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

Hermawan, Nanang Triagung Edi; Winarko, Edi; Ashari, Ahmad

doi:10.1063/5.0041856

Cited by 4 publications

(3 citation statements)

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“…Proses perumusan algoritma RSA didasarkan pada Teorema Euler, setelah itu diperoleh kunci bersama dan kunci rahasia yang saling berkaitan. Saat proses penyandian pesan teks, ukuran kunci rahasia lebih besar dibandingkan dengan kunci umum, sehingga membutuhkan waktu yang lebih lama jika di hitung secara manual [9]. Hal ini digunakan untuk mencegah berbagai percobaan dalam memecahkan teks rahasia, semakin besar bilangan prima yang digunakan sebagai kunci, semakin susah ditemukan angka besar sebagai faktornya [1].…”

Section: Pendahuluanunclassified

Implementation of Cryptography Using the RSA (Rivest-Shamir-Adleman) Algorithm in Encoding Text Messages and Documents

Sari,

Resmawan,

Yahya

et al. 2024

JOSTECH

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Cryptography can be used in prevent data, one of the preventive measures is by encoding messages. Cryptography is the study of encoding messages or ways of data protection. In encoding the content of messages, there is an algorithm conventionally used nowadays, the RSA (Rivest-Shamir-Adleman) algorithm. The RSA algorithm is a method that has two different keys for each encryption and decryption process but is still interrelated to maintain security in processing the data. In finding the key, the RSA algorithm utilizes the rule of prime number. The larger the prime number used as a key, the harder it is to find a large number as a factor. This research describes the process of encrypting text messages, the content of documents using the RSA algorithm, and the key generation process. Those processes are done by converting plaintext into ciphertext using ASCII code, which is 256 long, and using PKCS (Public Key Cryptography Standards) is the encryption process on the RSA algorithm. This study uses Pyhton programming language to implement the RSA algorithm on text messages and documents. As a recommendation to the subsequent studies, it is proper to use algorithms or other programming languages to secure messages.

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Section: Pendahuluanunclassified

Implementation of Cryptography Using the RSA (Rivest-Shamir-Adleman) Algorithm in Encoding Text Messages and Documents

Sari,

Resmawan,

Yahya

et al. 2024

JOSTECH

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“…Keamanan pada algoritme RSA terletak pada bilangan prima yang dibangkitkan pada proses pembangkitan kunci. Bilangan prima yang dibangkitkan diharapkan memiliki nilai yang besar sehingga algoritme tidak mudah ditembus [3]. Sebaliknya apabila bilangan prima yang digunakan kecil maka semakin kecil pula keamanan dan mengakibatkan algoritme ini condong untuk mudah ditembus [4] [5].…”

Section: Pendahuluanunclassified

Analisis dan Implementasi Algoritma Asimetris Dual Modulus RSA (DM-RSA) pada Aplikasi Chat

Aminudin

Nuryasin

2021

RESTI

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The RSA algorithm is one of the cryptographic algorithms with an asymmetric model where the algorithm has two keys, namely the public key and the private key. However, as time goes on, these algorithms are increasingly exposed to security holes and make this algorithm vulnerable to being hacked by people who do not have authority. The vulnerability stems from the algorithm's public keys (e and n). The strength of the RSA algorithm is based on the difficulty of factoring two prime numbers that are generated during the key generation process, if these values can be known using certain methods, the public key and private key values will be found. Therefore, there are many studies that improvise the RSA algorithm, one of which is the Dual Modulus RSA (DM-RSA) algorithm. The algorithm uses four prime numbers which produce 2 modulus and 4 keys (2 public keys and 2 private keys). From the results of the Kraitchik factorization test, it was found that the DM-RSA algorithm was proven to be more resistant up to 2 times or even more than the standard RSA algorithm. This is evidenced by the fact that the value of n is 24 bits, the RSA algorithm can last up to 63204 ms (1 minute 22 seconds) while the Dual Modulus RSA algorithm lasts up to 248494123 ms (142 minutes 47 seconds).

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“…The modified RSA algorithms usually use more than two prime numbers than standard RSA that uses two prime numbers [36]. On the other side, the CRT method is used to shorten the decryption exponent bit size by hiding incompatible systems to have a better speed in decryption processing [37].…”

Section: Introductionmentioning

confidence: 99%

Eight Prime Numbers of Modified RSA Algorithm Method for More Secure Single Board Computer Implementation

Hermawan¹,

Winarko²,

Ashari³

2021

International Journal on Advanced Science, Engineering and Information Technology

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RSA is the most popular public-key cryptography. The main strength of the algorithm is based on the difficulty of factoring in a large integer number. RSA has also been applied in a system with limited resource environments like single-board computers (SBC). To ensure data security, a recommendation to use a key size longer than 2048 bits generates challenges for implementing RSA in the SBC. This research proposes an EPNR (Eight Prime Numbers of Modified RSA) method, a modified double RSA based on eight prime numbers combined with the CRT method, to speed up the random key generation and decryption mechanism. The method is implemented in a Raspberry Pi 4 Model B+. The running time and security performances of the EPNR were analyzed and compared to the other models. Compared to the others model based on the standard RSA scheme, the proposed model is faster 21.78 times in a random key generation, 9.03 times in encryption and decryption processing. The EPNR has resistance to Wiener, statistical, and factorization attacks (GNFS and Fermat). Using standard RSA in the second encryption mechanism, the GNFS is not yet effective for attacking the proposed model. The modified Fermat Factorization algorithm is more difficult and needed more extra times for factoring a large composite number into eight prime numbers correctly. The method will be useful for implementing certificates authentication and distribution of the secret key. It is very suitable to enhance more secure RSA implementation in an SBC environment.

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

Cited by 4 publications

References 1 publication

Implementation of Cryptography Using the RSA (Rivest-Shamir-Adleman) Algorithm in Encoding Text Messages and Documents

Implementation of Cryptography Using the RSA (Rivest-Shamir-Adleman) Algorithm in Encoding Text Messages and Documents

Analisis dan Implementasi Algoritma Asimetris Dual Modulus RSA (DM-RSA) pada Aplikasi Chat

Eight Prime Numbers of Modified RSA Algorithm Method for More Secure Single Board Computer Implementation

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