RustSA

A CLI for RSA implemented in Rust.

This an implementation of the RSA encryption algorithm for the command line written in rust. All of the mathematical algorithms, including the extended euclidean algorithm, the fast powering algorithm, and Miller-Rabin primality testing, have been coded from first principles using the 5 basic arithmetic operations (additons, subtraction, multiplication, division, and remainder). Uses rust-gmp crate to allow for abitrary integer precision, instead of limiting the program to 128 bit integers that are the default maximum in Rust.

Commands

The three basic operations this program has implemented are key creation, encrypting message, and decrypting cipher texts. To use them, refer to this table

Command	Usage	Description
new_key	./RustSA new_key key_size	Creates a new public/private key pair, with primes being key_size bits in size. key_size must be greater than 4.
encrypt	./RustSA encrypt message N e	Encrypts message, which is a number, using the public key (N, e), where N is the product of the secret primes and e is the public exponent.
decrypt	./RustSA encrypt message N d	Decrypts cipher, which is a number, using the private key (N, d), where N is the product of the secret primes and d is the private exponent.

Example

Create a public and private key using 16 bit primes.

$ ./RustSA new_key 16
Public Key = (2996203831, 2258472011)
Private Key = (2996203831, 1701586155)

Encrypt the message 31415 with a public key.

$ ./RustSA encrypt 31415 2996203831 2258472011
Encrypted cipher: 2698985146

Decrypt the ciphertext 2698985146 with a private key.

$ ./RustSA decrypt 2698985146 2996203831 1701586155
Decrypted message: 31415

Possible Extensions

• Implement built-in ASCII to integer encoding and decoding for easier message sharing.
• Implement the RSA Digtial Signature algorithm, mainly signing and verifying algorithms.
  • Also include reading/signing/verifying documents from the file system along with some hashing method.
• Optimize the existing algorithms for speed and make benchmarks for the program.