Feat/shor classical implementation

[khushipy]

This PR adds a classical implementation of Shor’s Algorithm to the cryptography module. The algorithm factors a given composite number N by:

• Checking for trivial factors using GCD
• Finding the order of a random integer a modulo N
• Using the order to derive factors of N
  Changes:
  Added shor_algorithm.py in cryptography directory
  Implemented modular exponentiation and order-finding methods
  Added tests in cryptography
  Issue Reference: Request to Implement Shor Algorithm #12318

[algorithms-keeper]

Click here to look at the relevant links ⬇️

🔗 Relevant Links

Repository:

• Contributing guidelines
• Project Euler solution guidelines

Python:

• Formatted string literals (f-strings)
• Type hints
• doctest
• unittest
• pytest

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[algorithms-keeper]

Please provide descriptive name for the parameter: n

[algorithms-keeper]

Please provide descriptive name for the parameter: a

Please provide descriptive name for the parameter: b

Please provide descriptive name for the parameter: m

[algorithms-keeper]

Please provide descriptive name for the parameter: n

[dcq01]

Hi! I'm a grad student working on a research project about using large language models to automate code review. Based on your commit c568a09 and the changes in cryptography/shor_algorithm.py, my tool generated this comment:

1. In the shor_classical function, ensure that n is greater than 2 before the random.randrange(2, n - 1) call, or handle the case where n is 2 or less appropriately.
2. In the modexp function, add a check to ensure that m is greater than zero before proceeding with the calculations.
3. In the is_prime function, consider raising an exception or returning a specific error message for negative numbers or zero.
4. In the shor_classical function, check if factor1 and factor2 are valid factors (greater than 1 and less than n) to ensure meaningful results.
5. Consider raising exceptions instead of returning a string message for failure cases in the shor_classical function. This would allow calling code to handle errors more flexibly and facilitate logging or other error-handling strategies in the future.
6. Ensure that the environment where this code will run supports the syntax str | tuple[int, int]. If not, it may lead to a type error.
7. Ensure that the codebase is consistent with type hinting styles. If the rest of the code uses Union, it might be better to stick with that for consistency.
8. Consider adding logging statements to capture the input values, the results of primality checks, and the factors found (if any) in the shor_classical function.
9. The variable names factor1 and factor2 could be more descriptive. Consider renaming them to first_factor and second_factor to clarify their purpose in the context of the function.
10. The variable g is used to store the greatest common divisor, but the name g does not convey this meaning clearly. A more descriptive name like gcd_value or greatest_common_divisor would enhance readability.
11. The variable r is used as a counter in the while loop, but it is not immediately clear what it represents. A name like order or exponent_order could provide better context.
12. The variable x is used to store the result of the modular exponentiation, but its purpose is not clear from the name alone. Consider renaming it to mod_exp_result or exponentiation_result for clarity.
13. Update the docstring of shor_classical to replace N with n in the examples for consistency.
14. Ensure that any other documentation or comments referring to N are also updated to n to avoid confusion.

As part of my research, I'm trying to understand how useful these comments are in real-world development. If you have a moment, I'd be super grateful if you could quickly reply to these two yes/no questions:

1. Does this comment provide suggestions from a dimension you hadn’t considered?
2. 2. Do you find this comment helpful?

Thanks a lot for your time and feedback! And sorry again if this message is a bother.