A New Boundary of Minimum Private Key on Wiener Attack Against RSA Algorithm

Cryptography is divided into two types, namely symmetric cryptography and asymmetric cryptography. In symmetric cryptography, the key used in the encryption and decryption process is the same, while in asymmetric cryptography, the encryption and decryption processes have their keys. One of the most famous public key algorithms is the RSA algorithm, created by Rivest, Shamir, and Adleman in 1987. The strength of the RSA algorithm is based on the Integer Factorization Problem (IFP), in which when there is an integer, it will be challenging to determine the factors of that number. In its development, several attacks have been tried to find the vulnerabilities in RSA. One example of a successful attack is the attack by Wiener and Bunder & Tonien. This attack uses a continued fraction that exploits the vulnerability of using private values that are too small, which causes the need for a minimum private value boundary to overcome the vulnerability. From the research that the author has done, it is found by derivative function such that the minimum boundary of Wiener and Bunder & Tonien on private values has been successfully upgraded.