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""" 

Abstract base class for generators of polynomial systems. 

 

AUTHOR: 

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

""" 

 

from sage.structure.sage_object import SageObject 

 

class MPolynomialSystemGenerator(SageObject): 

""" 

Abstract base class for generators of polynomial systems. 

""" 

 

def __getattr__(self, attr): 

""" 

EXAMPLES:: 

 

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator 

sage: msg = MPolynomialSystemGenerator() 

sage: msg.R 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

if attr == "R": 

self.R = self.ring() 

return self.R 

else: 

raise AttributeError("'%s' object has no attribute '%s'"%(self.__class__,attr)) 

 

def varformatstr(self, name): 

""" 

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 

""" 

raise NotImplementedError 

 

def varstrs(self, name, round): 

""" 

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) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError 

 

def vars(self, name, round): 

""" 

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 

""" 

raise NotImplementedError 

 

def ring(self): 

""" 

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 

""" 

raise NotImplementedError 

 

def block_order(self): 

""" 

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 

""" 

raise NotImplementedError 

 

def __call__(self, P, K): 

""" 

Encrypt plaintext P using the key K. 

 

INPUT: 

P -- plaintext (vector, list) 

K -- key (vector, list) 

 

EXAMPLES:: 

 

sage: from sage.crypto.mq.mpolynomialsystemgenerator import MPolynomialSystemGenerator 

sage: msg = MPolynomialSystemGenerator() 

sage: msg(None, None) 

Traceback (most recent call last): 

... 

NotImplementedError 

""" 

raise NotImplementedError 

 

def sbox(self): 

""" 

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' 

""" 

return self._sbox 

 

def polynomial_system(self, P=None, K=None): 

""" 

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 

""" 

raise NotImplementedError 

 

def random_element(self): 

""" 

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 

""" 

raise NotImplementedError