From 7f70f46742fb4e8c9ad41552eae52e2c9712ab9d Mon Sep 17 00:00:00 2001
From: vis4rd <alagaesia.vrael@gmail.com>
Date: Tue, 7 Nov 2023 21:40:29 +0100
Subject: [PATCH] Add lab4

---
 lab4/zad1.py | 45 +++++++++++++++++++++++++++++++++
 lab4/zad2.py | 70 ++++++++++++++++++++++++++++++++++++++++++++++++++++
 lab4/zad3.py | 40 ++++++++++++++++++++++++++++++
 3 files changed, 155 insertions(+)
 create mode 100644 lab4/zad1.py
 create mode 100644 lab4/zad2.py
 create mode 100644 lab4/zad3.py

diff --git a/lab4/zad1.py b/lab4/zad1.py
new file mode 100644
index 0000000..a18d20f
--- /dev/null
+++ b/lab4/zad1.py
@@ -0,0 +1,45 @@
+def zad1():
+    def KSA(key):
+        S = [i for i in range(0, 256)]
+        j = 0
+        for i in range(0, 256):
+            j = (j+ S[i] + ord(key[i % len(key)])) % 256
+            S[i], S[j] = S[j], S[i]
+        return S
+
+    def Stream_Generator(plaintext, S):
+        i = 0
+        j = 0
+        for k in range(0, len(plaintext)):
+            i = (i+1) % 256
+            j = (j+S[i]) % 256
+            S[i], S[j] = S[j], S[i]
+            byte_key : int = S[(S[i] + S[j]) % 256]
+            yield byte_key
+
+    def encode(plaintext, keystream):
+        plaintext_num = [ord(i) for i in plaintext]
+        plaintext_hex = ''.join([f'{i:02X}' for i in plaintext_num])
+        retval = ''
+        for p, k in zip(plaintext_hex, keystream):
+            retval += f'{(int(p, 16) ^ int(k, 16)):X}'
+        return retval
+
+    def RC4(plaintext, key):
+        print(f"Plaintext: {plaintext}")
+        print(f"Key: {key}")
+        gen = Stream_Generator(plaintext, KSA(key))
+        keystream = ''.join([f'{i:02X}' for i in gen])
+        print(f"Keystream: {keystream}")
+        ciphertext = encode(plaintext, keystream)
+        print(f"Ciphertext:{ciphertext}\n")
+
+    RC4("Attack at dawn", "Secret")
+    RC4("Plaintext", "Key")
+    RC4("pedia", "Wiki")
+
+def main():
+    zad1()
+
+if __name__ == '__main__':
+    main()
diff --git a/lab4/zad2.py b/lab4/zad2.py
new file mode 100644
index 0000000..9c8fd64
--- /dev/null
+++ b/lab4/zad2.py
@@ -0,0 +1,70 @@
+import math
+
+def zad2():
+    P = ['a', 'b', 'c']
+    C = [1, 2, 3, 4]
+    K = ["K1", "K2", "K3"]
+
+    Pr_P = {'a': 1.0/2.0, 'b': 1.0/3.0, 'c': 1.0/6.0}
+    Pr_K = {'K1': 1.0/3.0, 'K2': 1.0/3.0, 'K3': 1.0/3.0}
+    Pr_C = {
+        1: (Pr_P['a'] * Pr_K['K1']) + (Pr_P['c'] * Pr_K['K3']),
+        2: (Pr_P['a'] * Pr_K['K2']) + (Pr_P['b'] * Pr_K['K1']),
+        3: (Pr_P['a'] * Pr_K['K3']) + (Pr_P['b'] * Pr_K['K2']) + (Pr_P['c'] * Pr_K['K1']),
+        4: (Pr_P['b'] * Pr_K['K3']) + (Pr_P['c'] * Pr_K['K2'])
+    }
+
+    def H(target):
+        sum = 0
+        for k, v in target.items():
+            if v == 0:
+                continue
+            sum += v * math.log2(v)
+        return -sum
+
+    def HH(target, req):
+        sum = 0
+        for r in req:
+            for k, v in target.items():
+                if v == 0:
+                    continue
+                sum += r * v * math.log2(v)
+        return -sum
+
+    H_P = H(Pr_P)
+    print(f"{H_P=}")
+
+    H_C = H(Pr_C)
+    print(f"{H_C=}")
+
+    H_K = H(Pr_K)
+    print(f"{H_K=}")
+
+    H_KC = H_K + H_P - H_C
+    print(f"{H_KC=}")
+
+    Pr_PC = {
+        'a1': (Pr_P['a'] * Pr_K['K1']) / Pr_C[1],
+        'a2': (Pr_P['a'] * Pr_K['K2']) / Pr_C[2],
+        'a3': (Pr_P['a'] * Pr_K['K3']) / Pr_C[3],
+        'a4': (Pr_P['a'] * 0) / Pr_C[4],
+        'b1': (Pr_P['b'] * 0) / Pr_C[1],
+        'b2': (Pr_P['b'] * Pr_K['K1']) / Pr_C[2],
+        'b3': (Pr_P['b'] * Pr_K['K2']) / Pr_C[3],
+        'b4': (Pr_P['b'] * Pr_K['K3']) / Pr_C[4],
+        'c1': (Pr_P['c'] * Pr_K['K3']) / Pr_C[1],
+        'c2': (Pr_P['c'] * 0) / Pr_C[2],
+        'c3': (Pr_P['c'] * Pr_K['K1']) / Pr_C[3],
+        'c4': (Pr_P['c'] * Pr_K['K2']) / Pr_C[4],
+    }
+
+    H_PC = HH(Pr_PC, Pr_C)
+    print(f"{H_PC=}")
+
+
+
+def main():
+    zad2()
+
+if __name__ == '__main__':
+    main()
diff --git a/lab4/zad3.py b/lab4/zad3.py
new file mode 100644
index 0000000..c843b46
--- /dev/null
+++ b/lab4/zad3.py
@@ -0,0 +1,40 @@
+import math
+import matplotlib.pyplot as plt
+
+def zad3():
+    def H(target):
+            sum = 0
+            for k, v in target.items():
+                if v == 0:
+                    continue
+                sum += v * math.log2(v)
+            return -sum
+
+    def coin_entropy(o, r):
+        Pr = {
+            'o': o,
+            'r': r
+        }
+        return H(Pr)
+
+    print(f"{coin_entropy(0.5, 0.5)=}")
+    print(f"{coin_entropy(1.0/4.0, 3.0/4.0)=}")
+    print(f"{coin_entropy(99.0/100.0, 1.0/100.0)=}")
+
+    def calc():
+        retval = []
+        for i in range(1, 31):
+            p = 2**i
+            retval.append(coin_entropy((p-1)/p, 1/p))
+        return retval
+
+    plt.title("Entropy of a biased coin, y = entropy, x = power of 2")
+    plt.plot(calc())
+    plt.show()
+
+
+def main():
+    zad3()
+
+if __name__ == '__main__':
+    main()