Add lab11

lab11/zad1.py

@@ -0,0 +1,36 @@
+# Aleksander Kluczka
+
+
+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
+
+
+def zad1():
+    j, k = 57, 93
+    result = nwd(57, 93)
+    print(f"nwd({j}, {k}) = {result}")
+    d, s, t = nwd_expanded(57, 93)
+    assert (j * s + k * t) == result
+    print(f"{s=}, {t=}")
+
+
+def main():
+    zad1()
+
+
+if __name__ == "__main__":
+    main()

lab11/zad2.py

@@ -0,0 +1,47 @@
+# Aleksander Kluczka
+
+
+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
+
+
+def multiplicative_inverse(a, n):
+    d, x, y = nwd_expanded(a, n)
+    reverse_a = x % n
+    assert (a * reverse_a) % n == 1
+    return reverse_a
+
+
+def zad2():
+    exercises = {
+        "a": [17, 101],
+        "b": [357, 1234],
+        "c": [3125, 9987],
+    }
+
+    for exercise, values in exercises.items():
+        a, n = values[0], values[1]
+        reverse_a = multiplicative_inverse(a, n)
+        print(f"{exercise}: {a=:5}, {n=:5}, result={reverse_a:5}")
+
+
+def main():
+    zad2()
+
+
+if __name__ == "__main__":
+    main()

lab11/zad3.py

@@ -0,0 +1,50 @@
+# Aleksander Kluczka
+
+
+def nwd(j, k):
+    if j == 0:
+        return k
+    r = k % j
+    return nwd(r, j)
+
+
+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
+
+
+def multiplicative_inverse(a, n):
+    d, x, y = nwd_expanded(a, n)
+    reverse_a = x % n
+    assert (a * reverse_a) % n == 1
+    return reverse_a
+
+
+def chi(a1, a2, a3, m1, m2, m3):
+    M = m1 * m2 * m3
+    M1 = M // m1
+    M2 = M // m2
+    M3 = M // m3
+    print(f"{M=}, {M1=}, {M2=}, {M3=}")
+    y1 = multiplicative_inverse(M1, m1)
+    y2 = multiplicative_inverse(M2, m2)
+    y3 = multiplicative_inverse(M3, m3)
+    print(f"chi^(-1)(x) = {a1}*{y1}*{M1}, {a2}*{y2}*{M2}, {a3}*{y3}*{M3} % {M}")
+    return ((a1 * M1 * y1) + (a2 * M2 * y2) + (a3 * M3 * y3)) % M
+
+
+def zad3():
+    print(chi(2, 2, 3, 3, 5, 7))
+
+
+def main():
+    zad3()
+
+
+if __name__ == "__main__":
+    main()

lab11/zad4.py

@@ -0,0 +1,50 @@
+# Aleksander Kluczka
+
+
+def nwd(j, k):
+    if j == 0:
+        return k
+    r = k % j
+    return nwd(r, j)
+
+
+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
+
+
+def multiplicative_inverse(a, n):
+    d, x, y = nwd_expanded(a, n)
+    reverse_a = x % n
+    assert (a * reverse_a) % n == 1
+    return reverse_a
+
+
+def chi(a1, a2, a3, m1, m2, m3):
+    M = m1 * m2 * m3
+    M1 = M // m1
+    M2 = M // m2
+    M3 = M // m3
+    print(f"{M=}, {M1=}, {M2=}, {M3=}")
+    y1 = multiplicative_inverse(M1, m1)
+    y2 = multiplicative_inverse(M2, m2)
+    y3 = multiplicative_inverse(M3, m3)
+    print(f"chi^(-1)(x) = {y1}*{a1}, {y2}*{a2}, {y3}*{a3}")
+    return ((a1 * M1 * y1) + (a2 * M2 * y2) + (a3 * M3 * y3)) % M
+
+
+def zad4():
+    print(chi(12, 9, 23, 25, 26, 27))
+
+
+def main():
+    zad4()
+
+
+if __name__ == "__main__":
+    main()

lab11/zad5.py

@@ -0,0 +1,50 @@
+# Aleksander Kluczka
+
+
+def nwd(j, k):
+    if j == 0:
+        return k
+    r = k % j
+    return nwd(r, j)
+
+
+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
+
+
+def multiplicative_inverse(a, n):
+    d, x, y = nwd_expanded(a, n)
+    reverse_a = x % n
+    assert (a * reverse_a) % n == 1
+    return reverse_a
+
+
+def chi(a1, a2, m1, m2):
+    M = m1 * m2
+    M1 = M // m1
+    M2 = M // m2
+    y1 = multiplicative_inverse(M1, m1)
+    y2 = multiplicative_inverse(M2, m2)
+    return ((a1 * M1 * y1) + (a2 * M2 * y2)) % M
+
+
+def zad5():
+    a = multiplicative_inverse(13, 99)
+    b = multiplicative_inverse(15, 101)
+    print(f"{a=}, {b=}")
+    result = chi(4 * a, 56 * b, 99, 101)
+    print(f"x = {result}")
+
+
+def main():
+    zad5()
+
+
+if __name__ == "__main__":
+    main()

lab11/zad6.py

@@ -0,0 +1,90 @@
+# Aleksander Kluczka
+
+import math
+
+
+def nwd(j, k):
+    if j == 0:
+        return k
+    r = k % j
+    return nwd(r, j)
+
+
+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
+
+
+def multiplicative_inverse(a, n):
+    d, x, y = nwd_expanded(a, n)
+    reverse_a = x % n
+    assert (a * reverse_a) % n == 1
+    return reverse_a
+
+
+def chi(a1, a2, m1, m2):
+    M = m1 * m2
+    M1 = M // m1
+    M2 = M // m2
+    y1 = multiplicative_inverse(M1, m1)
+    y2 = multiplicative_inverse(M2, m2)
+    return ((a1 * M1 * y1) + (a2 * M2 * y2)) % M
+
+
+def square_power(a, e, n):
+    d = 1
+    e_bin = f"{e:b}"
+    s = len(e_bin) - 1
+    assert s <= math.log2(n)
+    while s >= 0:
+        d = (d * d) % n
+        if e_bin[s - 1] == "1":
+            d = (d * a) % n
+        s -= 1
+    return d
+
+
+def zad6():
+    def lecture():
+        p = 23
+        g = 5
+
+        a = 6
+        A = square_power(g, a, p)
+
+        b = 15
+        B = square_power(g, b, p)
+        print(f"{A=}, {B=}")
+        alicja_s = square_power(B, a, p)
+        bob_s = square_power(A, b, p)
+        print(f"{alicja_s=}, {bob_s=}\n")
+
+    def next():
+        p = 12987461
+        g = 3606738
+
+        a = 357
+        b = 199
+
+        A = square_power(g, a, p)
+        B = square_power(g, b, p)
+        print(f"{A=}, {B=}")
+        alicja_s = square_power(B, a, p)
+        bob_s = square_power(A, b, p)
+        print(f"{alicja_s=}, {bob_s=}")
+
+    lecture()
+    next()
+
+
+def main():
+    zad6()
+
+
+if __name__ == "__main__":
+    main()