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hw3.py

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+from sys import argv
+from fractions import gcd
+
+class Polynomial():
+    def __init__(self, lst, mod):
+        self.poly = list(map(lambda x: x % mod, lst))    
+        self.mod = mod
+        self.normalize()
+    def normalize(self):
+        while self.poly and self.poly[-1] == 0:
+            self.poly.pop() 
+
+    #zwraca jednomian stopnia n 
+    @staticmethod
+    def Monomial(n, c, mod):
+        zeros = [0]*n
+        zeros.append(c)
+        return Polynomial(zeros, mod)
+
+    def __add__(self, p2):
+        p1 = self
+        len_p1, len_p2= len(p1.poly), len(p2.poly)
+        res = [0] * max(len_p1, len_p2)
+        if len_p1 > len_p2:
+            for _ in range(len_p1-len_p2):
+                p2.poly.append(0)
+        else:
+            for _ in range(len_p2-len_p1):
+                p1.poly.append(0)
+
+        for i in range(len(res)):
+            res[i] = (p1.poly[i] + p2.poly[i]) % self.mod
+        return Polynomial(res, self.mod)
+
+    def __sub__(self, p2):
+        p1 = self
+        res = []
+        len_p2 = len(p2.poly)
+        for i in range(len(p1.poly)):
+            if i < len_p2:
+                res.append(p1.poly[i] - p2.poly[i] % self.mod)
+            else:
+                res.append(p1.poly[i])
+        return Polynomial(res, self.mod)
+
+    def __mul__(self, p2):
+        res = [0]*(len(self.poly)+len(p2.poly)-1)
+        for i, x1 in enumerate(self.poly):
+            for j, x2 in enumerate(p2.poly):
+                res[i+j] += x1 * x2 % self.mod
+        return Polynomial(res, self.mod)
+    
+    def __truediv__(self, p2):
+        p1 = self
+        m = self.mod
+        
+        if len(p1.poly) < len(p2.poly):
+            return p1
+        
+        if len(p2.poly) == 0:
+            raise ZeroDivisionError
+            
+        divisor_coeff = p2.poly[-1]
+        divisor_exp = len(p2.poly) - 1 
+        while len(p1.poly) >= len(p2.poly):   
+            max_coeff_p1 = p1.poly[-1] #wspolczynnik przy najwyzszej potedze
+            try:
+              tmp_coeff = modDiv(max_coeff_p1, divisor_coeff, m)
+            except ZeroDivisionError as e:
+                raise e
+            
+            tmp_exp = len(p1.poly)-1 - divisor_exp
+            tmp = [0] * tmp_exp
+            tmp.append(tmp_coeff)
+            sub = Polynomial(tmp, m) * p2
+            p1 = p1 - sub
+        p1.normalize()
+        return Polynomial(p1.poly, m)
+
+def modDiv(a, b, m): # a*b^-1 (mod m)
+    if gcd(b, m) != 1:
+        raise ZeroDivisionError
+    else:
+        return (a * modinv(b, m)) % m
+#rozszerzony algorytm euklidesa
+def egcd(a, b):
+    if a == 0:
+        return (b, 0, 1)
+    else:
+        g, y, x = egcd(b % a, a)
+        return (g, x - (b // a) * y, y)
+
+def modinv(a, m):
+    g, x, y = egcd(a, m)
+    return x % m
+#lista stringow binarnych -> lista intow 0/1
+def bin_str_to_list(lst):
+    res = []
+    for elem in lst:
+        for ch in elem:
+            res.append(int(ch))
+    return res
+
+def mod8format(lst):
+    while len(lst) % 8 != 0:
+        lst.append(0)
+    return lst
+
+def to_bin(x):
+    data = bin(ord(x)).replace('b', '')
+    while len(data) != 8:
+        if len(data) < 8:
+            data = str(0) + data
+        else:
+            data.replace(data[0], '')
+    return data
+
+def to_ascii_val(lst):
+    sum = 0
+    for i in range(len(lst)):
+        if lst[i] == 1:
+            sum += 2**(7-i)
+    return chr(sum)
+
+def data():
+    p = bin_str_to_list(list(map(lambda x: to_bin(x), m)))
+    p.reverse()
+    Lx = Polynomial([1] * 16, 2)        #L(x)
+    X16 = Polynomial.Monomial(16, 1, 2) #X^16
+    Gx = Polynomial([1,0,0,0,0,1,0,0,0,0,0,0,1,0,0,0,1], 2) #G(x)
+    return (p, Lx, X16, Gx)
+
+def fcs(m):
+    p, Lx, X16,  Gx = data()
+    Mx = Polynomial(p, 2)               #M(x)           #X^16
+    Xnsub16 = Polynomial.Monomial(len(m)*8, 1, 2)    #X^(n-16)
+    rhs = Xnsub16 * Lx
+    lhs = X16 * Mx
+    xor = lhs + rhs                   
+    fcs = xor/Gx
+    #algorytm dzielenia ucina zera, trzeba dopelnic do 16 bitow
+    for i in range(16 - len(fcs.poly)):
+        fcs.poly.append(0)
+    fcs.poly.reverse()
+    return fcs.poly
+
+def check(m):
+    p, Lx, X16, Gx = data()
+    Xn = Polynomial.Monomial(len(p), 1, 2) #X^n
+    Cx = Polynomial(p, 2)
+    Cx = X16 * Cx
+    Cx.poly = mod8format(Cx.poly)
+    Sx = (Cx + Xn * Lx) / Gx
+    if Sx.poly == []: 
+        return True
+    return False
+
+def main():
+    global m
+    m = list(argv[1])
+    mode = argv[2]  # flagi -e -d (encode, decode)
+    if mode == '-e':
+        res = fcs(m)
+        fcs_ch1 = to_ascii_val(res[:8])
+        fcs_ch2 = to_ascii_val(res[8:])
+        m.append(fcs_ch1)
+        m.append(fcs_ch2)
+        print(''.join(m))
+    elif mode == '-d':
+        print(check(m))
+    
+if __name__ == '__main__':
+    main()