Add lab12

lab12/zad1.py

@@ -0,0 +1,302 @@
+# Aleksander Kluczka
+
+
+def multiplicative_inverse(a, n):
+    def nwd(j, k):
+        if j == 0:
+            return k
+        r = k % j
+        return nwd(r, j)
+
+    def nwd_expanded(j, k):
+        assert 0 <= j < k
+        if j == 0:
+            return k, 0, 1
+        r = k % j
+        d, xp, yp = nwd_expanded(r, j)
+        x = yp - (k // j) * xp
+        y = xp
+        return d, x, y
+
+    d, x, y = nwd_expanded(a, n)
+    reverse_a = x % n
+    assert (a * reverse_a) % n == 1
+    return reverse_a
+
+
+def zad1():
+    n = 18923
+    b = 1261
+    n_1 = 127
+    n_2 = 149
+    phi_n = 18648
+
+    a = multiplicative_inverse(b, phi_n)
+    encrypted = [
+        12423,
+        11524,
+        7243,
+        7459,
+        14303,
+        6127,
+        10964,
+        16399,
+        9792,
+        13629,
+        14407,
+        18817,
+        18830,
+        13556,
+        3159,
+        16647,
+        5300,
+        13951,
+        81,
+        8986,
+        8007,
+        13167,
+        10022,
+        17213,
+        2264,
+        961,
+        17459,
+        4101,
+        2999,
+        14569,
+        17183,
+        15827,
+        12693,
+        9553,
+        18194,
+        3830,
+        2664,
+        13998,
+        12501,
+        18873,
+        12161,
+        13071,
+        16900,
+        7233,
+        8270,
+        17086,
+        9792,
+        14266,
+        13236,
+        5300,
+        13951,
+        8850,
+        12129,
+        6091,
+        18110,
+        3332,
+        15061,
+        12347,
+        7817,
+        7946,
+        11675,
+        13924,
+        13892,
+        18031,
+        2620,
+        6276,
+        8500,
+        201,
+        8850,
+        11178,
+        16477,
+        10161,
+        3533,
+        13842,
+        7537,
+        12259,
+        18110,
+        44,
+        2364,
+        15570,
+        3460,
+        9886,
+        8687,
+        4481,
+        11231,
+        7547,
+        11383,
+        17910,
+        12867,
+        13203,
+        5102,
+        4742,
+        5053,
+        15407,
+        2976,
+        9330,
+        12192,
+        56,
+        2471,
+        15334,
+        841,
+        13995,
+        17592,
+        13297,
+        2430,
+        9741,
+        11675,
+        424,
+        6686,
+        738,
+        13874,
+        8168,
+        7913,
+        6246,
+        14301,
+        1144,
+        9056,
+        15967,
+        7328,
+        13203,
+        796,
+        195,
+        9872,
+        16979,
+        15404,
+        14130,
+        9105,
+        2001,
+        9792,
+        14251,
+        1498,
+        11296,
+        1105,
+        4502,
+        16979,
+        1105,
+        56,
+        4118,
+        11302,
+        5988,
+        3363,
+        15827,
+        6928,
+        4191,
+        4277,
+        10617,
+        874,
+        13211,
+        11821,
+        3090,
+        18110,
+        44,
+        2364,
+        15570,
+        3460,
+        9886,
+        9988,
+        3798,
+        1158,
+        9872,
+        16979,
+        15404,
+        6127,
+        9872,
+        3652,
+        14838,
+        7437,
+        2540,
+        1367,
+        2512,
+        14407,
+        5053,
+        1521,
+        297,
+        10935,
+        17137,
+        2186,
+        9433,
+        13293,
+        7555,
+        13618,
+        13000,
+        6490,
+        5310,
+        18676,
+        4782,
+        11374,
+        446,
+        4165,
+        11634,
+        3846,
+        14611,
+        2364,
+        6789,
+        11634,
+        4493,
+        4063,
+        4576,
+        17955,
+        7965,
+        11748,
+        14616,
+        11453,
+        17666,
+        925,
+        56,
+        4118,
+        18031,
+        9522,
+        14838,
+        7437,
+        3880,
+        11476,
+        8305,
+        5102,
+        2999,
+        18628,
+        14326,
+        9175,
+        9061,
+        650,
+        18110,
+        8720,
+        15404,
+        2951,
+        722,
+        15334,
+        841,
+        15610,
+        2443,
+        11056,
+        2186,
+    ]
+
+    def find_power(code):
+        power = 0
+        while code >= 26**power:
+            power += 1
+        return power - 1
+
+    def decode_to_letters(code: int) -> str:
+        temp: int = code + 0
+        numbers = []
+        power: int = find_power(temp)
+        while power >= 0:
+            min_val = 26**power
+            number = temp // min_val
+            numbers.append(number)
+            temp = temp - min_val * number
+            power -= 1
+
+        letters: str = "".join([chr(ord("a") + number) for number in numbers])
+
+        return letters
+
+    for code in encrypted:
+        decrypted = pow(code, a, n)
+        letters = decode_to_letters(decrypted)
+        print(f"{letters}", end="")
+
+
+def main():
+    zad1()
+
+
+if __name__ == "__main__":
+    main()

lab12/zad2.py

@@ -0,0 +1,48 @@
+# Aleksander Kluczka
+
+
+def multiplicative_inverse(a, n):
+    def nwd_expanded(j, k):
+        if j == 0:
+            return k, 0, 1
+        r = k % j
+        d, xp, yp = nwd_expanded(r, j)
+        x = yp - (k // j) * xp
+        y = xp
+        return d, x, y
+
+    d, x, y = nwd_expanded(a, n)
+    reverse_a = x % n
+    assert (a * reverse_a) % n == 1
+    return reverse_a
+
+
+def zad2():
+    p = 1511
+    q = 2003
+    d = 1234577
+    dp = d % (p - 1)
+    dq = d % (q - 1)
+    mp = multiplicative_inverse(q, p)
+    mq = multiplicative_inverse(p, q)
+    n = (p - 1) * (q - 1)
+
+    print(f"{dp=}, {dq=}, {mp=}, {mq=}")
+
+    def ctr(n, dp, dq, mp, mq, y):
+        xp = pow(y, dp, p)
+        xq = pow(y, dq, q)
+        print(f"{xp=}, {xq=}")
+        x = ((mp * q * xp) + (mq * p * xq)) % n
+        return x
+
+    x = ctr(n, dp, dq, mp, mq, 152702)
+    print(f"{x=}")
+
+
+def main():
+    zad2()
+
+
+if __name__ == "__main__":
+    main()

lab12/zad3.py

@@ -0,0 +1,24 @@
+# Aleksander Kluczka
+
+
+def square_remainders(p):
+    return set([pow(i, 2, p) for i in range(p)])
+
+
+def euler_criteria(p):
+    return [0] + [i for i in range(p) if pow(i, (p - 1) // 2, p) == 1]
+
+
+def zad3():
+    square = square_remainders(13)
+    print(square)
+    euler = euler_criteria(13)
+    print(euler)
+
+
+def main():
+    zad3()
+
+
+if __name__ == "__main__":
+    main()