Pseudo-random bit generator based on multi-modal maps

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• 作者：M. García-Martínez ; E. Campos-Cantón
• 关键词：Chaotic behavior ; Lyapunov exponent ; Bifurcation parameter ; Bifurcation diagram ; Pseudo ; random generator ; NIST ; Stream cipher ; Key stream ; k ; modal maps
• 刊名：Nonlinear Dynamics
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：82
• 期：4
• 页码：2119-2131
• 全文大小：3,268 KB
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• 作者单位：M. García-Martínez (1) (2)
  E. Campos-Cantón (1)
  
  1. División de Matemáticas Aplicadas, Instituto Potosino de Investigación Cientfica y Tecnológica, Camino a la Presa San José 2055, 78216, San Luis Potosí, S.L.P., México
  2. Colegio de la Frontera Sur CHETUMAL, Av. del Centenario Km. 5.5, 77900, Chetumal, Q. Roo, México
  
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems and Control
  Mechanics
  Mechanical Engineering
  Automotive and Aerospace Engineering and Traffic
  
• 出版者：Springer Netherlands
• ISSN：1573-269X

文摘

In this work we present a pseudo-random Bit Generator via unidimensional multi-modal discrete dynamical systems called k-modal maps. These multi-modal maps are based on the logistic map and are useful to yield pseudo-random sequences with longer period, i.e., in order to attend the problem of periodicity. In addition the pseudo-random sequences generated via multi-modal maps are evaluated with the statistical suite of test from NIST and satisfactory results are obtained when they are used as key stream. Furthermore, we show the impact of using these sequences in a stream cipher resulting in a better encryption quality correlated with the number of modals of the chaotic map. Finally, a statistical security analysis applied to cipher images is given. The proposed algorithm to encrypt is able to resist the chosen-plaintext attack and differential attack because the same set of encryption keys generates a different cipher image every time it is used. Keywords Chaotic behavior Lyapunov exponent Bifurcation parameter Bifurcation diagram Pseudo-random generator NIST Stream cipher Key stream k-modal maps