Document Type : Original Manuscript
Authors
1
Faculty of Marine Engineering, Khorramshahr University of Marine Science and Technology, Khorramshahr, Iran.
2
Department of Computer Engineering, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
3
Department of Computer Engineering, Karoon Institute of Higher Education, Ahvaz, Iran.
Abstract
Abstract
With the growth of technology, the need for data and information security over communication channels is necessary. One of the most critical issues is establishing information security in marine communications. The RSA encryption algorithm is one of the most popular and most asymmetric algorithms used for secure data transfer. In the RSA encryption system, due to the very long key length, the encryption and decryption step speeds decrease, so it needs to improve its speed. One of the improved ways of RSA is RPrime RSA, which includes the highest decryption speed of RSA. In this paper, the encryption and decryption speed of the RPrime RSA algorithm is improved using an efficient residual number system. The result of implementation and comparison shows that the proposed method has an average of % 22% and % 36% improvement in the encryption and decryption speed over the RPrime RSA algorithm.
1. INTRODUCTION
Encryption algorithms are divided into two categories: symmetric (Beitabdollah et al., 2016) and public key (asymmetric) (Rivest et al., 1978). The RSA encryption system is one of the public key encryption algorithms. This algorithm was designed by Rivest, Shamir, and Edelman in 1978. This encryption system has attracted the attention of researchers in recent years as one of the most prominent asymmetric encryption methods due to its capabilities, such as high security and simplicity of use. Currently, prime factors of 1024 and 2048 bits are considered for complexity with a high workload. The main security parameter in RSA encryption is the length of the key; the longer it is, the more secure the communication becomes. However, increasing the length of the key can greatly reduce the speed of the encryption and decryption processes. In order to use these algorithms in maritime environments, such as communications between ships and also communications between ships and ground stations that require secure transmission of information, it is necessary to improve this algorithm in terms of encryption and decryption speed.
2. MATERIALS AND METHODS
The RPrime RSA method was introduced by Caesar in 2003 (Paixao Filho, 2003). The idea of this method is to combine two RSA methods, namely Rebalanced RSA and MultiPrime RSA, to further improve the decryption speed. The general idea of this scheme is to use the Rebalanced RSA key generation algorithm (modified for t components) together with the MultiPrime RSA decryption algorithm.
In the proposed method, first, an efficient residue number system is presented, and an efficient reverse converter is designed for the proposed modulus set. Then, the RPrime RSA algorithm is improved using the proposed residue number system. The residue number system increases the speed of computational operations by operating on a small parallel channel.
3. RESULTS
In this section, the proposed modulo set and the designed reverse converter are evaluated and compared with the works in the literature. Then, the RNS version of the RPrime RSA algorithm is evaluated with the RPrime RSA algorithm.
The results of the ASIC implementation for n =5, 15, 25, 35 are shown in Table 1. In this table, the performance of the proposed reverse converter is compared with the reverse converters introduced in (Mohan and Premkumar, 2007; Sousa et. al., 2012; Patronik and piestrak, 2017). According to the results, the proposed converter improves the hardware delay (AT) compared to the converters in the literature. Figure 1) shows the improvement in hardware (A), delay (T), and hardware-delay (AT) metrics compared to the schemes introduced in the studies (Mohan and Premkumar, 2007; Sousa et al., 2012; Patronik and piestrak, 2017).
4. CONCLUSION
In this paper, a new architecture is proposed to improve the speed of the RPrime RSA cryptography algorithm based on the residue number system. In order to increase the efficiency of the residue number system in the RPrime RSA algorithm, a balanced and well-formed moduli set and its efficient reverse converter with a two-level structure based on the New CRT-I algorithm were designed and implemented. The implementation results show that the proposed design has improved the encryption and decryption speed compared to the original RPrime RSA algorithm.
REFERENCES
Beitabdollah, M., Esmaeildoust M. and Kaabi, A., 2016. Performance Evaluation of Symmetric Key Cryptography Algorithms. Journal of Marine Sceince and technology, 19(1), pp. 404-455. https://doi.org/10.22113/jmst.2016.40455.
Mohan, P.A. and Premkumar, A.B., 2007. RNS-to-Binary Converters for Two Four-Moduli Sets $\{2^{n}-1, 2^{n}, 2^{n}+ 1, 2^{{n}+ 1}-1\} $ and $\{2^{n}-1, 2^{n}, 2^{n}+ 1, 2^{{n}+ 1}+ 1\} $. IEEE Transactions on Circuits and Systems I: Regular Papers, 54(6), pp.1245-1254. https://doi.org/10.1109/TCSI.2007.895515
Paixao Filho, C.A.M., 2003. DLG: An efficient variant of the RSA cryptosystem. Eprint Archive.
Patronik, P. and Piestrak, S.J., 2017. Design of Reverse Converters for a New Flexible RNS Five-Moduli Set {2 k, 2 n-1, 2 n+ 1, 2 n+ 1-1, 2 n-1-1}(n Even). Circuits, Systems, and Signal Processing, 36(11), pp.4593-4614. https://doi.org/10.1007/s00034-017-0530-9.
Rivest, R.L., Shamir, A. and Adleman, L., 1978. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, 21, pp. 120-126. https://doi.org/10.1145/359340.359342.
Sousa, L., Antão, S. and Chaves, R., 2012. On the Design of RNS Reverse Converters for the Four-Moduli Set ${\bf\{2^{\mmb n}+ 1, 2^{\mmb n}-1, 2^{\mmb n}, 2^{{\mmb n}+ 1}+ 1\}} $. IEEE transactions on very large scale integration (VLSI) systems, 21(10), pp.1945-1949. 10.1109/TVLSI.2012.2219564
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