Abstract base class for generators of polynomial systems

AUTHOR:

Martin Albrecht <malb@informatik.uni-bremen.de>

class sage.crypto.mq.mpolynomialsystemgenerator.MPolynomialSystemGenerator[source]

Bases: SageObject

Abstract base class for generators of polynomial systems.

block_order()[source]

Return a block term ordering for the equation systems generated by self.

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.block_order()
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.block_order()
Traceback (most recent call last):
...
NotImplementedError
polynomial_system(P=None, K=None)[source]

Return a tuple F,s for plaintext P and key K where F is an polynomial system and s a dictionary which maps key variables to their solutions.

INPUT:

  • P – plaintext (vector, list)

  • K – key (vector, list)

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.polynomial_system()
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.polynomial_system()
Traceback (most recent call last):
...
NotImplementedError
random_element()[source]

Return random element. Usually this is a list of elements in the base field of length ‘blocksize’.

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.random_element()
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.random_element()
Traceback (most recent call last):
...
NotImplementedError
ring()[source]

Return the ring in which the system is defined.

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.ring()
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.ring()
Traceback (most recent call last):
...
NotImplementedError
sbox()[source]

Return SBox object for self.

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.sbox()
Traceback (most recent call last):
...
AttributeError: '<class 'sage.crypto.mq.mpolynomialsystemgenerator.MPolynomialSystemGenerator'>' object has no attribute '_sbox'...

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.sbox()
Traceback (most recent call last):
...
AttributeError: '<class 'sage.crypto.mq.mpolynomialsystemgenerator.MPolynomialSystemGenerator'>' object has no attribute '_sbox'...
varformatstr(name)[source]

Return format string for a given name ‘name’ which is understood by print et al.

Such a format string is used to construct variable names. Typically those format strings are somewhat like ‘name%02d%02d’ such that rounds and offset in a block can be encoded.

INPUT:

  • name – string

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.varformatstr('K')
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.varformatstr('K')
Traceback (most recent call last):
...
NotImplementedError
vars(name, round)[source]

Return a list of variables given a name ‘name’ and an index ‘round’.

INPUT:

  • name – string

  • round – integer index

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.vars('K',0)
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.vars('K',Integer(0))
Traceback (most recent call last):
...
NotImplementedError
varstrs(name, round)[source]

Return a list of variable names given a name ‘name’ and an index ‘round’.

This function is typically used by self._vars.

INPUT:

  • name – string

  • round – integer index

EXAMPLES:

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
sage: msg = MPolynomialSystemGenerator()
sage: msg.varstrs('K', i)                                                   # needs sage.all
Traceback (most recent call last):
...
NotImplementedError

>>> from sage.all import *
>>> from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator
>>> msg = MPolynomialSystemGenerator()
>>> msg.varstrs('K', i)                                                   # needs sage.all
Traceback (most recent call last):
...
NotImplementedError