diff --git a/Ring.py b/Ring.py new file mode 100644 index 0000000..88345d4 --- /dev/null +++ b/Ring.py @@ -0,0 +1,48 @@ +from fractions import gcd + +class Modulo: + + def __init__(self, n): + self.n = int(n) + self.modulo_set = list(range(self.n)) + self.answer = [] + + def get_inverse_elements(self): + self.inverse_elements = [] + for i in self.modulo_set: + if gcd(i, self.n) == 1: + self.inverse_elements.append(i) + self.answer.append(self.inverse_elements) + + def get_zero_divisors(self): + self.zero_divisors = [] + for i in self.modulo_set: + for j in self.modulo_set: + if (i * j) % self.n == 0 and i != 0 and j != 0: + self.zero_divisors.append(i) + self.answer.append(list(set(self.zero_divisors))) + + def get_nilpotent_elements(self): + self.nilpotent_elements = [] + for i in self.modulo_set: + for j in range(1, len(self.inverse_elements) + 1): + if (i**j) % self.n == 0 and i != 0: + self.nilpotent_elements.append(i) + self.answer.append(list(set(self.nilpotent_elements))) + + def get_idempotent_elements(self): + self.idempotent_elements = [] + for i in self.modulo_set: + if (i*i) % self.n == i: + self.idempotent_elements.append(i) + self.answer.append(self.idempotent_elements) + + def get_all(self): + self.get_inverse_elements() + self.get_zero_divisors() + self.get_nilpotent_elements() + self.get_idempotent_elements() + return self.answer + +s = Modulo(input("Enter n: ")) +print(s.get_all()) diff --git a/crc16.py b/crc16.py new file mode 100644 index 0000000..0a44f74 --- /dev/null +++ b/crc16.py @@ -0,0 +1,85 @@ +from poly import Polynomial +import sys +import ast + +Polynomial.n = 2 + +def normalize_byte(data): + while len(data) != 8: + if len(data) < 8: + data = str(0) + data + else: + data = data[1:] + return data + + +def encode(in_data): + data = in_data + data = list(data) + data_binary = [bin(ord(char)).replace('b', '') for char in data] + data_binary = [normalize_byte(byte) for byte in data_binary] + data_binary = [int(bit) for bit in list(''.join(data_binary))] + data_binary.reverse() + + M = [0] * 16 + data_binary + L = [0] * (len(data_binary)) + [1] * 16 + G = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1] + result_poly = Polynomial.divide(Polynomial.add(Polynomial(M), Polynomial(L)), Polynomial(G)) + result = result_poly.coefficients + [0] * (16 - len(result_poly.coefficients)) + + result.reverse() + data_binary.reverse() + data_binary = data_binary + result + data_binary = [data_binary[i:i+8] for i in range(0, len(data_binary), 8)] + data_binary = [int(''.join(map(str, byte)), 2) for byte in data_binary] + + fcs = [hex(byte) for byte in data_binary] + fcs = fcs[-2:] + + data = [chr(byte) for byte in data_binary] + data = ''.join(data[0:-2]) + + return data, fcs + + +def check_fcs(in_data, fcs): + data = in_data + data = list(data) + data_binary = [bin(ord(char)).replace('b', '') for char in data] + data_binary = [normalize_byte(byte) for byte in data_binary] + data_binary = [int(bit) for bit in list(''.join(data_binary))] + fcs_binary = [bin(int(in_hex, 16)).replace('b', '') for in_hex in fcs] + fcs_binary = [normalize_byte(byte) for byte in fcs_binary] + fcs_binary = [int(bit) for bit in list(''.join(fcs_binary))] + data_binary += fcs_binary + data_binary.reverse() + + C = [0] * 16 + data_binary + L = [0] * len(data_binary) + [1] * 16 + G = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1] + S = Polynomial.divide(Polynomial.add(Polynomial(C), Polynomial(L)), Polynomial(G)) + + if S.coefficients == []: + return True + + return False + + +def main(): + try: + if sys.argv[1] == '-e' or sys.argv[1] == '-encode': + arg, fcs = encode(sys.argv[2]) + print(arg, fcs) + print(check_fcs(arg, fcs)) # powinno zawsze zwracać true + elif sys.argv[1] == '-c' or sys.argv[1] == '-check': + arg = sys.argv[2] + fcs = ast.literal_eval(sys.argv[3]) + print(check_fcs(arg, fcs)) + else: + raise IndexError + except IndexError: + print("To encode: python3 CRC16.py -e [argument]\nTo check result: python3 CRC16.py -c [argument] [fcs]") + + +if __name__ == "__main__": + main() \ No newline at end of file diff --git a/poly.py b/poly.py new file mode 100644 index 0000000..d9ddd32 --- /dev/null +++ b/poly.py @@ -0,0 +1,75 @@ +import sys +import ast + +class Polynomial: + + n = 0 + + def __init__(self, coef_list): + self.degree = len(coef_list) - 1 + self.coefficients = [x % Polynomial.n for x in coef_list] + + @staticmethod + def add(p1, p2): + result = [] + f = p1.coefficients + g = p2.coefficients + if len(f) >= len(g): + result = f + for i in range(0, len(g)): + result[i] = f[i] + g[i] + else: + result = g + for i in range(0, len(f)): + result[i] = f[i] + g[i] + result = [x % int(Polynomial.n) for x in result] + return Polynomial(result) + + @staticmethod + def multiply(p1, p2): + result = [0] * (p1.degree + p2.degree + 1) + f = p1.coefficients + g = p2.coefficients + for i in range(0, len(f)): + for j in range(0, len(g)): + result[i+j] += f[i] * g[j] + result = [x % int(Polynomial.n) for x in result] + return Polynomial(result) + + @staticmethod + def divide(p1, p2): + def inverse(x): + for i in range(1, int(Polynomial.n)): + r = (i * x) % int(Polynomial.n) + if r == 1: + break + else: + raise ZeroDivisionError + return i + if p1.degree < p2.degree: + return p1 + f = p1.coefficients + g = p2.coefficients + g_lead_coef = g[-1] + g_deg = p2.degree + while len(f) >= len(g): + f_lead_coef = f[-1] + tmp_coef = f_lead_coef * inverse(g_lead_coef) + tmp_exp = len(f) - 1 - g_deg + tmp = [] + for _ in range(tmp_exp): + tmp.append(0) + tmp.append(tmp_coef) + tmp_poly = Polynomial(tmp) + sub = Polynomial.multiply(p2, tmp_poly) + f = [x - y for x, y in zip(f, sub.coefficients)] + f = [x % int(Polynomial.n) for x in f] + while f and f[-1] == 0: + f.pop() + return Polynomial(f) + + @staticmethod + def gcd(p1, p2): + if len(p2.coefficients) == 0: + return p1 + return Polynomial.gcd(p2, Polynomial.divide(p1, p2))