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Improvement and Implementation of Public Key Encryption Algorithm RSA

Author: SunWei
Tutor: XuChao
School: Anhui University
Course: Electronics and Communication Engineering
Keywords: RSA enciphering algorithm Three prime factors combinatorial algorithm Chinese remainder theorem The efficiency of algorithm
CLC: TN918.4
Type: Master's thesis
Year: 2014
Downloads: 4
Quote: 0
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Abstract


With the rapid development of network information technology, security problems are becoming increasingly prominent. The theoretical basis of the network information security is cryptography, among which RSA encryption algorithm is the most widely used public key encryption algorithm, which can be used in both the data encryption and digital signature. However, with the continuous improvement of factorization technique, that is, the improvement of the ability to decompose large numbers into factors, the security of the RSA encryption algorithm is threatened. In order to guarantee the security of the RSA encryption algorithm, the bits of keys have been increased by people. For example, in December2009, researchers completed a768RSA algorithm (i.e.,232-digit number RSA-768key) factorization. Meanwhile, researchers claim that the commonly used1024-bits key is expected to be defeated in10years and the1024-bits key needs to be transited into2048-bits key in the coming few years.Although the increase in key bits ensures its security, it led to the decrease in the efficiency of the algorithm operation caused by the difficulties in selecting keys and the more complex process of encryption and decryption, greatly limiting its scope of application. In order to improve the efficiency of RSA encryption and decryption algorithms, this paper introduces and analyzes the RSA encryption algorithm, and improves the RSA encryption algorithm. Specific scheme to improve RSA algorithm is as follows:1) It introduces the traditional RSA encryption algorithm. As for the problems brought by the increase of bits the key, the RSA encryption algorithm of the three prime factors is adopted, increasing the number of prime factors but reducing the number of bits. Consequently, the difficulty of selecting large prime factor is lessened and the efficiency is thus improved.2) In the process of encryption algorithms, the commonly used encryption algorithms are introduced:traditional BR algorithms algorithm,2k hex decimal arithmetic algorithms and extensions. The advantages and disadvantages of these algorithms are analyzed. The last step is the combination of the SMM algorithm and the extended2k decimal arithmetic algorithms. With their merits, a new combination algorithm can be invented.3) In the decryption algorithm, a decryption algorithm based on the Chinese remainder theorem is used. Compared with the previous algorithm, the difference in this article lies in the fact that it uses three prime factors and process of decryption algorithm under the premise of three prime factors is given. The modulo operation of decryption algorithm is transformed into modulo operation with the three smaller prime factors, reducing the amount of calculation in modulo arithmetic.4) Finally, the design and implementation of RSA encryption and decryption software is completed. The software can perform encryption and decryption with different algorithms and calculate the time required to complete the encryption and decryption process. The improved algorithm is compared with the traditional algorithm in the aspect of efficiency and the efficiency of the improved algorithm has been improved to some extent.

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CLC: > Industrial Technology > Radio electronics, telecommunications technology > Communicate > Confidentiality of communications and communications security > Password encryption and decryption
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