The New Equation for RSA's Decryption Process Appropriate with High Private Key Exponent

RSA is the best well - known public key cryptography using a pair of keys for encryption and decryption process. Usually, the private key is generated higher than public key to avoid attacking by third parties easily. However, with the high private key, it affects to finish decryption process slowly. In this paper, the new equation for RSA's decryption process is proposed to speed up the computation time. In fact, the key is that the modular inverse of ciphertext is chosen instead of the ciphertext for the computation with the new exponent. In addition, the new exponent is computed from the relation between the private key and euler value. Furthermore, the proposed method is the better choice when the high private key is chosen because the new exponent becomes a small value. The experimental results show that the proposed method can finish RSA's decryption process very fast whenever the private key is high especially when it is very close too euler value. On the other hand, if the private key is a small value, the process must take very high computation cost. However, after the proposed method is presented, it implies that the private key should not be assigned close to euler value because it will become the easy way for the third parties to recover original plaintext without knowing the private key.