Serial encryption using the functions of real variable

Context. Using the functions of a real variable in cryptosystems as keys allow increasing their cryptographic strength since it is more difficult to select such keys. Therefore, the development of such systems is relevant. Objective. Cryptosystems with symmetric keys are proposed for encrypting and decrypting a sequence of characters represented as a one-dimensional numerical array of ASCII codes. These keys are functions of a real variable that satisfies certain restrictions. They can be both continuous and discrete. Method. Two cryptosystem options are proposed. In the first embodiment, the transmitting and receiving sides select two functions, the first transmitted symbol, the area of the function definition, and the step of changing the function argument. Discrete messages are encrypted by calculating the first-order integral disproportion of the encrypted array using a function. The corresponding value of the second function is added to the obtained cipher of each symbol for scrambling to complicate the analysis of the intercepted message. On the receiving side, the second function is subtracted and decryption performed by the inverse transformation of the formula for integral disproportion. In the second version, sequential encryption is performed when the cipher obtained using one of the key functions in the first stage is encrypted again by calculating the disproportion using the second function, the key. Accordingly, in two stages, decryption is performed. Results. Examples of encryption and decryption of a sequence of text characters are presented. It is shown that the same character is encoded differently depending on its position in the message. In the given examples it is presented the difficulty of key functions parameters choosing and the cryptographic strength of the proposed cryptosystem. Conclusions. Variants of the cryptosystem using the first-order integral disproportion function are proposed, in which the functions of a real variable serve as keys. To “crack” such a system, it is necessary not only to select the form of each function but also to find the values of its parameters with high accuracy. The system has high cryptographic strength.

Analysis of Low Probability of Detection Capability for Chaotic Standard Map-Based FH-OFDMA System

A frequency hopping orthogonal frequency division multiple access (FH-OFDMA) can provide low probability of detection (LPD) and anti-jamming capabilities to users against adversary detectors. To obtain an extreme LPD capability that cannot be provided by the basic symbol-by-symbol (SBS)-based FH pattern, we proposed two FH patterns, namely chaotic standard map (CSM) and cat map for FH-OFDMA systems. In our previous work, through analysis of complexity to regenerate the transmitted symbol sequence, at the point of adversary detectors, we found that the CSM had a lower probability of intercept than the cat map and SBS. It is possible when a detector already knows symbol and frame structures, and the detector has been synchronized to the FH-OFDMA system. Unlike the previous work, here, we analyze whether the CSM provides greater LPD capability than the cat map and SBS by detection probability using spectrum sensing technique. We analyze the detection probability of the CSM and provide detection probabilities of the cat map and SBS compared to the CSM. Based on our analysis of the detection probability and numerical results, it is evident that the CSM provides greater LPD capability than both the cat map and SBS-based FH-OFDMA systems.

A Joint Chip Equalization Adaptive Rake Receiver for DS-CDMA UWB Systems over ISI Channels

There is serious inter-symbol interference (ISI) when ultra-wideband (UWB) wireless communication systems work at high data speed since there is much larger channel delay spread. The serious ISI becomes a major factor that affects the performance of UWB systems. In this paper, suppression ISI is developed for direct sequence spread-code division multiple access (DS-CDMA) UWB systems with a high data speed, and a joint chip equalization adaptive Rake (JCE-Rake) receiver is proposed. The proposed JCE-Rake receiver spreads the number of traditional Rake receiver taps to collect multi-path component and equalize the inter-chip interference simultaneously. Then the soft output of JCE-Rake receiver is despreaded with the user's spreading code. Finally the decision is made to recover the transmitted symbol. The simulation results verify that ISI is suppressed effectively and the system performance is improved evidently.

A PROBABILISTIC SYMMETRIC ENCRYPTION SCHEME FOR VERY FAST SECURE COMMUNICATION BASED ON CHAOTIC SYSTEMS OF DIFFERENCE EQUATIONS

We present a new probabilistic symmetric key encryption scheme based on the chaotic dynamics of properly designed chaotic systems. This technique exploits the concept of virtual attractors, which are not real attractors of the underlying chaotic dynamics but are created and maintained artificially. Each virtual attractor represents a symbol of the alphabet used to encode messages. The state space is partitioned over the virtual attractors creating clusters of states. The enciphering process randomizes over the set of states mapped to a virtual attractor in order to construct the ciphertext for the transmited symbol. The receiver can reconstruct perfectly this virtual state space, given the possession of the same chaotic system of difference equations with parameters tuned perfectly to those of the transmitter. Therefore, from the ciphertext chunk corresponding to a state, the virtual attractor can be derived from the details of the virtual state space. The knowledge of the virtual attractor leads to the recovery of the transmitted symbol. We demonstrate that the new algorithm is secure, reliable and very fast. It uses discrete time chaotic recurrent systems and is simple, flexible and modular. These systems can be constructed easily dynamically from an alphanumeric encryption key. The cryptographic security of the algorithm is evaluated with combinatorial arguments.