Implementation of RSA in Java using BigInteger Library. RSA is a public-key asymetric encryption method used for secure data transfers. This repository provides the implementation in java, as well as an analysis of algorithms' time complexities.

The program starts by generating two random prime numbers of 32 bits. (Note: The classic variables (p, q, e, etc.) are used in order to provide quick reference and better understanding for the reader.) After p and q are generated, they are multiplied in order to achieve 𝑁𝑁, which is part of both the public and private key pair. After that, we calculate ∅(𝑁) which is used in the calculations of both the variables e and d, that are used in public and private key pairs respectively. e is a number relatively prime to ∅(𝑁), while d is found as the modular multiplicative inverse of the pair (𝑒,∅(N)).

Find time complexity analysis here.

Java JDK 13 or newer. Older versions might also work.

An intuitive terminal program is available for testing the implementation by running the main() method of RSA.

----Public Keys are made available----
Bob says: Hello world, my public key is N=506843262446850739 and e=65537 
Alice says: Hello world, my public key is N=12647022965299532473 and e=65537

----Message from Alice to Bob----
What should Alice say:
Hello Bob!
Alice says: Hello Bob!
Charlie reads (encoded text):
�u��+>Q���a��;{v
Bob reads (decoded text): Hello Bob!


----Message from Bob to Alice----
What should Bob say:
Hello Alice
Bob says: Hello Alice
Charlie reads (encoded text):
�u��+>Q���a��;{vbD�Sd�V� ����5�)
Alice reads (decoded text): Hello Alice 

----Charlie started breaking RSA---- 
Time to find Bob's Decryption key: 29 sec 
Charlie found decryption key of Bob: 112687690016002265 
Charlie decrypted message send to Bob: Hello Bob! 
Time to find Alice's Decryption key: 26 sec 
Charlie found decryption key of Alice: 12063658592921248169 
Charlie decrypted message send to Alice: Hello Alice

Contributors names and contact info:

Erges Mema
@MemaErges

• 0.1
  • Initial Release

Pseudocode references from:

Dasgupta, S., Papadimitriou, C. H., & Vazirani, U. V. (2006). Algorithms. Boston: McGraw-Hill Higher Education.