Abstract
In recent years, a variety of chaos-based cryptosystems have been proposed. Some of these systems are used in designing a pseudo random bit generator (PRBG) for stream cipher applications. Most of the chaotic systems used in cryptography have good chaotic properties like ergodicity, sensitivity to initial values and sensitivity to control parameters. However, some of them are not very suitable for use in cryptography because of their non-uniform density function, and their relatively small key space. To be used in cryptography, a PRBG may need to meet stronger requirements than for other applications. In particular, various statistical tests can be applied to the outputs of such generators to conclude whether the generator produces a truly random sequence or not. In this paper, we propose a PRBG based on the use of the standard chaotic map with large key space and the Engle Continued Fractions (ECF) map. The outputs of the standard map are used as the inputs of ECF-map. The chaotic nature of the standard map and the good statistical properties of the ECF map motivate us to design a new PRBG for stream cipher applications. The numerical simulation analysis indicates that our PRBG produces bit sequences possessing excellent statistical and cryptographic properties.
Highlights
A variety of crypto-systems have been proposed
We propose a pseudo random bit generator (PRBG) based on the use of the standard chaotic map with large key space and the Engle Continued Fractions (ECF) map
Zi x n i 1 with a uniform distribution. These properties, which are very useful in cryptography, motivate us to propose a new PRBG for stream cipher applications based on ECF-map
Summary
A variety of crypto-systems have been proposed. Many of them are based on chaotic systems [1,2,3,4,5] which possess good cryptographic characteristics. Chaos systems have many important features like ergodicity, sensitivity to initial condition, sensitivity to control parameters and randomness. The logistic map is weak in security because it neither satisfies the uniform distribution property nor does its key space [19,20] For this map, the key size is determined by the initial value x0 and the control parameter ; 50 bits with a precision of 10-14. In [11], Patidar and Sud proposed a PRBG for stream cipher applications based on two chaotic standard maps running side-by-side and starting from randomly inde. ECF-map conserves the cryptography properties of the chaotic system; like sensitivity to initial values/control parameters, non periodicity and randomness; and adds interesting statistical properties such uniform distribution density function and zero co-correlation.
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