Release 0.4.4

* Removed unnecessary line breaks

* README.md updated

* ElGamal homomorphic ciphertext extension

Author: lonkey

README.md

@@ -4,11 +4,7 @@ Python library for demonstrating the functionality of common cryptographic algor
 
 ## Requirements
 
-Python 3.7.9 or later including pip for installing the following requirements:
-
-```shell
-pip install -r requirements.txt
-```
+Python 3.7.9 or later.
 
 ### Creating a virtual environment
 

cryptographic_functions/elgamal_calculations.py

@@ -301,6 +301,62 @@ def homomorphic_multiplicative_scheme(public_key, private_key, c_1, c_2, print_m
     return m
 
 
+# ElGamal homomorphic ciphertext extension
+def homomorphic_ciphertext_extension(public_key, private_key, m_1, a_b, print_matrix=False,
+                                     print_linear_factorization=True):
+    print(tabulate([['Homomorphe Erweiterung des Geheimtextes']], tablefmt='fancy_grid'))
+
+    # Unpack both keys into its components
+    p, g, e = public_key
+    p_v, d = private_key
+
+    # Unpack the combined ciphertext into its components
+    a, b = a_b
+
+    # The value of p must be identical in both keys
+    if p != p_v:
+        print(f'Die Variablen p = {p} und p_v = {p_v} müssen identisch sein.')
+        return -1
+
+    # Calculation of m
+    a_d = (a ** d) % p
+    a_i = modulo_inverse_multiplicative.mim(p, a_d, print_matrix, print_linear_factorization, 1)
+    m = (a_i * b) % p
+
+    # Calculation of m_2
+    m_1_i = modulo_inverse_multiplicative.mim(p, m_1, print_matrix, print_linear_factorization, 2)
+    m_2 = (m * m_1_i) % p
+
+    # Calculation path output
+    print(
+        f'Gegeben sind K(pub) = {{p, g, e}} = {{{p}, {g}, {e}}} und K(priv) = {{p, d}} = {{{p_v}, {d}}} mit dem aus '
+        f'Geheimtext 1 und 2 erweiterten Geheimtext a_b = {{a, b}} = {{{a}, {b}}}. Ebenfalls bekannt ist der zu '
+        f'Geheimtext 1 zugehörige Klartext m_1 = {m_1}. Durch die Umkehrung der Geheimtext-Erweiterung soll nun der '
+        f'Klartext m_2 ermittelt werden.', end='\n\n')
+    print(
+        f'Der zum erweiterten Geheimtext (a, b) gehörende Klartext m ergibt sich aus der Gleichung a^d * m = b mod p '
+        f'zu:\n'
+        f'm = b * (a^d)^-1 mod p\n'
+        f'm = {b} * ({a}^{d})^-1 mod {p}\n'
+        f'm = {b} * {a_d}^-1 mod {p}\n'
+        f'<AUXILIARY 1>Achtung: Die Namen der Variablen können abweichen!</AUXILIARY 1>\n'
+        f'm = {b} * {a_i} mod {p}\n'
+        f'm = {m}', end='\n\n')
+    print(
+        f'Der Klartext m_2, welcher zur Erweiterung des Klartexts m_1 verwendet wurde, ergibt sich aus:\n'
+        f'm_2 = m * m_1^-1 mod p\n'
+        f'm_2 = {m} * {m_1}^-1 mod {p}\n'
+        f'<AUXILIARY 2>Achtung: Die Namen der Variablen können abweichen!</AUXILIARY 2>\n'
+        f'm_2 = {m} * {m_1_i} mod {p}\n'
+        f'm_2 = {m_2}', end='\n\n')
+    print(
+        f'Verifikation:\n'
+        f'm = m_1 * m_2 mod p\n'
+        f'{m} = {m_1} * {m_2} mod {p}\n'
+        f'{m} = {(m_1 * m_2) % p}', end='\n\n')
+    return m_2
+
+
 # ElGamal homomorphic multiplicative decryption
 def homomorphic_multiplicative_decryption(public_key, private_key, m_1, c_1, c_2, print_matrix=False,
                                           print_linear_factorization=True):

cryptographic_functions/modulo_calculations.py

@@ -34,7 +34,6 @@ def addition(m, a, b):
           f'({a} + {b}) / {m} = {q} + ({r} / {m})\n'
           f'{a} + {b} = {q} * {m} + {r}\n'
           f'Daraus folgt: {a} ⊕ {b} = {r}', end='\n\n')
-
     return r
 
 
@@ -88,7 +87,6 @@ def multiplication(m, a, b):
           f'({a} * {b}) / {m} = {q} + ({r} / {m})\n'
           f'{a} * {b} = {q} * {m} + {r}\n'
           f'Daraus folgt: {a} ⊙ {b} = {r}', end='\n\n')
-
     return r
 
 

cryptographic_functions/modulo_cyclic_groups.py

@@ -54,5 +54,4 @@ def mcg(m, print_matrix=False):
         print(f'Für die zyklische Gruppe der Ordnung m = {m} konnten keine nicht-primitiven Elemente ermittelt werden.',
               end='\n\n')
         n = -1
-
     return p, n

cryptographic_functions/shared_functions.py

@@ -32,7 +32,6 @@ def gcd_extended(m, a):
         list_r.append(r)
         m = a
         a = r
-
     return list_m, list_a, list_q, list_r
 
 
@@ -72,7 +71,6 @@ def linear_factorization(list_m, list_a, list_q, list_r):
         list_y_calc.append(f'{x} - {q} * ({list_x[-1]}) = {y}')
         list_y.append(y)
         x = list_x[-1]
-
     return list_m, list_a, list_q, list_r, list_x[::-1], list_y_calc[::-1], list_y[::-1]
 
 

main.py

@@ -99,6 +99,7 @@
     elgamal_p_n = 3
     elgamal_s = 7
     elgamal_signed_message = (elgamal_plaintext, elgamal_p_n, elgamal_s)
+    elgamal_homomorphic_a_b = (3, 3)
     elgamal_homomorphic_c_1 = (3, 3)
     elgamal_homomorphic_c_2 = (6, 3)
     elgamal_homomorphic_m_1 = 6
@@ -112,6 +113,9 @@
     # elgamal_calculations.homomorphic_multiplicative_scheme(elgamal_public_key, elgamal_private_key,
     #                                                        elgamal_homomorphic_c_1, elgamal_homomorphic_c_2,
     #                                                        print_matrix, print_linear_factorization)
+    # elgamal_calculations.homomorphic_ciphertext_extension(elgamal_public_key, elgamal_private_key,
+    #                                                       elgamal_homomorphic_m_1, elgamal_homomorphic_a_b,
+    #                                                       print_matrix, print_linear_factorization)
     # elgamal_calculations.homomorphic_multiplicative_decryption(elgamal_public_key, elgamal_private_key,
     #                                                            elgamal_homomorphic_m_1, elgamal_homomorphic_c_1,
     #                                                            elgamal_homomorphic_c_2, print_matrix,