A secure, proactive and robust implementation of the RSA Signature Scheme which employs FDH
firstPrimes.py
Generate all prime numbers less than value t using the Sieve of Eratosthenes and store them in a file named FfirstPrimes.txt These are used later for generation of large random primes for RSA.
generatePrime.py
Generates a random n bit prime number. The gen_prime_2(n) method is called with n representing the number of bits desired.
Random number generation is done in 2 steps.
- Low Level Primality Test:
gen_prime_1(n)is called to randomly choose an odd value with minimum n bits. A low level primality test is applied by attempting division of the generated value with the first few hundred, pre-generated primes (see firstPrimes.py) - High Level Primality Test: As a probabilistic method of testing primality of the probable prime which passes the Low Level Primality test, Miller Rabin test is used. 20 iterations of the test are carried out by default.
fileOp.py
Contains functions to read and write data from and into files. All files are stored locally in a ".txt" format.
NOTE: All files will be written to a Directory named RSAfiles within the working directory. To change the location
where these files are saved, modify the following line and provide the location of the desired directory address: save_path = getcwd() + "\RSAfiles\\".
initRSAsignature.py
Initializes the various required values for generating RSA based signatures.
Generates random primes, encryption keys, decryption keys and RSA Modulus.
Values are stored in the same directory i.e. RSAfiles.
Calls the prime generation method described in generatePrime.py (default prime size = 1024 bits) to generate a prime pair and the key generation method described in keyGeneration.py to generate public & private keys.
keyGeneration.py
Generates the public & private keys using the RSA formulae.
Note: The public key is randomly generated instead of being a conventional value such as 65537
fdh.py
For signing of a file, the hash of the file has to be generated as it is subsequently signed using RSA. In this implementation, a modified version of SHA-256 hashing algorithm is used. The idea being to utilize the full domain of the message space in RSA. Since the default primes are 1024 bits in size, the modulus will be of 2048 bit size. Using plain SHA-256 under-utilizes the RSA capabilities to handle upto 2048 but input sizes.
For this, the file is hashed into a digest size of 2048 bits using this function utilizing repeated SHA-256 hashing.
signRSA.py
Generates a signature for a given input text file.
Takes a text file as input and generates its Full Domain Hash (FDH) and signs it using the RSA public key. The signature is saved to a a file Fsignature.txt
verifyRSA.py
Verifies a given signature of a file.
Takes a file to be tested and the publically available signature to verify the file. The file is hashed using the same FDH method and the public signature is raised to the private key value to regenerate the original hash. If the two hashes are the same, the authenticity of the file is verified.
Under construction: A proactivization mechanism to refresh shares