Using the Logistic Coupled Map for Public Key Cryptography under a Distributed Dynamics Encryption Scheme

Solís-Sánchez, Hugo; Barrantes, Elena Gabriela

doi:10.3390/info9070160

Cited by 8 publications

(5 citation statements)

References 16 publications

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“…In addition to providing a concrete setting to explore these theoretical concepts, coupled iterated-map systems have found an application in cryptography. In fact, coupled logistic maps have been recently proposed as a vehicles for distributed dynamic encryption [8,9] by utilizing their strange attractors to hide a message.…”

Section: Introductionmentioning

confidence: 99%

An experimental survey of chaos and symmetry breaking in coupled and driven logistic maps

et al. 2019

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In this paper we report on the experimentally measured dynamics exhibited by a system comprised of two coupled circuits whose input–output relation follow the logistic-map function. The circuit takes in two external voltages that control the initial conditions, and we employ this capability to examine the phenomenon of symmetry breaking and to submit theoretical/numerical results on this dynamical system to experimental test. We demonstrate that symmetry-broken solutions manifest in this circuit for appropriately chosen initial conditions, and proceed to investigate experimentally the basins of attraction of these solutions, as well as their dependence on the coupling strength, ϵ. We illustrate the full power of this circuit by investigating the chaotic regime and by constructing experimental bifurcation diagrams. One intriguing phenomenon captured here involves the transition from synchronized chaos to decoherent chaos as the coupling is increased. Finally, we experimentally implement uni-directional coupling and explore the dynamics of a driven logistic map.

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Section: Introductionmentioning

confidence: 99%

An experimental survey of chaos and symmetry breaking in coupled and driven logistic maps

et al. 2019

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“…Many generator functions can produce CSPRNG-based random numbers, with the logistic function f (x) = rx(1x) being the most famous, interatively given by x i+1 = rx i (1−x i ). In research [2] - [5], it is used as a complement in the algorithm. Research [6] tests polynomial functions of degree-1, degree-2, and degree-3, and then transforms them into iterative functions with xed-point iteration.…”

Section: Introductionmentioning

confidence: 99%

Chaos CSPRNG Design As a Key in Symmetric Cryptography Using Logarithmic Functions

Nathanael,

Wowor

2024

JIIKM

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This research uses the logarithm function as a key component in generating random numbers in the Chaos CSPRNG framework. The main problem addressed here is the generation of keys for cryptography, recognizing the important role of cryptographic keys in safeguarding sensitive information. By using mathematical functions, specifically logarithmic functions, as a key generation method, this research explores the potential for increasing the uncertainty and strength of cryptographic keys. The proposed approach involves the systematic utilization of various mathematical functions to generate diverse and unpredictable data sets. This data set, derived from the application of logarithmic functions, serves as the basis for generating random numbers. Through a series of tests such as Randomness Test and Cryptography Test, this research shows that the data generated from these functions can be utilized effectively as a reliable source for generating random numbers, and has a low correlation value, thereby contributing to the overall security of a symmetric cryptographic system.

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“…e study of logistic function as a quadratic map shows that it does not stay fixed in its transformation as the control parameter λ keeps alternating or changing [13,14]. e logistic function is a nonlinear system which is a type of difference equation and a quadratic in nature.…”

Section: Introductionmentioning

confidence: 99%

Using the Logistic Map as Compared to the Cubic Map to Show the Convergence and the Relaxation of the Period–1 Fixed Point

Mensah

Obeng–Denteh

Issaka

et al. 2022

International Journal of Mathematics and Mathematical Sciences

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In this paper, we employ the logistic map and the cubic map to locate the relaxation and the convergence to the periodic fixed point of a system, specifically, the period—1 fixed point. The study has shown that the period—1 fixed point of a logistic map as a recurrence has its convergence at a transcritical bifurcation having its power-law fit with exponent β = − 1 when α = 1 and μ = 0 . The cubic map shows its convergence to the fixed point at a pitchfork bifurcation decaying at a power law with exponent β = − 1 / 2 α = 1 and μ = 0 . However, the system shows their relaxation time at the same power law with exponents and z = − 1 .

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Using the Logistic Coupled Map for Public Key Cryptography under a Distributed Dynamics Encryption Scheme

Cited by 8 publications

References 16 publications

An experimental survey of chaos and symmetry breaking in coupled and driven logistic maps

An experimental survey of chaos and symmetry breaking in coupled and driven logistic maps

Chaos CSPRNG Design As a Key in Symmetric Cryptography Using Logarithmic Functions

Using the Logistic Map as Compared to the Cubic Map to Show the Convergence and the Relaxation of the Period–1 Fixed Point

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