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High-Speed and Secure PRNG for Cryptographic Applications I. J. Computer Network and Information Security, 2020, 3, 1-10 Published Online June 2020 in MECS (http://www.mecs-press.org/) DOI: 10.5815/ijcnis.2020.03.01 High-Speed and Secure PRNG for Cryptographic Applications Zhengbing Hu School of Educational Information Technology, Central China Normal University, Wuhan, China E-mail: [email protected] Sergiy Gnatyuk, Tetiana Okhrimenko Faculty of Cybersecurity, Computer and Software Engineering, National Aviation University, Kyiv, Ukraine E-mail: [email protected], [email protected] Sakhybay Tynymbayev Almaty University of Power Engineering and Telecommunication, Almaty, Kazakhstan E-mail: [email protected] Maksim Iavich Scientific Cyber Security Association, Caucasus University, Tbilisi, Georgia E-mail: [email protected] Received: 24 March 2020; Accepted: 30 March 2020; Published: 08 June 2020 Abstract—Due to the fundamentally different approach underlying quantum cryptography (QC), it has not only I. INTRODUCTION become competitive, but also has significant advantages With the rapid development of information and over traditional cryptography methods. Such significant communication technologies (ICT), most of the world is advantage as theoretical and informational stability is faced with the problem of supporting cybersecurity achieved through the use of unique quantum particles and the inviolability of quantum physics postulates, in addition it (information security). On the one hand, new powerful ICT does not depend on the intruder computational capabilities. contribute to the cybersecurity development, and on the other, they create new threats. For the past few years, However, even with such impressive reliability results, QC number of reported cybersecurity incidents of confidential methods have some disadvantages. For instance, such information leaks increases every month. promising trend as quantum secure direct communication – Today, the reliability and security of traditional eliminates the problem of key distribution, since it allows to cryptographic methods mostly depends on the attacker's transmit information by open channel without encrypting it. computational power and the ability to solve a particular However, in these protocols, each bit is confidential and class of mathematical problems in polynomial time. But should not be compromised, therefore, the requirements for since the advent of such technologies as GRID computing, protocol stability are increasing and additional security supercomputer and quantum computer, which perform methods are needed. For a whole class of methods to ensure qutrit QC protocols stability, reliable trit generation method complex calculations in minutes – companies, states and is required. In this paper authors have developed and studied scientists have to look for new alternatives to existing security and privacy methods. trit generation method and software tool TriGen v.2.0 PRNG. There are two major classes of methods to replace Developed PRNG is important for various practical traditional cryptography – the first one is quantum cryptographic applications (for example, trit QC systems, cryptography (QC) [1], based on the fundamental IoT and Blockchain technologies). Future research can be difference, the use of the unique capabilities of quantum related with developing fully functional version of testing mechanics; the second is post-quantum cryptography (PQC) technique and software tool. [2], based on the more complicated mathematical problems (for example, lattice-based cryptosystems, syndrome-based Index Terms—Quantum cryptography, information cryptosystems and others). security, pseudorandom numbers (sequences), PRNG, evaluation, trit, quantum deterministic protocol, Unlike most classical cryptosystems, whose security is evaluation, trit, NIST STS. based on unproven mathematical assumptions, the security Copyright © 2020 MECS I.J. Computer Network and Information Security, 2020, 3, 1-10 2 High-Speed and Secure PRNG for Cryptographic Applications of QC systems relies on fundamental laws of quantum operations in finite fields (for example, Genoa generators, mechanics, which, with proper implementation makes it Golman, and others) [20, 21, 24, 27]. fundamentally impossible to intercept information and However, all PRNG developed today are binary breach its confidentiality. One of the most advanced QC sequences oriented, so developing a trit PRNG is an technologies, along with quantum key distribution (QKD), urgent scientific task. In view of this, the authors is quantum secure direct communication (QSDC), which previously proposed a new method for generating trit allows to transmit information through an open channel PRN in [12]. To verify this method appropriate software directly (without encryption, so the problem of key needs to be developed. In view of this, the purpose of the distribution is eliminated) [3]. Today, a large number of article is to carry out detailed experimental study of the QSDC methods are proposed [4, 6, 8] based on various proposed trit PRNG for its effectiveness evaluation in quantum technologies and can be used both for secure various cryptographic applications. information transmission (using qubits or qudits) and for the cryptographic keys distribution [22, 25]. However, in deterministic QSDC protocols, every bit is confidential and III. THEORETICAL BASIS OF THE PROPOSED METHOD AND should not be compromised, so the requirements for its PRNG CONSTRUCTION stability are much higher than for QKD protocols. The The trit generation method includes the following main deterministic QSDC protocols disadvantage is that they steps: 1) initialization of the internal state vector; 2) have only asymptotic resistance (security) to non-coherent directly PRN generation. Consider shortly each step: attacks and, of course, require security enhancement (amplification) methods. Step 1. Initialization of the internal state vector U is performed. Based on initialization vector VI and secret II. RELATED WORKS AND PROBLEM STATEMENT key K , UV p , VI Ve , KV n , let’s consider : In [6], the methods of enhancing the QSDC protocols U xxxxxxyyyykkkk12345612341234,,,,,,,,,,,,,, security are described, and the authors proposed and where xi , y j , k j are parts of internal state vector U theoretically substantiated method of ensuring QSDC protocols stability. The method developed in [6] requires ( xVil , yVjl , kVjl , i 1,6 , j 1,4 ); the generation of ternary (trit) pseudorandom number VI VI,,,,,,,,,, VI VI VI VI VI VI VI VI VI where generator (PRNG) [23], thus increasing the information 12345678910 capacity of transmission protocols. The analysis revealed VIo are initialization vector parts VI ( VIol V , a sufficient number of existing PRNG that can be used o1,10 ); KKKKK 1,,, 2 3 4 , where Kw are secret for various applications [4, 5, 7-11, 14, 16]. The ISO/IEC 18031 standard [5], which sets out key parts K ( KVwl , w 1,4 ). conceptual models, terminology and requirements relating Then, the internal vector state U is initialized this way: to the structural elements and properties of systems used xii VI , yjj VI6 , kKjj , i 1,6 , j 1,4 . to generate random bits in cryptographic applications, defines two types of PRNG: non-deterministic (random bit generation mechanism that uses an entropy source to Step 2. Progressive generation of the output sequence generate a random bit stream) and deterministic (bit is performed MMM 1,..., b , MV m , Mq are parts generation mechanism that uses deterministic of the generated sequence M , MV , . mechanisms such as cryptographic algorithms on an qnqb1, entropy source to generate a random bit stream). PRNG can be classified according to different Sub step 2.1. To generate part of the output sequence distribution principles [4], but the most complete Mq r -times the following calculations are done: classification is presented in [7]. According to this 2.1.1. New values of vectors x1, x2, x3; classification, PRNG are divided into crypto-resistant and 2.1.2. New values of vectors k , k , y , y ; non-crypto-resistant. Crypto-resistant include: based on 1 2 1 2 2.1.3. New vectors x , x , x ; streaming ciphers (e.g., Dragon-128, SEAL, RC4, RC5, 4 5 6 2.1.4. New values of vectors k , k , y , y . RC6, Grain, Yamb, Phelix), based on block ciphers (for 3 4 3 4 example, GOST 28147-89, AES, ANSI X9.17, DES), Sub step 2.2. Using the vector concatenation, the initial based on one-way functions (for example, BBS, RSA, Dual_EC_DRBG (elliptic curves), GPSSD (linear codes), sequence is calculated Mq : Mq y1| y 2 | y 3 | y 4 . etc.) and non-crypto-resistant: based on elementary Based on this method TriGen v.2.0 PRNG was recursors (for example, linear congruent, polynomial developed. Detail algorithm of this PRNG realization is congruent, additive Fibonacci, additive Fibonacci delayed presented on Fig. 1. and multiplicative Fibonacci delayed PRNG), based on Copyright © 2020 MECS I.J. Computer Network and Information Security, 2020, 3, 1-10 High-Speed and Secure PRNG for Cryptographic Applications 3 TriGen v.2.0 Input: initialization vector VI , secret key K , VI V240 , KV 96 , parameter b . Output: output sequence MMM 1,..., b , MV 96b , MVq 96 , qb1, . Fig.1. Pseudocode of TriGen v.2.0 PRNG A. Testing PRN by the NIST STS method IV. EXPERIMENTAL STUDY OF THE TRIT PRNG Initially, the proposed method of trit PRN generating The purpose of the experiments is to investigate the was decided to test by the NIST STS method [18] in effectiveness of the developed PRNG in comparison with order to check whether
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