Multi prime numbers principle to expand implementation of CRT method on RSA algorithm

Abstract

One of the uses of the Chinese Remainder Theorem (CRT) is to shorten the time in the RSA Cryptosystem decryption process. However, in applying a combination of the CRT method and the RSA Algorithm with Python programming modules, recursion errors often occurred when determining the inverse modulus to establish the private key. The error was caused by limitation iterations of the related algorithm. Some Python library needs more iteration processes to calculate the inverse modulus for larger key size. This is a pure computational problem. The standard RSA algorithm uses two prime numbers to generate their key pairs. The multi-prime RSA modification based on more than two prime numbers can be applied to solve the problem. A modified RSA was applied in Python programming that generates keys based on 2, 4, 8, 16, and 32 prime numbers. Regarding on our experiments, the combination of the CRT method and RSA algorithm based on four prime numbers can be applied without recursion error up to a key length of 6280 bits, with eight primes up to 12,560 bits, with sixteen primes up to 25,120 bits, and with thirty-two primes up to 50,240 bits. Implementation of more multi-prime numbers can expand to combine the CRT method and RSA Algorithm for longer key sizes by approximation relation y = 1567,8x + 63,333, which y is the key size and x is the number of primes numbers. The method also can increase key generation and decryption rate significantly.