laboratory-work-2-encryption

Implementation of secure transmission of messages by using the RSA algorithm and
fast exponentiation algorithm in modular arithmetic.

RSA algorithm

rsa_algorithm.py In the implementation of the algorithm, we used such libraries:

• Math - for calculations
• Secrets - for generation of 2048-bits prime numbers
• Sumpy - for generation of 2048-bits prime numbers
• Hashlib - for generation of hash of a messages

1. The algorithm starts by generating two 2048-bit prime numbers using the libraries.
2. Then we calculate the first part of the public key by multiplying the previously found prime numbers.
3. The next step is finding a small odd number whose gcd with (p-1)(q-1), where p and q are 1024-bit prime numbers, equals 1.
4. And the last step is the calculation of the private key, which is an integer, the reciprocal of a small number modulo (p-1)(q-1)

rsa_algorithm function returns a dictionary with all data needed for later encryption & decryption of messages.

Encryption & Decryption

For encryption and decryption, we used the algorithm provided in lecture 8.2 - block cipher
The main idea of this cipher is to calculate a new block by the formula: $$C = M^e modn$$
Decryption happens by this formula: $$M = C^d modn$$

In the encrypt function:

1. We find the maximum length of a block of symbols for the public key
2. Then we transform each symbol to a numeric value by the ord function, adding zeros to match the length of a block
3. Next, we divide the message into blocks of max length - numeric values to encrypt
4. The last step is the encryption of the numeric value we got from the formula

In the decrypt function:

1. We find the maximum length of a block of symbols for the public key
2. Next is decryption by the formula and filling it with zeros to match the length of a block
3. The last step is to loop through the message by breaking it into small blocks of max length
   and convert it to a symbol using the built-in function chr

User-server communication

In this part, we worked according to the socket.io library and instructions in Client & Server files.

• Client
  The core functions of the class are read_handler and write_handler.
  read_handler
  Client receives an encrypted message and a hash from the server, decrypts it, and if the hash value is the same prints it out; else, it shows the user that an error has occurred. write_handler
  The client is asked to write a message. If it does not consist of whitespaces only, the message gets encrypted, and the hash value is created to be sent to a server.

• Server
  The core functions of the class are start, handle_client, and broadcast.
  start
  In this function, the server begins to run, receives the keys from client(s), keeps track of connected users, and does all the manual connection job. handle client
  In this function, the server receives the message from a client(s), decrypts it, and compares the hash values as well. broadcast
  In this function, the server sends the message from a client(s), encrypts it, and creates the hash value.

Hash of messages

For the implementation of this checking, we used hashlib library.
Example:
When a user sends a message, he sends a hash of this message as well, generated in hash_message function. Later, when the server decrypts it, it generates a hash of the decrypted message and compares those hashes with check_message_integrity function.

Contributors

• Oksana Moskviak
• Anastasiia Yablunovska

The laboratory work was a collaborative effort between the two of us.
@ Created by CS UCU students, April 2025