of n bits, where n is prime, to
produce some error-perfect random bits.
"""
from __future__ import annotations

from math import floor, log2
from typing import cast

from cryptomite.utils import BitsT, closest_prime, conv, log_2

__all__ = ['Circulant']


class Circulant:
""" Circulant extractor based on [Foreman23]_. """
def __init__(self, n: int, m: int):
"""Create a Circulant Extractor.
Parameters
----------
n : int
The length of the input bits.
*** n + 1 should be prime. ***
m : int
The length of the output bits.
"""
self.n, self.m = n, m

def extract(self, input1: BitsT, input2: BitsT) -> BitsT:
""" Extract randomness.
Parameters
----------
input1 : list of bits
The first list of bits, the 'input'.
input2 : list of bits
The second list of bits, the '(weak) seed'.
Returns
-------
list of bits
The extracted output.
"""
n, m = self.n, self.m
assert len(input1) == len(input2) - 1 == n
assert n >= m
n = n + 1
l = log_2(2 * n - 2)
L = 1 << l
input1 = input1 + [0]
input1, input2 = list(input1), list(input2)
input1 = input1[0:1] + input1[1:][::-1] + [0] * (L - n)
input2 = input2 + [0] * (L - len(input2))
conv_output = conv(l, input1, input2)
output: BitsT = cast(BitsT, [
(conv_output[i] + conv_output[i + n]) & 1 for i in range(m)])
return output

@staticmethod
def from_params(
min_entropy1: float,
min_entropy2: float,
log2_error: float,
input_length1: int,
input_length2: int,
markov_q_proof: bool,
verbose: bool = True) -> Circulant:
"""
Calculate a valid input and output size for this extractor,
given the initial lengths and min-entropies of the input sources
and generate the associated extractor.
The input_length2 must be prime, else the code will chose a
valid input_length2 choice and adjust the other parameters
accordingly.
The min_entropy inputs are a lower bound on the
:term:`min-entropy` of the related input string.
Parameters
----------
min_entropy1 : float
The min-entropy of input source 1, the 'input'.
min_entropy2 : float
The min-entropy of input source 2, the '(weak) seed'.
log2_error : float
The acceptable maximum extractor error, in the
form error = b where extractor error = :math:`2 ^ b`.
input_length1 : int
The initial length of input source.
input_length2 : int
The initial length of the (weak) seed.
markov_q_proof : bool
Boolean indicator of whether the extractor parameters
should be calculated to account for being quantum-proof
in the Markov model or not.
Returns
-------
Circulant
The Circulant extractor.
"""
if log2_error >= 0:
raise Exception("""Cannot extract with these parameters.
log2_error must be < 0.""")
input_length = closest_prime((input_length1 + input_length2)//2)
if input_length1 > input_length - 1:
min_entropy1 -= input_length1 - input_length
if input_length2 > input_length:
min_entropy2 -= input_length2 - input_length
output_length = floor(min_entropy1 + min_entropy2
- input_length + 2 * log2_error)
if markov_q_proof:
output_length = floor(0.2 * (min_entropy1 + min_entropy2
- input_length + 8 * log2_error
+ 8 - 4 * log2(3)))
if output_length <= 0:
raise Exception("""Cannot extract with these parameters.
Increase min_entropy1 and/or min_entropy2
and/or log2_error.""")
if verbose:
print('Min entropy1: ', min_entropy1,
'Min entropy2: ', min_entropy2,
'Log error: ', log2_error,
'Input length1: ', input_length - 1,
'Input length2: ', input_length,
'Output length: ', output_length)
print('Adjust length of the input and (weak) seed accordingly')
return Circulant(n=input_length, m=output_length)
93 changes: 55 additions & 38 deletions cryptomite/dodis.py
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Expand Up @@ -7,20 +7,21 @@
from math import floor, log2
from typing import cast

from cryptomite.utils import BitsT, conv, log_2, na_set
from cryptomite.utils import BitsT, closest_na_set, conv, log_2

__all__ = ['Dodis']


class Dodis:
""" Dodis extractor based on [Dodis20]_. """
""" Dodis extractor based on [Dodis2004]_. """
def __init__(self, n: int, m: int):
"""Create a Dodis Extractor.
Parameters
----------
n : int
The length of the two input bits.
*** This should be prime with primitive root 2. ***
m : int
The length of the output bits.
"""
Expand All @@ -32,9 +33,9 @@ def extract(self, input1: BitsT, input2: BitsT) -> BitsT:
Parameters
----------
input1 : list of bits
The first list of bits.
The first list of bits, the 'input'.
input2 : list of bits
The second list of bits.
The second list of bits, the '(weak) seed'.
Returns
-------
Expand All @@ -56,55 +57,71 @@ def extract(self, input1: BitsT, input2: BitsT) -> BitsT:

@staticmethod
def from_params(
min_entropy1: float,
min_entropy2: float,
log2_error: float,
input_length1: int,
input_length2: int,
entropy1: int,
entropy2: int,
error: int,
q_proof: bool) -> Dodis:
markov_q_proof: bool,
verbose: bool = True) -> Dodis:
"""
Calculate the input size and output size for this 2-source
extractor.
Calculate a valid input and output size for this extractor,
given the initial lengths and min-entropies of the input sources
and generate the associated extractor.
The input_length -1 must be in :py:func:`~.na_set`.
The entropy inputs are a lower bound on the :term:`min-entropy`
of the related input string.
The input_length must be prime with primitive root 2, else
the code will chose a valid input_length choice and adjust the
other parameters accordingly.
The min entropy inputs are a lower bound on the
:term:`min-entropy` of the related input string.
Parameters
----------
input_length1 : int
The initial length of input source 1.
input_length2 : int
The initial length of input source 2.
entropy1 : int
The min-entropy of input source 1.
entropy2 : int
The min-entropy of input source 2.
error : int
min_entropy1 : float
The min-entropy of input source 1, the 'input'.
min_entropy2 : float
The min-entropy of input source 2, the '(weak) seed'.
log2_error : float
The acceptable maximum extractor error, in the
form error = b where extractor error = :math:`2 ^ b`.
q_proof : bool
input_length1 : int
The initial length of input source.
input_length2 : int
The initial length of the (weak) seed.
markov_q_proof : bool
Boolean indicator of whether the extractor parameters
should be calculated to account for quantum side
information or not.
should be calculated to account for being quantum-proof
in the Markov model or not.
Returns
-------
Dodis
The Dodis extractor.
"""
if error > 0:
raise Exception('Cannot extract with these parameters.'
'Error must be < 0.')
input_length = na_set(min(input_length1, input_length2) - 1) + 1
entropy1 -= input_length1 - input_length
entropy2 -= input_length2 - input_length
output_length = floor(
entropy1 + entropy2 - input_length + 1 + 2 * error)
if q_proof:
output_length = floor(0.2 * (entropy1 + entropy2 - input_length)
+ 8 * error + 9 - 4 * log2(3))
if log2_error >= 0:
raise Exception("""Cannot extract with these parameters.
log2_error must be < 0.""")
input_length = closest_na_set((input_length1 + input_length2)//2)
if input_length1 > input_length:
min_entropy1 -= input_length1 - input_length
if input_length2 > input_length:
min_entropy2 -= input_length2 - input_length
output_length = floor(min_entropy1 + min_entropy2
- input_length + 1 + 2 * log2_error)
if markov_q_proof:
output_length = floor(0.2 * (min_entropy1 + min_entropy2
- input_length + 8 * log2_error
+ 9 - 4 * log2(3)))
if output_length <= 0:
raise Exception('Cannot extract with these parameters. '
'Increase entropy1 and/or entropy2.')
raise Exception("""Cannot extract with these parameters.
Increase min_entropy1 and/or min_entropy2
and/or log2_error.""")
if verbose:
print('Min entropy1: ', min_entropy1,
'Min entropy2: ', min_entropy2,
'Log error: ', log2_error,
'Input length1: ', input_length,
'Input length2: ', input_length,
'Output length: ', output_length)
print('Adjust length of the input and (weak) seed accordingly')
return Dodis(n=input_length, m=output_length)
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