Boolean functions play an important role in symmetric ciphers. One of important open problems on Boolean functions is determining the maximum possible resiliency order of n-variable Boolean functions with optimal algebraic immunity. In this letter, we search Boolean functions in the rotation symmetric class, and determine the maximum possible resiliency order of 9-variable Boolean functions with optimal algebraic immunity. Moreover, the maximum possible nonlinearity of 9-variable rotation symmetric Boolean functions with optimal algebraic immunity-resiliency trade-off is determined to be 224.

Construction of resilient Boolean functions in odd variables having strictly almost optimal (SAO) nonlinearity appears to be a rather difficult task in stream cipher and coding theory. In this paper, based on the modified High-Meets-Low technique, a general construction to obtain odd-variable SAO resilient Boolean functions without directly using PW functions or KY functions is presented. It is shown that the new class of functions possess higher resiliency order than the known functions while keeping higher SAO nonlinearity, and in addition the resiliency order increases rapidly with the variable number n.

In this letter, we consider a global stabilization problem for a class of feedforward systems by an event-triggered control. This is an extended work of [10] in a way that there are uncertain feedforward nonlinearity and time-varying input delay in the system. First, we show that the considered system is globally asymptotically stabilized by a proposed event-triggered controller with a gain-scaling factor. Then, we also show that the interexecution times can be enlarged by adjusting a gain-scaling factor. A simulation example is given for illustration.

The r-th nonlinearity of Boolean functions is an important cryptographic criterion associated with higher order linearity attacks on stream and block ciphers. In this paper, we tighten the lower bound of the second-order nonlinearity of a class of Boolean function over finite field F2n, fλ(x)=Tr(λxd), where λ∈F*2r, d=22r+2r+1 and n=7r. This bound is much better than the lower bound of Iwata-Kurosawa.

In this paper, we report an experimental and numerical analysis of ultrahigh-speed coherent Nyquist pulse transmission. First, we describe a low-nonlinearity dispersion compensator for ultrahigh-speed coherent Nyquist pulse transmission; it is composed of a chirped fiber Bragg grating (CFBG) and a liquid crystal on silicon (LCoS) device. By adopting CFBG instead of inverse dispersion fiber, the nonlinearity in a 160km transmission line was more than halved. Furthermore, by eliminating the group delay fluctuation of the CFBG with an LCoS device, the residual group delay was reduced to as low as 1.42ps over an 11nm bandwidth. Then, by using the transmission line with the newly constructed low-nonlinearity dispersion compensator, we succeeded in improving the BER performance of single-channel 15.3Tbit/s-160km transmission by one-third compared with that of a conventional dispersion-managed transmission line and obtained a spectral efficiency of 8.7bit/s/Hz. Furthermore, we numerically analyzed the BER performance of its Nyquist pulse transmission. The numerical results showed that the nonlinear impairment in the transmission line is the main factor limiting the transmission performance in a coherent Nyquist pulse transmission, which becomes more significant at higher baud rates.

Construction of multiple output functions is one of the most important problems in the design and analysis of stream ciphers. Generally, such a function has to be satisfied with several criteria, such as high nonlinearity, resiliency and high algebraic degree. But there are mutual restraints among the cryptographic parameters. Finding a way to achieve the optimization is always regarded as a hard task. In this paper, by using the disjoint linear codes and disjoint spectral functions, two classes of resilient multiple output functions are obtained. It has been proved that the obtained functions have high nonlinearity and high algebraic degree.

In this paper, we propose a robust output feedback control method for nonlinear systems with uncertain time-varying parameters associated with diagonal terms and there are additional external disturbances. First, we provide a new practical guidance of obtaining a compact set which contains the allowed time-varying parameters by utilizing a Lyapunov equation and matrix inequalities. Then, we show that all system states and observer errors of the controlled system remain bounded by the proposed controller. Moreover, we show that the ultimate bounds of some system states and observer errors can be made (arbitrarily) small by adjusting a gain-scaling factor depending on the system nonlinearity. With an application example, we illustrate the effectiveness of our control scheme over the existing one.

Phase-sensitive amplification (PSA) has unique properties, such as the quantum-limited noise figure of 0 dB and the phase clamping effect. This study investigates PSA characteristics when a chirped pulse is incident. The signal gain, the output waveform, and the noise figure for an optical pulse having been chirped through chromatic dispersion or self-phase modulation before amplification are analyzed. The results indicate that the amplification properties for a chirped pulse are different from those of a non-chirped pulse, such that the signal gain is small, the waveform is distorted, and the noise figure is degraded.

Boolean functions and vectorial Boolean functions are the most important components of stream ciphers. Their cryptographic properties are crucial to the security of the underlying ciphers. And how to construct such functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper, using two small nonlinear functions with t-1 resiliency, we provide a method on constructing t-resilient n variables Boolean functions with strictly almost optimal nonlinearity >2n-1-2n/2 and optimal algebraic degree n-t-1. Based on the method, we give another construction so that a large class of resilient vectorial Boolean functions can be obtained. It is shown that the vectorial Boolean functions also have strictly almost optimal nonlinearity and optimal algebraic degree.

Boolean functions used in the filter model of stream ciphers should have balancedness, large nonlinearity, optimal algebraic immunity and high algebraic degree. Besides, one more criterion called strict avalanche criterion (SAC) can be also considered. During the last fifteen years, much work has been done to construct balanced Boolean functions with optimal algebraic immunity. However, none of them has the SAC property. In this paper, we first present a construction of balanced Boolean functions with SAC property by a slight modification of a known method for constructing Boolean functions with SAC property and consider the cryptographic properties of the constructed functions. Then we propose an infinite class of balanced functions with optimal algebraic immunity and SAC property in odd number of variables. This is the first time that such kind of functions have been constructed. The algebraic degree and nonlinearity of the functions in this class are also determined.

Rotation symmetric Boolean functions which are invariant under the action of cyclic group have been used in many different cryptosystems. This paper presents a new construction of balanced odd-variable rotation symmetric Boolean functions with optimum algebraic immunity. It is checked that, at least for some small variables, such functions have very good behavior against fast algebraic attacks. Compared with some known rotation symmetric Boolean functions with optimum algebraic immunity, the new construction has really better nonlinearity. Further, the algebraic degree of the constructed functions is also high enough.

We propose a recursive algorithm to reduce the computational complexity of the r-order nonlinearity of n-variable Boolean functions. Applying the algorithm and using the sufficient and necessary condition put forward by [1] to cut the vast majority of useless search branches, we show that the covering radius of the Reed-Muller Code R(3, 7) in R(5, 7) is 20.

Boolean functions used in stream ciphers and block ciphers should have high second-order nonlinearity to resist several known attacks and some potential attacks which may exist but are not yet efficient and might be improved in the future. The second-order nonlinearity of Boolean functions also plays an important role in coding theory, since its maximal value equals the covering radius of the second-order Reed-Muller code. But it is an extremely hard task to calculate and even to bound the second-order nonlinearity of Boolean functions. In this paper, we present a lower bound on the second-order nonlinearity of the generalized Maiorana-McFarland Boolean functions. As applications of our bound, we provide more simpler and direct proofs for two known lower bounds on the second-order nonlinearity of functions in the class of Maiorana-McFarland bent functions. We also derive a lower bound on the second-order nonlinearity of the functions which were conjectured bent by Canteaut and whose bentness was proved by Leander, by further employing our bound.

Semi-bent functions have very high nonlinearity and hence they have many applications in symmetric-key cryptography, binary sequence design for communications, and combinatorics. In this paper, we focus on studying the additive autocorrelation of semi-bent functions. We provide a lower bound on the maximum additive autocorrelation absolute value of semi-bent functions with three-level additive autocorrelation. Semi-bent functions with three-level additive autocorrelation achieving this bound with equality are said to have perfect three-level additive autocorrelation. We present two classes of balanced semi-bent functions with optimal algebraic degree and perfect three-level additive autocorrelation.

Dual-motor driving servo systems are widely used in many military and civil fields. Since backlash nonlinearity affects the dynamic performance and steady-state tracking accuracy of these systems, it is necessary to study a control strategy to reduce its adverse effects. We first establish the state-space model of a system. To facilitate the design of the controller, we simplify the model based on the state-space model. Then, we design an adaptive controller combining a projection algorithm with dynamic surface control applied to a dual-motor driving servo system, which we believe to be the first, and analyze its stability. Simulation results show that projection algorithm-based dynamic surface control has smaller tracking error, faster tracking speed, and better robustness and stability than mere dynamic surface control. Finally, the experimental analysis validates the effectiveness of the proposed control algorithm.

This paper investigates approaches that can cancel nonlinear phase noise effectively for the phase-conjugate pair diversity transmission of 16-QAM WDM signals through multi-core fiber. The geometric mean is introduced for the combination of the phase-conjugate pair. A numerical simulation suggests that span-by-span chromatic dispersion compensation is more effective at cancelling phase noise in long distance transmission than lumped compensation at the receiver. Simulations suggest the span-wise compensation described herein yields Q-value enhancement of 7.8 and 6.8dB for CD values of 10 and 20.6ps/nm/km, respectively, whereas the lumped compensation equivalent attains only 3.5dB. A 1050km recirculating loop experiment confirmed a Q-value enhancement of 4.1dB for 20.6ps/nm/km, span-wise compensation transmission.

Research on permutation polynomials over the finite field F22k with significant cryptographical properties such as possibly low differential uniformity, possibly high nonlinearity and algebraic degree has attracted a lot of attention and made considerable progress in recent years. Once used as the substitution boxes (S-boxes) in the block ciphers with Substitution Permutation Network (SPN) structure, this kind of polynomials can have a good performance against the classical cryptographic analysis such as linear attacks, differential attacks and the higher order differential attacks. In this paper we put forward a new construction of differentially 4-uniformity permutations over F22k by modifying the inverse function on some specific subsets of the finite field. Compared with the previous similar works, there are several advantages of our new construction. One is that it can provide a very large number of Carlet-Charpin-Zinoviev equivalent classes of functions (increasing exponentially). Another advantage is that all the functions are explicitly constructed, and the polynomial forms are obtained for three subclasses. The third advantage is that the chosen subsets are very large, hence all the new functions are not close to the inverse function. Therefore, our construction may provide more choices for designing of S-boxes. Moreover, it has been checked by a software programm for k=3 that except for one special function, all the other functions in our construction are Carlet-Charpin-Zinoviev equivalent to the existing ones.

This paper proposes an iterative cancellation technique for adjacent channel interference (ACI), induced by amplifier nonlinearity in millimeter wave (mmW) communication systems. In mmW communications, a large spectrum leak is expected because of the amplifier nonlinearity, and such a spectrum leak disturbs multichannel utilization. In order to mitigate the ACI, iterative interference cancellation in the receiver side is designed in this paper. Typically, iterative interference cancellation is conducted by generating a soft replica of interference from the feedback of the decoder, and subtracting the replica from the received signals. In this case, the canceller must know the amplifier nonlinearity in order to regenerate a soft replica of ACI. In this paper, amplifier nonlinearity is estimated by subjecting the received pilot signals to polynomial regression. We reveal that using only pilot signals in estimating amplifier nonlinearity is insufficient for guaranteeing replica accuracy. To address this issue, the proposed scheme exploits the detected data sequence in the regression analysis. We demonstrate that the proposed ACI cancellation technique can effectively mitigate ACI in multichannel utilization.

This paper proposes two linearity enhancement techniques for open-loop amplifiers. One technique is nonlinearity cancellation. An amplifier with reversed nonlinearity is proposed to cascade with a conventional common source amplifier. The product of these two nonlinear gains demonstrates much higher linearity. It achieves a SFDR of 71 dB when differential output range is 600 mV. Compared with the conventional common source amplifier, about 24 dB improvement is achieved. Another proposed technique is gain adapting. An input amplitude detector utilizing second order nonlinearity is combined with a source-degenerated amplifier. It can adjust the gain automatically according to the input amplitude, and compensate the gain compression when the input amplitude becomes larger. A SFDR of 69 dB is realized when the differential output range is 600 mV. An improvement of 23 dB is achieved after gain is adapted. Furthermore, mismatch calibration for the two proposed linearity enhancement techniques is investigated. Finally, comparison between two proposed amplifiers is introduced. The amplifier with nonlinearity cancellation has advantage in large signal range while the amplifier utilizing gain adapting is more competitive on accurate calibration, fast response and low noise.

Radio frequency over fiber (RoF) advanced technology is already integrated into current 3G and 4G radio access networks in which the digital unit and remote radio head equipped with nonlinear high power amplifiers (HPAs) are connected through the RoF-based fronthaul links. In this study, we investigated the degradation in the adjacent channel leakage ratio (ACLR) of equipment with the adaptive linearizer RF HPA when both the direct and feedback paths of the transmitting system include RoF links. We show that an ACLR exceeding -57dBc @ 5-MHz offset, which completely satisfies the requirements of the 3GPP technical specifications, can be achieved for a 20-W-class Doherty power amplifier linearized through commercial RoF links. Experiments showed that the achieved ACLR strongly depends on the RoF-link noise figure and that most of the nonlinear distortions caused by RoF can be completely suppressed with the proposed joint linearization approach for simultaneous linearization of RoF and HPA nonlinearities with a single common “joint” linearizer. Experimental results confirm significant ACLR performance enhancements as a result of RoF noise floor reduction, which is achieved under RoF driving conditions optimized together with joint RoF and HPA linearization. Our joint linearization approach via RoF links is confirmed to be applicable for next-generation mobile fronthaul architectures.