A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation

Moysis, Lazaros; Тутуева, Александра; Volos, Christos; Butusov, Denis N.; Muñoz‐Pacheco, Jesús M.; Nistazakis, Hector E.

doi:10.3390/sym12050829

Cited by 34 publications

(24 citation statements)

References 38 publications

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“…e test results show that the PRNG designed in this paper has passed the sp800-22 randomness test, and the test index value is equivalent to that of the literature [18,19,22,23].…”

Section: Discussionmentioning

confidence: 61%

“…In the field of cryptography, the research of pseudorandom number generator based on chaotic system mainly focuses on the following aspects: proposing new chaotic system and designing controller to realize chaotic synchronization [18] and improving the existing chaotic system to enhance its complexity and make it have greater Lyapunov [19,20]. Some mathematical methods are used to improve the random performance of pseudorandom number generator [21], the software and hardware implementation of pseudorandom number generator [22], and the encryption scheme and cryptosystem based on chaotic pseudorandom number generator [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

Zang

Yuan

Wei

2021

Mathematical Problems in Engineering

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This paper proposes three types of one-dimensional piecewise chaotic maps and two types of symmetrical piecewise chaotic maps and presents five theorems. Furthermore, some examples that satisfy the theorems are constructed, and an analysis and model of the dynamic properties are discussed. The construction methods proposed in this paper have a certain generality and provide a theoretical basis for constructing a new discrete chaotic system. In addition, this paper designs a pseudorandom number generator based on piecewise chaotic map and studies its application in cryptography. Performance evaluation shows that the generator can generate high quality random sequences efficiently.

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“…e test results show that the PRNG designed in this paper has passed the sp800-22 randomness test, and the test index value is equivalent to that of the literature [18,19,22,23].…”

Section: Discussionmentioning

confidence: 61%

Section: Introductionmentioning

confidence: 99%

Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

Zang

Yuan

Wei

2021

Mathematical Problems in Engineering

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“…λ indicates Lyapunov value and if this value is positive then the system is chaotic. Furthermore, bigger λ describes much more complicated behavior in the system, hence better performance of the chaotic behavior (Moysis et al, 2020). Lyapunov analyses for all chaotic maps are shown in Figure 2.…”

Section: Lyapunov Analysismentioning

confidence: 99%

“…Zhou et al (2012); Tur and Ogras (2021); for Steganographic systems in Ogras (2019), Kar et al (2018), Bilal et al (2014), Battikh et al (2014), and Saeed (2013). There are also some important studies using chaotic systems as secret key or bit generators in cryptography (Addabbo et al, 2009;Alhadawi et al, 2019;Moysis et al, 2020;Oğraş & Mustafa, 2017). All scientific studies here show that the concept of chaos can be used effectively in data security as an alternative to modern digital encryption techniques.…”

Section: Introductionmentioning

confidence: 99%

An efficient color image encryption scheme based on a matrix scrambling method and a new hybrid chaotic map

Oğraş

2021

Cogent Engineering

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In this paper, an efficient chaos-based image encryption scheme for color images is proposed. This paper includes a strong displacement structure through a specified matrix scrambling method for pixel positions and a new hybrid chaotic map as a key generator for encryption. Chaotic Logistic map is used to generate binary bitstream for controlling diffusion process. The designed map exhibits superior performance in terms of key space range, complexity and chaotic substantiality that enhances security of the whole system. NPCR, UACI, MSE and PSNR values, which are frequently used in performance and security analysis in the field of image encryption, are at a satisfactory level and all parameters have successfully met the necessary conditions. For instance, in a good image encryption algorithm, ideal values of NPCR and UACI parameters should be 99.60% and 33.46%, respectively. The average results obtained in this study are very close to their ideal values as 99.6046 and 33.4733 for NPCR and UACI, respectively. According to a scientific study presented in the similar field, MSE value should be greater than 9,555; PSNR value must be less than 8.3875. In this study, average MSE and PSNR values calculated for six different test images are 10,315 and 7.9961, respectively. Some important analysis results have been compared to that of well-known Advanced Encryption Standard (AES) algorithm and a similar study presented in this field. Theoretical analysis and experimental results confirm that the proposed algorithm has great security and effectively encrypts and decrypts the color images with different sizes as well.

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“…A modified logistic map was utilized to generate PRNG in two phases, including initial pseudorandom sequence and normal pseudo-random sequence using the value obtained in the previous phase (Wang and Cheng 2019). Another modified logistic map was successfully applied to generate random bit sequences by performing a comparison between maps, XOR, and bit reversal (Moysis et al 2020b). An original logistic map was coupled with a piecewise map to implement a chaotic pseudo-random number generator (Sahari and Boukemara 2018).…”

Section: Introductionmentioning

confidence: 99%

Designing a Pseudo-Random Bit Generator Using Generalized Cascade Fractal Function

Agarwal¹

2021

Chaos Theory and Applications

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A cascade function is designed by combining two seed maps that resultantly has more parameters, high complexity, randomness, and more unpredictable behavior. In the paper, a cascade fractal function, i.e. cascade-PLMS is proposed by considering the phoenix and lambda fractal functions. The constructed cascade-PLMS exhibits the required fractal features such as fractional dimension, self-similar structure, and covering entire phase space by the data sequence in addition to the chaotic properties. Due to the chaotic behavior, the proposed function is utilized to generate a pseudo-random number sequence in both integer and binary format. This is the result of an extreme scalability feature of a fractal function that can be implemented on a large scale. A sequence generator is designed by performing the linear function operation to the real and imaginary part of a cascade-PLMS, cascade-PLJS separately, and the iteration number at which the cascade-PLJS converges to the fixed point. The performance analysis results show that the given method has a large key space, fast key generation speed, high key sensitivity, and strong randomness. Therefore, the scheme can be efficiently used further to design a secure cryptosystem with the ability to withstand various attacks.

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A Two-Parameter Modified Logistic Map and Its Application to Random Bit Generation

Cited by 34 publications

References 38 publications

Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

Research on Pseudorandom Number Generator Based on Several New Types of Piecewise Chaotic Maps

An efficient color image encryption scheme based on a matrix scrambling method and a new hybrid chaotic map

Designing a Pseudo-Random Bit Generator Using Generalized Cascade Fractal Function

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