Removed redundant greatest_common_divisor code (#9358)

* Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder

* Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder, also fixed comments

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Deleted greatest_common_divisor def from many files and instead imported the method from Maths folder, also fixed comments

* Imports organized

* recursive gcd function implementation rolledback

* more gcd duplicates removed

* more gcd duplicates removed

* Update maths/carmichael_number.py

* updated files

* moved a file to another location

---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Tianyi Zheng <tianyizheng02@gmail.com>

ciphers/affine_cipher.py

@@ -1,6 +1,8 @@
 import random
 import sys
 
+from maths.greatest_common_divisor import gcd_by_iterative
+
 from . import cryptomath_module as cryptomath
 
 SYMBOLS = (
@@ -26,7 +28,7 @@ def check_keys(key_a: int, key_b: int, mode: str) -> None:
             "Key A must be greater than 0 and key B must "
             f"be between 0 and {len(SYMBOLS) - 1}."
         )
-    if cryptomath.gcd(key_a, len(SYMBOLS)) != 1:
+    if gcd_by_iterative(key_a, len(SYMBOLS)) != 1:
         sys.exit(
             f"Key A {key_a} and the symbol set size {len(SYMBOLS)} "
             "are not relatively prime. Choose a different key."
@@ -76,7 +78,7 @@ def get_random_key() -> int:
     while True:
         key_b = random.randint(2, len(SYMBOLS))
         key_b = random.randint(2, len(SYMBOLS))
-        if cryptomath.gcd(key_b, len(SYMBOLS)) == 1 and key_b % len(SYMBOLS) != 0:
+        if gcd_by_iterative(key_b, len(SYMBOLS)) == 1 and key_b % len(SYMBOLS) != 0:
             return key_b * len(SYMBOLS) + key_b
 
 

ciphers/cryptomath_module.py

@@ -1,11 +1,8 @@
-def gcd(a: int, b: int) -> int:
-    while a != 0:
-        a, b = b % a, a
-    return b
+from maths.greatest_common_divisor import gcd_by_iterative
 
 
 def find_mod_inverse(a: int, m: int) -> int:
-    if gcd(a, m) != 1:
+    if gcd_by_iterative(a, m) != 1:
         msg = f"mod inverse of {a!r} and {m!r} does not exist"
         raise ValueError(msg)
     u1, u2, u3 = 1, 0, a

ciphers/hill_cipher.py

@@ -39,19 +39,7 @@ import string
 
 import numpy
 
-
-def greatest_common_divisor(a: int, b: int) -> int:
-    """
-    >>> greatest_common_divisor(4, 8)
-    4
-    >>> greatest_common_divisor(8, 4)
-    4
-    >>> greatest_common_divisor(4, 7)
-    1
-    >>> greatest_common_divisor(0, 10)
-    10
-    """
-    return b if a == 0 else greatest_common_divisor(b % a, a)
+from maths.greatest_common_divisor import greatest_common_divisor
 
 
 class HillCipher:

ciphers/rsa_key_generator.py

@@ -2,6 +2,8 @@ import os
 import random
 import sys
 
+from maths.greatest_common_divisor import gcd_by_iterative
+
 from . import cryptomath_module, rabin_miller
 
 
@@ -27,7 +29,7 @@ def generate_key(key_size: int) -> tuple[tuple[int, int], tuple[int, int]]:
     # Generate e that is relatively prime to (p - 1) * (q - 1)
     while True:
         e = random.randrange(2 ** (key_size - 1), 2 ** (key_size))
-        if cryptomath_module.gcd(e, (p - 1) * (q - 1)) == 1:
+        if gcd_by_iterative(e, (p - 1) * (q - 1)) == 1:
             break
 
     # Calculate d that is mod inverse of e