ts is SO ASS

what.py

@@ -0,0 +1,114 @@
+from math import gcd
+
+
+def ex1(x):
+    table = [
+        [14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7],
+        [0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8],
+        [4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0],
+        [15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13],
+    ]
+    r = ((x & 0b100000) >> 4) | (x & 1)
+    c = (x & 0b11110) >> 1
+    return r, c, table[r][c]
+
+
+def ex2p1():
+    # 1a
+    p, q = 139, 227
+    potential_e = {122, 123, 124, 125}
+    e = next(e for e in potential_e if gcd(e, (p - 1) * (q - 1)) == 1)
+    # 1b
+    d = pow(e, -1, (p - 1) * (q - 1))
+    print(f"{e = }, {d = }")
+    return p * q, e, d
+
+
+def ex2p2_pre():
+    p_ca = 997
+    alpha = 6
+    d_ca = 25
+
+    beta = pow(alpha, d_ca, p_ca)
+    return (p_ca, alpha, beta), d_ca
+
+
+def elgamal_generate(x, k_E, p_ca, alpha, d_ca):
+    beta = pow(alpha, d_ca, p_ca)
+    r = pow(alpha, k_E, p_ca)
+    kei = pow(k_E, -1, p_ca - 1)  # mod p - 1
+    uhh = (x - d_ca * r) % (p_ca - 1)
+    print(f"{x = }, {d_ca = }, {beta = }, {r = }, {uhh = }, {kei = }")
+    s = (uhh * kei) % (p_ca - 1)
+    return (r, s)
+
+
+def elgamal_verify(x, r, s, p_ca, alpha, beta):
+    br = pow(beta, r, p_ca)
+    rs = pow(r, s, p_ca)
+    t = (br * rs) % p_ca
+    ax = pow(alpha, x, p_ca)
+    print(f"{br = }, {rs = }, {t = }, {ax = }")
+    return (t - ax) % p_ca == 0, t
+
+
+def ex2p2(x):
+    (p_ca, alpha, beta), d_ca = ex2p2_pre()
+    _, e, _ = ex2p1()
+    k_E = 185
+    (r, s) = elgamal_generate(x + e, k_E, p_ca, alpha, d_ca)
+    v, t = elgamal_verify(x + e, r, s, p_ca, alpha, beta)
+    assert v, f"{t = }"
+    return x + e, (r, s)
+
+
+def rsa_encrypt(M, e, n):
+    return pow(M, e, n)
+
+
+def ex2p3():
+    M = 20260
+    N, e, _ = ex2p1()
+    C = rsa_encrypt(M, e, N)
+    return M, C
+
+
+def ex3():
+    M = 20260
+    l = (M + 64) % 512
+    p = 512 - l
+    return l, p, M
+
+
+def key(p, g, k):
+    "g could be an existing key or the generator."
+    return pow(g, k, p)
+
+
+def ex4():
+    p = 27361
+    k_a, k_b = ex2p3()
+    g = 6
+    # public
+    ka = key(p, g, k_a)
+    kb = key(p, g, k_b)
+    # exchange
+    kab = key(p, kb, k_a)
+    kab2 = key(p, ka, k_b)
+    assert kab == kab2
+    return p, g, (k_a, k_b), (ka, kb), kab
+
+
+def main():
+    x = 21
+    print(ex1(x))
+    print(ex2p1())
+    print(ex2p2_pre())
+    print(ex2p2(x))
+    print(ex2p3())
+    print(ex3())
+    print(ex4())
+
+
+if __name__ == "__main__":
+    main()