Improving the efficiency of the 'mod_inv' method within the 'mathsHelper' class. Currently, it uses a brute-force approach to find the modular inverse, which may not be optimal for large values of 'm'. Instead, we can utilize the Extended Euclidean Algorithm to compute the modular inverse more efficiently.

.github/workflows/python-package.yml

@@ -0,0 +1,40 @@
+# This workflow will install Python dependencies, run tests and lint with a variety of Python versions
+# For more information see: https://docs.github.com/en/actions/automating-builds-and-tests/building-and-testing-python
+
+name: Python package
+
+on:
+ push:
+ branches: [ "master" ]
+ pull_request:
+ branches: [ "master" ]
+
+jobs:
+ build:
+
+ runs-on: ubuntu-latest
+ strategy:
+ fail-fast: false
+ matrix:
+ python-version: ["3.9", "3.10", "3.11"]
+
+ steps:
+ - uses: actions/checkout@v3
+ - name: Set up Python ${{ matrix.python-version }}
+ uses: actions/setup-python@v3
+ with:
+ python-version: ${{ matrix.python-version }}
+ - name: Install dependencies
+ run: |
+ python -m pip install --upgrade pip
+ python -m pip install flake8 pytest
+ if [ -f requirements.txt ]; then pip install -r requirements.txt; fi
+ - name: Lint with flake8
+ run: |
+ # stop the build if there are Python syntax errors or undefined names
+ flake8 . --count --select=E9,F63,F7,F82 --show-source --statistics
+ # exit-zero treats all errors as warnings. The GitHub editor is 127 chars wide
+ flake8 . --count --exit-zero --max-complexity=10 --max-line-length=127 --statistics
+ - name: Test with pytest
+ run: |
+ pytest

ciphey/mathsHelper.py

@@ -49,20 +49,23 @@ def gcd(a, b) -> int:
 
  @staticmethod
  def mod_inv(a: int, m: int) -> Optional[int]:
- """
- Returns the modular inverse of a mod m, or None if it does not exist.
-
- The modular inverse of a is the number a_inv that satisfies the equation
- a_inv * a mod m === 1 mod m
-
- Note: This is a naive implementation, and runtime may be improved in several ways.
- For instance by checking if m is prime to perform a different calculation,
- or by using the extended euclidean algorithm.
- """
- for i in range(1, m):
- if (m * i + 1) % a == 0:
- return (m * i + 1) // a
- return None
+ # Extended Euclidean Algorithm
+ old_r, r = a, m
+ old_s, s = 1, 0
+ old_t, t = 0, 1
+
+ while r != 0:
+ quotient = old_r // r
+ old_r, r = r, old_r - quotient * r
+ old_s, s = s, old_s - quotient * s
+ old_t, t = t, old_t - quotient * t
+
+ if old_r == 1:
+ # Ensure the result is positive
+ return old_s % m
+ else:
+ # Modular inverse does not exist
+ return None
 
  @staticmethod
  def percentage(part: float, whole: float) -> float: