Abstract
The aim of this paper is to present a new methodology to find the private key of RSA. A new initial value which is generated from a new equation is selected to speed up the process. In fact, after this value is found, brute force attack is chosen to discover the private key. In addition, for a proposed equation, the multiplier of Euler totient function to find both of the public key and the private key is assigned as 1. Then, it implies that an equation that estimates a new initial value is suitable for the small multiplier. The experimental results show that if all prime factors of the modulus are assigned larger than 3 and the multiplier is 1, the distance between an initial value and the private key is decreased about 66%. On the other hand, the distance is decreased less than 1% when the multiplier is larger than 66. Therefore, to avoid attacking by using the proposed method, the multiplier which is larger than 66 should be chosen. Furthermore, it is shown that if the public key equals 3, the multiplier always equals 2.
Highlights
Nowadays, communication which is sent through opening a network such as internet and the machine is very popular because data is rapidly transmitted
The experiment is divided into 4 tables: Table 1 is the considering f from n =
174279334060020221413, which is the modulus from examples 1 to 3; Table 2 is to consider n =
Summary
Communication which is sent through opening a network such as internet and the machine is very popular because data is rapidly transmitted. Opening a network is known as unsecure channel. With this problem, security and confidentiality of information becomes exceedingly important. Cryptography [1], which is one of security methods, is a technique to protect information by converting original message or plaintext as the unreadable message, or ciphertext. Ciphertext will be transmitted via the channel instead of plaintext. That means intruders cannot understand data which is trapped on the network. After ciphertext is arrived to receivers, they can use the decryption process to recover original plaintext
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