In this paper, methods are shown how to adapt invertible two-dimensional chaotic maps on a torus or on a square to create new symmetric block encryption schemes. A chaotic map is first generalized by introducing parameters and then discretized to a finite square lattice of points which represent pixels or some other data items. Although the discretized map is a permutation and thus cannot be chaotic, it shares certain properties with its continuous counterpart as long as the number of iterations remains small. The discretized map is further extended to three dimensions and composed with a simple diffusion mechanism. As a result, a symmetric block product encryption scheme is obtained. To encrypt an N×N image, the ciphering map is iteratively applied to the image. The construction of the cipher and its security is explained with the two-dimensional Baker map. It is shown that the permutations induced by the Baker map behave as typical random permutations. Computer simulations indicate that the cipher has g...

Symmetric Ciphers Based on Two-Dimensional Chaotic Maps

Chaotic cryptology is widely investigated recently. This paper reviews the progress in this area and points out some existent problems in digital chaotic ciphers. As a comprehensive solution to these problems, a novel pseudo-random bit generator based on a couple of chaotic systems called CCS-PRBG is presented. Detailed theoretical analyses show that it has perfect cryptographic properties, and can be used to construct stream ciphers with higher security than other chaotic ciphers. Some experiments are made for confirmation. Finally, several examples of stream ciphers based on digital CCS-PRBG are given, and their security is discussed.

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Pseudo-random Bit Generator Based on Couple Chaotic Systems and Its Applications in Stream-Cipher Cryptography

A cable television system provides conditional access to services. The cable television system includes a headend from which service 'instances', or programs, are broadcast and a plurality of set top units for receiving the instances and selectively decrypting the instances for display to system subscribers. The service instances are encrypted using public and/or private keys provided by service providers or central authorization agents. Keys used by the set tops for selective decryption may also be public or private in nature, and such keys may be reassigned at different times to provide a cable television system in which piracy concerns are minimized.

Verification of the source of program of information in a conditional access system

An automobile door lock receiver module (30) and a plurality of keychain fob transmitter units (16) contain identification numbers, secret initial values, and secret feedback masks so as to authenticate encrypted messages from any of the assigned fobs, indicative of commands registered by closing switches on the fob. Each fob is synchronized with the receiving module by means of a truly random number concatenated with a secret initial value and encrypted, through a linear feedback shift register or other operations. A second secret initial value is encrypted and command bits are exclusive ORed into the low order bit positions; the two encrypted numbers are concatenated and encrypted to form a key word which is transmitted with the fob ID. Synchronization includes decrypting to recover the truly random number and the secret initial value concatenated therewith; the truly random number is compared with previously received random numbers in order to avoid copying of recently transmitted synchronization commands. Successive lock-related commands utilize the number encrypted from the truly random number and the second secret initial value as starting values, employing a pseudorandom number of encryption iterations. A half-second delay between responses mitigates gaining access through numerical trials. An authenticated panic alarm command operates the headlights and horn of the vehicle but does not alter the synchronization.

Pseudorandom number generation and cryptographic authentication

A method of performing numerical computations in a mathematical system with at least one function, including expressing the mathematical system in discrete terms, expressing at least one variable of the mathematical system as a fixed-point number, performing the computations in such a way that the computations include the at least one variable expressed as a fixed-point number, obtaining, from the computations, a resulting number, the resulting number representing at least one of at least a part of a solution to the mathematical system, and a number usable in further computations involved in the numerical solution of the mathematical system, and extracting a set of data which represents at least one of a subset of digits of the resulting number, and a subset of digits of a number derived from the resulting number.

Method of generating pseudo-random numbers in an electronic device, and a method of encrypting and decrypting electronic data

An encryption system and method based on the mathematics of Chaos theory, which provides protection of data from unauthorized modification and use during its storage and transmission. At its core are nonlinear equations which exhibits random, noise-like properties, given certain parameter values. When iterated, a periodic sequence is produced with an extremely long cycle length. A domain transformation process is then used to convert the floating-point iterates into binary form for summation with the digital data to be protected. The result is an encrypted message that cannot be modified, replaced, or understood by anyone other than the intended party. The use of Chaos theory in combination with the domain transformation process results in an easily implemented cryptographic system with extremely robust cryptographic properties. The concepts of the present invention also lend themselves well to either hardware or software implementations. The cryptographic system of the present invention may be employed to encrypt and decrypt sensitive information, to authenticate data and video links, or similar applications. It can also be used to provide a simple hash function for the secure storage of passwords in a computer system. Its simplicity, requiring only floating-point operations at its core, allows a lower cost and higher performance product with cryptographic security equivalent to conventional cryptographic systems.

An encryption system based on chaos theory

Verschlüsselungssystem auf Grundlage der Chaostheorie

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An encryption system based on chaos theory

Verschlüsselungssystem auf Grundlage der Chaostheorie