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tropicZ.py
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429
tropicZ.py
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# -*- coding: utf-8 -*-
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"""tropic.ipynb
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Automatically generated by Colab.
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Original file is located at
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https://colab.research.google.com/drive/14lR3A29PgCuP9jUS9quiNFYPcYhZvxLi
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"""
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class TropicZ(object):
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def __init__(self, infty = 1000, add_op = 'max'):
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self.__infty = infty
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self._posinf = infty
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self._neginf = -infty
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self.add_op = max
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if add_op == 'min':
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self.add_op = min
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@property
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def neginf(self):
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return TropicZ.TropicElement(self, self._neginf)
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@property
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def posinf(self):
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return TropicZ.TropicElement(self, self._posinf)
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def elem(self, val = 0):
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'''
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Формирует тропический элемента из целого числа val
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'''
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return TropicZ.TropicElement(self, val)
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class TropicElement(object):
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def __init__(self, outer_instance, val = 0):
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self.__outer_instance = outer_instance
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self._val = self.bound(val)
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def bound(self, val = 0):
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neginf = self.__outer_instance._neginf
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posinf = self.__outer_instance._posinf
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return min(max(int(val), neginf), posinf)
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def __repr__(self):
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return str(self)
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def __str__(self):
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return str(self._val)
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def __iter__(self):
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return self.entries.__iter__()
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def add(self, val):
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'''
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Тропическое сложение текущего элемента с значением val
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'''
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if isinstance(val, TropicZ.TropicElement):
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result = val._val
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else:
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result = int(val)
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op = self.__outer_instance.add_op
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result = op(self._val, result)
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return TropicZ.TropicElement(self.__outer_instance, result)
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def __add__(self, val):
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return self.add(val)
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def __iadd__(self, val):
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self._val = self.add(val)._val
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return self
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def __neg__(self):
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result = self.bound(-self._val)
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return TropicZ.TropicElement(self.__outer_instance, result)
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def mult(self, val):
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'''
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Тропическое умножение текущего элемента на val
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'''
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if isinstance(val, TropicZ.TropicElement):
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result = val._val
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else:
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result = int(val)
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result = self._val + result
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return TropicZ.TropicElement(self.__outer_instance, result)
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def __mul__(self, val):
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return self.mult(val)
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def __imul__(self, val):
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self._val = self.mult(val)._val
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return self
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def div(self, val):
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'''
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Тропическое деление текущего элемента на val
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'''
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if isinstance(val, TropicZ.TropicElement):
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result = val._val
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else:
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result = int(val)
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result = self._val - result
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return TropicZ.TropicElement(self.__outer_instance, result)
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def __truediv__(self, val):
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return self.div(val)
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def __floordiv__(self, val):
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return self.div(val)
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TZ = TropicZ(1000, 'max')
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TZmin = TropicZ(1000, 'min')
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TZmax = TropicZ(1000, 'max')
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a = TZ.elem(5)
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b = TZ.elem(6)
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stroka = TropicZ.TropicElement.__repr__(a)
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print(stroka)
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print(int(stroka)+5)
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print(-a)
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print(a * b)
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print(a + b)
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L = [TZ.elem(i) for i in range(7)]
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print(L)
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print(sum(L, TZ.neginf))
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print(a * TZ.neginf)
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import math
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class TropicalMatrix:
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def __init__(self, entries):
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self.entries = entries
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def __str__(self):
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return str(self.entries)
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def get_entry(self, i, j):
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return self.entries[i][j]
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def dual(self, dual):
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n = 2
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new_matrix = [[0, 0], [0, 0]]
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for i in range(n):
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for j in range(n):
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new_matrix[i][j] = dual.elem(self[i][j])
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return TropicalMatrix(new_matrix)
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def add_tropical_matrix(self, matrix, dual):
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n = 2
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new_matrix = [[0, 0], [0, 0]]
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self = TropicalMatrix.dual(self, dual)
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matrix = TropicalMatrix.dual(matrix, dual)
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for i in range(n):
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for j in range(n):
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new_matrix[i][j] = self.get_entry(i, j) + matrix.get_entry(i, j)
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return TropicalMatrix(new_matrix)
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def mult_scalar(self, scalar, dual):
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n = 2
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new_matrix = [[0, 0], [0, 0]]
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self = TropicalMatrix.dual(self, dual)
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for i in range(n):
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for j in range(n):
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new_matrix[i][j] = self.get_entry(i, j) * scalar
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return TropicalMatrix(new_matrix)
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def mult_tropical_matrix(self, matrix, dual):
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n = 2
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new_matrix = [[0, 0], [0, 0]]
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self = TropicalMatrix.dual(self, dual)
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matrix = TropicalMatrix.dual(matrix, dual)
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for i in range(n):
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for j in range(n):
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sum_list = []
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for k in range(n):
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sum_list.append(self.get_entry(i, k) * matrix.get_entry(k, j))
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new_matrix[i][j] = sum_list[0] + sum_list[1]
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return TropicalMatrix(new_matrix)
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def get_dimension(self):
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return len(self.entries)
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def __iter__(self): # метод для превращения тропической матрицы в список
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return self.entries.__iter__()
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if __name__ == "__main__":
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M = [[-1000, 10], [5, 3]]
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N = [[3, 6], [15, 1000]]
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A = [[5, -1000], [-1000, 5]]
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B = [[2, -1000], [-1000, 2]]
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p = TropicalMatrix.add_tropical_matrix(M, A, TZmax)
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t = TropicalMatrix.mult_tropical_matrix(N, N, TZmin)
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q = TropicalMatrix.add_tropical_matrix(M, B, TZmax)
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r = TropicalMatrix.mult_scalar(N, 3, TZmin)
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print('p(x) =', p)
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print('t(x) =', t)
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print('q(x) =', q)
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print('r(x) =', r)
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import math
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import random
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import numpy as np
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class TropicalMatrix_without_dual:
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def __init__(self, entries):
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self.entries = entries
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def __str__(self):
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return str(self.entries)
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def add_tropical_matrix_without_dual(self, matrix):
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n = 2
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new_matrix = [[0, 0], [0, 0]]
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for i in range(n):
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for j in range(n):
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new_matrix[i][j] = self.get_entry(i, j) + matrix.get_entry(i, j)
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return TropicalMatrix_without_dual(new_matrix)
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def mult_tropical_matrix_without_dual(self, matrix):
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n = 2
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new_matrix = [[0, 0], [0, 0]]
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for i in range(n):
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for j in range(n):
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sum_list = []
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for k in range(n):
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sum_list.append(self.get_entry(i, k) * matrix.get_entry(k, j))
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new_matrix[i][j] = sum_list[0] + sum_list[1]
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return TropicalMatrix(new_matrix)
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def get_entry(self, i, j):
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return self.entries[i][j]
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def __iter__(self): # метод для превращения тропической матрицы в список
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return self.entries.__iter__()
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if __name__ == "__main__":
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M = TropicalMatrix.dual([[-1000, 10], [5, 3]], TZmax)
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N = TropicalMatrix.dual([[3, 6], [15, 1000]], TZmin)
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l = TropicalMatrix_without_dual.add_tropical_matrix_without_dual(M, N)
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m = TropicalMatrix_without_dual.mult_tropical_matrix_without_dual(M, N)
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print(m)
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def convert(matrix):
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s = list(matrix)
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for i in range(2):
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for j in range(2):
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s[i][j] = int(TropicZ.TropicElement.__repr__(s[i][j]))
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return s
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def generate_random_matrix(n, min_elem, max_elem):
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new_matrix = [[0, 0], [0, 0]]
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for i in range(n):
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for j in range(n):
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new_matrix[i][j] = random.randint(min_elem, max_elem)
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return new_matrix
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def generate_random_tropical_poly(max_degree, min_coefficient, max_coefficient):
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"""
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Генерирует случайный (не константу) тропический многочлен с точностью до заданной степени.
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"""
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coefficients = []
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for d in range(0, random.randint(1, max_degree) + 1):
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coefficients.append(random.randint(min_coefficient, max_coefficient))
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return coefficients
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def MatrixMul(a, n):
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if (n <= 1):
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return a
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else:
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return TropicalMatrix_without_dual.mult_tropical_matrix_without_dual(MatrixMul(a, n-1), a)
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def evaluate_polynomial(tropical_matrix, coefficient_list, dual):
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"""
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Вычисляет многочлен (списком), заданный тропической матрицей.
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"""
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identity_matrix_Zmax = [[0, -1000], [-1000, 0]]
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identity_matrix_Zmin = [[0, 1000], [1000, 0]]
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null_matrix_Zmax = [[-1000, -1000], [-1000, -1000]]
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null_matrix_Zmin = [[1000, 1000], [1000, 1000]]
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sum_list = []
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# свободный член
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if coefficient_list[0] != 0:
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if dual == TZmin:
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sum_list.append(TropicalMatrix.mult_scalar(identity_matrix_Zmin, coefficient_list[0], dual))
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else:
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sum_list.append(TropicalMatrix.mult_scalar(identity_matrix_Zmax, coefficient_list[0], dual))
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if coefficient_list[0] == 0:
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if dual == TZmin:
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sum_list.append(TropicalMatrix.dual(null_matrix_Zmin, dual))
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else:
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sum_list.append(TropicalMatrix.dual(null_matrix_Zmax, dual))
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# для многочлена первой степени
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if (coefficient_list[1] != 0) and (coefficient_list[1] != 1):
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sum_list.append(TropicalMatrix.mult_scalar(tropical_matrix, coefficient_list[1], dual))
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if coefficient_list[1] == 1:
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sum_list.append(TropicalMatrix.dual(tropical_matrix, dual))
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if coefficient_list[1] == 0:
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if dual == TZmin:
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sum_list.append(TropicalMatrix.dual(null_matrix_Zmin, dual))
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else:
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sum_list.append(TropicalMatrix.dual(null_matrix_Zmax, dual))
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# для многочлена второй степени и выше
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for i in range(2, len(coefficient_list)):
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sum_list.append(TropicalMatrix.dual(tropical_matrix, dual))
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sum_list[i] = MatrixMul(sum_list[i], i)
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if (coefficient_list[i] != 1) and (coefficient_list[i] != 0):
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sum_list[i] = TropicalMatrix.mult_scalar(convert(sum_list[i]), coefficient_list[i], dual)
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if coefficient_list[i] == 0:
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if dual == TZmin:
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sum_list.append(TropicalMatrix.dual(null_matrix_Zmin, dual))
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else:
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sum_list.append(TropicalMatrix.dual(null_matrix_Zmax, dual))
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new_matrix = sum_list[0] # складываем все матрицы в sum_list
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for matrix in sum_list:
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new_matrix = TropicalMatrix_without_dual.add_tropical_matrix_without_dual(new_matrix, matrix)
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return TropicalMatrix(new_matrix)
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def get_polynomial_representation(coefficient_list):
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term_list = [str(coefficient_list[0])]
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for i in range(1, len(coefficient_list)):
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term_list.append(str(coefficient_list[i]) + "x^" + str(i))
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return " + ".join(term_list)
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def generate_key(public_term, public_matrix_a, public_matrix_b):
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left_term = TropicalMatrix.mult_tropical_matrix(public_matrix_a, public_term, TZmax)
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right_term = TropicalMatrix.mult_tropical_matrix(convert(left_term), public_matrix_b, TZmin)
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return right_term
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if __name__ == "__main__":
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p_x = [5, 1]
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t_x = [0, 0, 1]
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q_x = [2, 1]
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r_x = [0, 3]
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X = [[1, 2], [6, 10]]
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M = [[-1000, 10], [5, 3]]
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N = [[3, 6], [15, 1000]]
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p_M = convert(evaluate_polynomial(M, p_x, TZmax))
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t_N = convert(evaluate_polynomial(N, t_x, TZmin))
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q_M = convert(evaluate_polynomial(M, q_x, TZmax))
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r_N = convert(evaluate_polynomial(N, r_x, TZmin))
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print('p(x) =', p_M)
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print('t(x) =', t_N)
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print('q(x) =', q_M)
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print('r(x) =', r_N)
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Alica = TropicalMatrix.mult_tropical_matrix(p_M, X, TZmax)
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alice_public_key = TropicalMatrix.mult_tropical_matrix(convert(Alica), t_N, TZmin)
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print('Открытый ключ Алисы: ', alice_public_key)
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Bob = TropicalMatrix.mult_tropical_matrix(q_M, X, TZmax)
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bob_public_key = TropicalMatrix.mult_tropical_matrix(convert(Bob), r_N, TZmin)
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print('Открытый ключ Боба: ', bob_public_key)
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print('Секретный ключ Алисы: ', generate_key(convert(bob_public_key), p_M, t_N))
|
||||||
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print('Секретный ключ Боба: ', generate_key(convert(alice_public_key), q_M, r_N))
|
||||||
|
|
||||||
|
import random
|
||||||
|
|
||||||
|
def pprint_matrix(matrix):
|
||||||
|
print('\n'.join([' '.join([str(cell) for cell in row]) for row in matrix.entries]))
|
||||||
|
|
||||||
|
if __name__ == "__main__":
|
||||||
|
matrix_size = 2
|
||||||
|
min_matrix_term = -15
|
||||||
|
max_matrix_term = 15
|
||||||
|
min_polynomial_coefficient = -10
|
||||||
|
max_polynomial_coefficient = 10
|
||||||
|
max_polynomial_degree = 5
|
||||||
|
|
||||||
|
print('Генерация многочленов')
|
||||||
|
|
||||||
|
print("Секретные многочлены Алисы: ")
|
||||||
|
p_x = generate_random_tropical_poly(max_polynomial_degree, min_polynomial_coefficient, max_polynomial_coefficient)
|
||||||
|
t_x = generate_random_tropical_poly(max_polynomial_degree, min_polynomial_coefficient, max_polynomial_coefficient)
|
||||||
|
print('p(x) =', get_polynomial_representation(p_x))
|
||||||
|
print('t(x) =', get_polynomial_representation(t_x))
|
||||||
|
|
||||||
|
print('Секретные многочлены Боба: ')
|
||||||
|
q_x = generate_random_tropical_poly(max_polynomial_degree, min_polynomial_coefficient, max_polynomial_coefficient)
|
||||||
|
r_x = generate_random_tropical_poly(max_polynomial_degree, min_polynomial_coefficient, max_polynomial_coefficient)
|
||||||
|
print('q(x) =', get_polynomial_representation(q_x))
|
||||||
|
print('r(x) =', get_polynomial_representation(r_x))
|
||||||
|
|
||||||
|
print('Открытая матрица Алисы: ')
|
||||||
|
#M = generate_random_matrix(matrix_size, min_matrix_term, max_matrix_term)
|
||||||
|
M = [[68, 1000],[-1000, 11]]
|
||||||
|
print('M = ', M)
|
||||||
|
|
||||||
|
print('Открытая матрица Боба: ')
|
||||||
|
#N = generate_random_matrix(matrix_size, min_matrix_term, max_matrix_term)
|
||||||
|
N = [[15, 122],[78, 12]]
|
||||||
|
print('N = ', N)
|
||||||
|
|
||||||
|
X_matrix = generate_random_matrix(matrix_size, min_matrix_term, max_matrix_term)
|
||||||
|
print('Матрица X: ', X_matrix)
|
||||||
|
|
||||||
|
print('Алиса отправляет Бобу следующую матрицу')
|
||||||
|
p_M = convert(evaluate_polynomial(M, p_x, TZmax))
|
||||||
|
t_N = convert(evaluate_polynomial(N, t_x, TZmin))
|
||||||
|
Alica = TropicalMatrix.mult_tropical_matrix(p_M, X, TZmax)
|
||||||
|
alice_public_key = TropicalMatrix.mult_tropical_matrix(convert(Alica), t_N, TZmin)
|
||||||
|
print('Открытый ключ Алисы: ')
|
||||||
|
pprint_matrix(alice_public_key)
|
||||||
|
|
||||||
|
print('Боб отправляет Алисе следующую матрицу')
|
||||||
|
q_M = convert(evaluate_polynomial(M, q_x, TZmax))
|
||||||
|
r_N = convert(evaluate_polynomial(N, r_x, TZmin))
|
||||||
|
Bob = TropicalMatrix.mult_tropical_matrix(q_M, X, TZmax)
|
||||||
|
bob_public_key = TropicalMatrix.mult_tropical_matrix(convert(Bob), r_N, TZmin)
|
||||||
|
print('Открытый ключ Боба: ')
|
||||||
|
pprint_matrix(bob_public_key)
|
||||||
|
|
||||||
|
print('Алиса и Боб вычисляют секретные ключи')
|
||||||
|
print('Секретный ключ Алисы: ')
|
||||||
|
alice_key = generate_key(convert(bob_public_key), p_M, t_N)
|
||||||
|
pprint_matrix(alice_key)
|
||||||
|
|
||||||
|
print('Секретный ключ Боба: ')
|
||||||
|
bob_key = generate_key(convert(alice_public_key), q_M, r_N)
|
||||||
|
pprint_matrix(bob_key)
|
||||||
|
|
||||||
Loading…
Reference in New Issue
Block a user