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Abstract
Historically, cryptography has emerged as a response to the requirement of transmitting secret information. For a long time, it was only concerned with designing special methods of information transformation in order to represent it in a form incomprehensible to a potential opponent. After electronic methods of information processing and transmitting had developed, cryptography’s tasks became more varied. Modem cryptography issues include developing digital signature systems, computerized voting systems, coin tossing protocols, remote user authentication protocols, protection against creating false messages, etc. The wide use of computer technologies in data processing and control systems has aggravated the problem of protecting information from unauthorized access. There are many known threats to information, and they can be implemented both by inside and outside adversaries, a radical solution to the problem of protecting information that flows in high-performance computer systems can be obtained using cryptographic methods. In this case, it is important to utilize fast enciphering algorithms that don’t decrease the performance of the computer or telecommunication systems. Cryptographic data transformations are flexible and effective tools for providing data privacy, integrity, and authenticity. Using cryptographic methods in combination with technological and organizational methods can protect against a wide range of potential threats. This thesis gives an introduction to chaotic systems followed by proposed cryptographic schemes using chaotic systems, the Quadruple Logarithmic Algorithm & RSA using chaotic system. The chaotic function was applied as a symmetric secret key for both transmitter and receiver by mixing it with the message before encrypting it which will appear as a random noise, the strength of the algorithm was increased due to the chaotic behavior of chaos and proven by several methods of analysis. One of these methods is the frequency analysis, which is one of the most
powerful methods of analysis that is applied to algorithms before and using chaotic functions proving that the ciphertext which is the output of the chaotic function had the most flat distribution. Also a new chaotic public key multi-message multi-recipient signcryption scheme (CPK-MM-MR-SS) using a chaotic multi-key generator, and a chaotic message mixer, . followed by performance evaluation of the new algorithm which according to tests makes the system robust against the brute force attack. A provably secure signcryption scheme was proposed, three birds one stone chaotic signcryption (TBOSCS) it is based on EIGamal cryptosystem and on a new chaotic mapping function. After that Gaussian integers basic definitions followed by a new proposed chaotic Quadratic-Exponentiation Randomized (QER)
. cryptosystem in the Gaussian number domain was introduced. A new symmetric cipher enhanced by rotor in real and Gaussian domains (SCER) was proposed. WiMax Broadband Wireless Access Security System was explained and it was recommended to use SCER in real domain as a new data integrity algorithm for WiMax security system instead of AES due to the higher performance of SCER versus AES. Also the ”NIST” system statistics tests,