Cryptography

The practical cryptographical algorithms and tools.

List of Content:

• Required Python packages.
• Implementing RSA Cryptosystem.

Required Python packages:

1. sympy

Implementing RSA Cryptosystem. ← In Progress...

Process...:

1. Started implementing RSA.
2. Decided that I want to program an algorithm that will produce prime numbers up to n for me.
   1. I found Miller-Rabin test, which is not for generating primes but for testing a given number if it's a prime.
      1. Comment: Using a number testing algorithm to generate a list of primes gave me a proper headache. I need to learn to research more before jumping into implementing.
   2. I searched for effective prime generation algorithms and "Sieve of Eratosthenes" came up.
      1. Comment: Still I did not use as much time as I would like to ensure that I am implementing the algorithm correctly.
3. I used the primes that I generated in file Sieve_of_Eratosthenes. Since all primes are coprime to each other I can now pick the greates two and get p * q.
4. Now I can actually implement the RSA algorithm!
   1. Next → Make it handle encryption and decryption of numbers.
   2. Extend it to handle characters.

Extra for RSA:

• I implement my own gcd instead of using an library.

Coming next:

• Implement the Miller-Rabin test, and use it to check if a large number is a prime.
• Algorithms for Discrete Logarithm calculation.
• Digital Signature protocols.