Function Composition from Sine Function and Skew Tent Map and Its Application to Pseudorandom Number Generators

In cryptography, the pseudorandom number sequences must have random appearance to be used in secure information systems. The skew tent map (STM) is an attractive map to produce pseudorandom sequences due to its easy implementation and the absence of stability islands when it is in chaotic behavior. Using the STM and sine function, we propose and analyze a function composition to propose a pseudorandom number generator (PRNG). In the analysis of the function composition, we use the bifurcation diagram and the Lyapunov exponent to perform a behavioral comparison against the STM. We show that the proposed function composition is more sensitive to initial conditions than the STM, and then it is a better option than the STM for cryptography applications. For the proposed function we determine and avoid the chaos annulling traps. The proposed PRNG can be configured to generate pseudorandom numbers of 8, 16 or 32 bits and it can be implemented on microcontrollers with different architectures. We evaluate the pseudorandomness of the proposed PRNG using the NIST SP 800-22 and TestU01 suites. Additionally, to evaluate its quality, we apply tests such as correlation coefficient, key sensitivity, statistical and entropy analysis, key space, linear complexity, and speed. Finally, we performed a comparison with similar PRNGs that produce pseudorandom sequences considering numbers of 8 and 32 bits. The results show that the proposed PRNG maintains its security regardless of the selected configuration. The proposed PRNG has five important features: easy implementation, configurable to produce number with 8, 16 or 32 bits, high processing speed, high linear complexity, and wide key space. These features are necessary for cryptographic systems.

A Robust Image Encryption Method Using Chaotic Skew-Tent Map

Encryption is one of the most frequently used tools in data communications to prevent unwanted access to the data. In the field of image encryption, chaos-based encryption methods have become very popular in the recent years. Chaos-based methods provide a good security mechanism in image communication. In this chapter, chaotic skew-tent map is adapted to encode an image. Seventy-two bit external key is considered (besides the initial parameters of the chaotic system) initially, and after some processing operations, 64 bit internal key is obtained. Using this key, every pixel is processed. The internal key is transformed using some basic operations to enhance the security. The decryption method is very simple so that authentic users can retrieve the information very fast. Every pixel is encrypted using some basic mathematical operations. The values of various test parameters show the power and efficiency of the proposed algorithm, which can be used as a safeguard for sensitive image data and a secure method of image transmission.

A 1 Gbps Chaos-Based Stream Cipher Implemented in 0.18 μm CMOS Technology

In this work, a novel chaos-based stream cipher based on a skew tent map is proposed and implemented in a 0.18 μm CMOS (Complementary Metal-Oxide-Semiconductor) technology. The proposed ciphering algorithm uses a linear feedback shift register that perturbs the orbits generated by the skew tent map after each iteration. This way, the randomness of the generated sequences is considerably improved. The implemented stream cipher was capable of achieving encryption speeds of 1 Gbps by using an approximate area of ~ 20 , 000 2-NAND equivalent gates, with a power consumption of 24.1 mW. To test the security of the proposed cipher, the generated keystreams were subjected to National Institute of Standards and Technology (NIST) randomness tests, proving that they were undistinguishable from truly random sequences. Finally, other security aspects such as the key sensitivity, key space size, and security against reconstruction attacks were studied, proving that the stream cipher is secure.