Use of chaotic dynamical systems in cryptography.

*(English)*Zbl 0979.94038Chaotic dynamical systems exhibit some properties that make them quite attractive for possible use in cryptography. A number of proposals have been made to utilize the simulation of chaotic discrete dynamical systems on a computer for encryption. However, mathematical properties relevant to the use of such systems in cryptography have often been neglected. In this paper, some of these properties that may serve to assess the security of such cryptosystems are identified and reviewed.

The paper begins with an introduction to the area; some key problems (e.g. those related to the finiteness of the computer memory in numerical simulations of chaotic dynamical systems) are mentioned there as well. A systematic approach begins in Section 2, where the formal definition of a chaotic dynamical system is given together with some examples. Also the problem of iterating a dynamical system in a discrete and finite context (i.e. on a computer) is discussed here.

In Section 3, sensitivity to the initial conditions and probability distributions are briefly investigated. Results obtained here are subsequently applied in Section 4 to the concept of block and stream ciphers. Properties of some systems proposed in the literature are evaluated and some assessment of their security is given. At the end of the paper, some open research problem are identified.

The paper begins with an introduction to the area; some key problems (e.g. those related to the finiteness of the computer memory in numerical simulations of chaotic dynamical systems) are mentioned there as well. A systematic approach begins in Section 2, where the formal definition of a chaotic dynamical system is given together with some examples. Also the problem of iterating a dynamical system in a discrete and finite context (i.e. on a computer) is discussed here.

In Section 3, sensitivity to the initial conditions and probability distributions are briefly investigated. Results obtained here are subsequently applied in Section 4 to the concept of block and stream ciphers. Properties of some systems proposed in the literature are evaluated and some assessment of their security is given. At the end of the paper, some open research problem are identified.

Reviewer: Jozef Vyskoč (Bratislava)

##### MSC:

94A60 | Cryptography |

37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |

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\textit{R. Schmitz}, J. Franklin Inst. 338, No. 4, 429--441 (2001; Zbl 0979.94038)

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