An analysis of the RC4 family of stream ciphers against algebraic attacks

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on lin- ear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and inves- tigate its implications to potential algebraic attacks on the cipher. This is, to our knowledge, the first pa- per that evaluates the security of RC4 against alge- braic attacks through providing a full set of equations that describe the complex word manipulations in the system. For an arbitrary word size, we derive alge- braic representations for the three main operations used in RC4, namely state extraction, word addition and state permutation. Equations relating the inter- nal states and keystream of RC4 are then obtained from each component of the cipher based on these al- gebraic representations, and analysed in terms of their contributions to the security of RC4 against algebraic attacks. Interestingly, it is shown that each of the three main operations contained in the components has its own unique algebraic properties, and when their respective equations are combined, the resulting system becomes infeasible to solve. This results in a high level of security being achieved by RC4 against algebraic attacks. On the other hand, the removal of an operation from the cipher could compromise this security. Experiments on reduced versions of RC4 have been performed, which confirms the validity of our algebraic analysis and the conclusion that the full RC4 stream cipher seems to be immune to algebraic attacks at present.

State convergence in the initialisation of the Sfinks stream cipher

Sfinks is a shift register based stream cipher designed for hardware implementation. The initialisation state update function is different from the state update function used for keystream generation. We demonstrate state convergence during the initialisation process, even though the individual components used in the initialisation are one-to-one. However, the combination of these components is not one-to-one.

Algebraic analysis of the SSS stream cipher

Both the SSS and SOBER-t32 stream cipher designs use a single word-based shift register and a nonlinear filter function to produce keystream. In this paper we show that the algebraic attack method previously applied to SOBER-t32 is prevented from succeeding on SSS by the use of the key dependent substitution box (SBox) in the nonlinear filter of SSS. Additional assumptions and modifications to the SSS cipher in an attempt to enable algebraic analysis result in other difficulties that also render the algebraic attack infeasible. Based on these results, we conclude that a well chosen key-dependent substitution box used in the nonlinear filter of the stream cipher provides resistance against such algebraic attacks.

Slide attacks on the Sfinks stream cipher

Sfinks is a shift register based stream cipher designed for hardware implementation and submitted to the eSTREAM project. In this paper, we analyse the initialisation process of Sfinks. We demonstrate a slid property of the loaded state of the Sfinks cipher, where multiple key-IV pairs may produce phase shifted keystream sequences. The state update functions of both the initialisation process and keystream generation and also the pattern of the padding affect generation of the slid pairs.

Slid pairs in the initialisation of the A5/1 stream cipher

A5/1 is a shift register based stream cipher which uses a majority clocking rule to update its registers. It is designed to provide privacy for the GSM system. In this paper, we analyse the initialisation process of A5/1. We demonstrate a sliding property of the A5/1 cipher, where every valid internal state is also a legitimate loaded state and multiple key-IV pairs produce phase shifted keystream sequences. We describe a possible ciphertext only attack based on this property.

Weak key-IV pairs in the A5/1 stream cipher

A5/1 is a shift register based stream cipher which provides privacy for the GSM system. In this paper, we analyse the loading of the secret key and IV during the initialisation process of A5/1. We demonstrate the existence of weak key-IV pairs in the A5/1 cipher due to this loading process; these weak key-IV pairs may generate one, two or three registers containing all-zero values, which may lead in turn to weak keystream sequences. In the case where two or three registers contain only zeros, we describe a distinguisher which leads to a complete decryption of the affected messages.

Weaknesses in the initialisation process of the Common Scrambling Algorithm Stream Cipher

The Common Scrambling Algorithm Stream Cipher (CSASC) is a shift register based stream cipher designed to encrypt digital video broadcast. CSA-SC produces a pseudo-random binary sequence that is used to mask the contents of the transmission. In this paper, we analyse the initialisation process of the CSA-SC keystream generator and demonstrate weaknesses which lead to state convergence, slid pairs and shifted keystreams. As a result, the cipher may be vulnerable to distinguishing attacks, time-memory-data trade-off attacks or slide attacks.

The modulation of outdoor running speed : the influence of gradient

This thesis aimed to investigate the way in which distance runners modulate their speed in an effort to understand the key processes and determinants of speed selection when encountering hills in natural outdoor environments. One factor which has limited the expansion of knowledge in this area has been a reliance on the motorized treadmill which constrains runners to constant speeds and gradients and only linear paths. Conversely, limits in the portability or storage capacity of available technology have restricted field research to brief durations and level courses. Therefore another aim of this thesis was to evaluate the capacity of lightweight, portable technology to measure running speed in outdoor undulating terrain. The first study of this thesis assessed the validity of a non-differential GPS to measure speed, displacement and position during human locomotion. Three healthy participants walked and ran over straight and curved courses for 59 and 34 trials respectively. A non-differential GPS receiver provided speed data by Doppler Shift and change in GPS position over time, which were compared with actual speeds determined by chronometry. Displacement data from the GPS were compared with a surveyed 100m section, while static positions were collected for 1 hour and compared with the known geodetic point. GPS speed values on the straight course were found to be closely correlated with actual speeds (Doppler shift: r = 0.9994, p < 0.001, Δ GPS position/time: r = 0.9984, p < 0.001). Actual speed errors were lowest using the Doppler shift method (90.8% of values within ± 0.1 m.sec -1). Speed was slightly underestimated on a curved path, though still highly correlated with actual speed (Doppler shift: r = 0.9985, p < 0.001, Δ GPS distance/time: r = 0.9973, p < 0.001). Distance measured by GPS was 100.46 ± 0.49m, while 86.5% of static points were within 1.5m of the actual geodetic point (mean error: 1.08 ± 0.34m, range 0.69-2.10m). Non-differential GPS demonstrated a highly accurate estimation of speed across a wide range of human locomotion velocities using only the raw signal data with a minimal decrease in accuracy around bends. This high level of resolution was matched by accurate displacement and position data. Coupled with reduced size, cost and ease of use, the use of a non-differential receiver offers a valid alternative to differential GPS in the study of overground locomotion. The second study of this dissertation examined speed regulation during overground running on a hilly course. Following an initial laboratory session to calculate physiological thresholds (VO2 max and ventilatory thresholds), eight experienced long distance runners completed a self- paced time trial over three laps of an outdoor course involving uphill, downhill and level sections. A portable gas analyser, GPS receiver and activity monitor were used to collect physiological, speed and stride frequency data. Participants ran 23% slower on uphills and 13.8% faster on downhills compared with level sections. Speeds on level sections were significantly different for 78.4 ± 7.0 seconds following an uphill and 23.6 ± 2.2 seconds following a downhill. Speed changes were primarily regulated by stride length which was 20.5% shorter uphill and 16.2% longer downhill, while stride frequency was relatively stable. Oxygen consumption averaged 100.4% of runner’s individual ventilatory thresholds on uphills, 78.9% on downhills and 89.3% on level sections. Group level speed was highly predicted using a modified gradient factor (r2 = 0.89). Individuals adopted distinct pacing strategies, both across laps and as a function of gradient. Speed was best predicted using a weighted factor to account for prior and current gradients. Oxygen consumption (VO2) limited runner’s speeds only on uphill sections, and was maintained in line with individual ventilatory thresholds. Running speed showed larger individual variation on downhill sections, while speed on the level was systematically influenced by the preceding gradient. Runners who varied their pace more as a function of gradient showed a more consistent level of oxygen consumption. These results suggest that optimising time on the level sections after hills offers the greatest potential to minimise overall time when running over undulating terrain. The third study of this thesis investigated the effect of implementing an individualised pacing strategy on running performance over an undulating course. Six trained distance runners completed three trials involving four laps (9968m) of an outdoor course involving uphill, downhill and level sections. The initial trial was self-paced in the absence of any temporal feedback. For the second and third field trials, runners were paced for the first three laps (7476m) according to two different regimes (Intervention or Control) by matching desired goal times for subsections within each gradient. The fourth lap (2492m) was completed without pacing. Goals for the Intervention trial were based on findings from study two using a modified gradient factor and elapsed distance to predict the time for each section. To maintain the same overall time across all paced conditions, times were proportionately adjusted according to split times from the self-paced trial. The alternative pacing strategy (Control) used the original split times from this initial trial. Five of the six runners increased their range of uphill to downhill speeds on the Intervention trial by more than 30%, but this was unsuccessful in achieving a more consistent level of oxygen consumption with only one runner showing a change of more than 10%. Group level adherence to the Intervention strategy was lowest on downhill sections. Three runners successfully adhered to the Intervention pacing strategy which was gauged by a low Root Mean Square error across subsections and gradients. Of these three, the two who had the largest change in uphill-downhill speeds ran their fastest overall time. This suggests that for some runners the strategy of varying speeds systematically to account for gradients and transitions may benefit race performances on courses involving hills. In summary, a non – differential receiver was found to offer highly accurate measures of speed, distance and position across the range of human locomotion speeds. Self-selected speed was found to be best predicted using a weighted factor to account for prior and current gradients. Oxygen consumption limited runner’s speeds only on uphills, speed on the level was systematically influenced by preceding gradients, while there was a much larger individual variation on downhill sections. Individuals were found to adopt distinct but unrelated pacing strategies as a function of durations and gradients, while runners who varied pace more as a function of gradient showed a more consistent level of oxygen consumption. Finally, the implementation of an individualised pacing strategy to account for gradients and transitions greatly increased runners’ range of uphill-downhill speeds and was able to improve performance in some runners. The efficiency of various gradient-speed trade- offs and the factors limiting faster downhill speeds will however require further investigation to further improve the effectiveness of the suggested strategy.

Load compensation for systems with non-stiff source using state feedback

Various load compensation schemes proposed in literature assume that voltage source at point of common coupling (PCC) is stiff. In practice, however, the load is remote from a distribution substation and is supplied by a feeder. In the presence of feeder impedance, the PWM inverter switchings distort both the PCC voltage and the source currents. In this paper load compensation with such a non-stiff source is considered. A switching control of the voltage source inverter (VSI) based on state feedback is used for load compensation with non-stiff source. The design of the state feedback controller requires careful considerations in choosing a gain matrix and in the generation of reference quantities. These aspects are considered in this paper. Detailed simulation and experimental results are given to support the control design.

Output feedback control of discrete-time systems in networked environments

This correspondence paper addresses the problem of output feedback stabilization of control systems in networked environments with quality-of-service (QoS) constraints. The problem is investigated in discrete-time state space using Lyapunov’s stability theory and the linear inequality matrix technique. A new discrete-time modeling approach is developed to describe a networked control system (NCS) with parameter uncertainties and nonideal network QoS. It integrates a network-induced delay, packet dropout, and other network behaviors into a unified framework. With this modeling, an improved stability condition, which is dependent on the lower and upper bounds of the equivalent network-induced delay, is established for the NCS with norm-bounded parameter uncertainties. It is further extended for the output feedback stabilization of the NCS with nonideal QoS. Numerical examples are given to demonstrate the main results of the theoretical development.

A new feedback ANC system approach

We propose a new active noise control (ANC) technique. The technique has a feedback structure to have a simple configuration in practical implementation. In this approach, the secondary path is modelled online to ensure convergence of the system as the secondary paths are practically time varying or non-linear. The proposed method consists of two steps: a noise controller which is based on a modified FxLMS algorithm, and a new variable step size (VSS) LMS algorithm which is used to adapt the modelling filter with the secondary path. The proposed algorithm stops injection of the white noise at the optimum point and reactivate the injection during the operation, if needed, to maintain performance of the system. Eliminating continuous injection of the white noise increases the performance of the proposed method significantly and makes it more desirable for practical ANC systems. The computer simulations are presented to show the effectiveness of the proposed method.

Image based visual servo control for fixed wing UAVs tracking linear infrastructure in wind

This paper presents an Image Based Visual Servo control design for Fixed Wing Unmanned Aerial Vehicles tracking locally linear infrastructure in the presence of wind using a body fixed imaging sensor. Visual servoing offers improved data collection by posing the tracking task as one of controlling a feature as viewed by the inspection sensor, although is complicated by the introduction of wind as aircraft heading and course angle no longer align. In this work it is shown that the effects of wind alter the desired line angle required for continuous tracking to equal the wind correction angle as would be calculated to set a desired course. A control solution is then sort by linearizing the interaction matrix about the new feature pose such that kinematics of the feature can be augmented with the lateral dynamics of the aircraft, from which a state feedback control design is developed. Simulation results are presented comparing no compensation, integral control and the proposed controller using the wind correction angle, followed by an assessment of response to atmospheric disturbances in the form of turbulence and wind gusts

Using formative feedback to identify and support first year chemistry students with missing or misconceptions. A Practice Report

Students entering tertiary studies possess a diverse range of prior experiences in their academic preparation for tertiary chemistry so academics need tools to enable them to respond to issues in diversity in conceptual models possessed by entering students. Concept inventories can be used to provide formative feedback to help students identify concepts that they need to address to improve construction of subsequent understanding enabling their learning. Modular, formative learning activities that can be administered inside or outside of class in first year chemistry courses have been developed. These activities address key missing and mis-conceptions possessed by incoming student. Engagement in these learning activities by students and academics will help shift the culture of diagnostic and formative assessment within the tertiary context and address issues around the secondary/tertiary transition. This diagnostic/intervention framework is currently being trialed across five Australian tertiary institutions encompassing a large heterogeneous sample of students.

Non-linear position control for hover and automatic landing of unmanned aerial vehicles

This study presents a disturbance attenuation controller for horizontal position stabilisation for hover and automatic landings of a rotary-wing unmanned aerial vehicle (RUAV) operating close to the landing deck in rough seas. Based on a helicopter model representing aerodynamics during the landing phase, a non-linear state feedback H∞ controller is designed to achieve rapid horizontal position tracking in a gusty environment. Practical constraints including flapping dynamics, servo dynamics and time lag effect are considered. A high-fidelity closed-loop simulation using parameters of the Vario XLC gas-turbine helicopter verifies performance of the proposed horizontal position controller. The proposed controller not only increases the disturbance attenuation capability of the RUAV, but also enables rapid position response when gusts occur. Comparative studies show that the H∞ controller exhibits performance improvement and can be applied to ship/RUAV landing systems.

Output feedback optimal control with contraints

In Chapters 1 through 9 of the book (with the exception of a brief discussion on observers and integral action in Section 5.5 of Chapter 5) we considered constrained optimal control problems for systems without uncertainty, that is, with no unmodelled dynamics or disturbances, and where the full state was available for measurement. More realistically, however, it is necessary to consider control problems for systems with uncertainty. This chapter addresses some of the issues that arise in this situation. As in Chapter 9, we adopt a stochastic description of uncertainty, which associates probability distributions to the uncertain elements, that is, disturbances and initial conditions. (See Section 12.6 for references to alternative approaches to model uncertainty.) When incomplete state information exists, a popular observer-based control strategy in the presence of stochastic disturbances is to use the certainty equivalence [CE] principle, introduced in Section 5.5 of Chapter 5 for deterministic systems. In the stochastic framework, CE consists of estimating the state and then using these estimates as if they were the true state in the control law that results if the problem were formulated as a deterministic problem (that is, without uncertainty). This strategy is motivated by the unconstrained problem with a quadratic objective function, for which CE is indeed the optimal solution (˚Astr¨om 1970, Bertsekas 1976). One of the aims of this chapter is to explore the issues that arise from the use of CE in RHC in the presence of constraints. We then turn to the obvious question about the optimality of the CE principle. We show that CE is, indeed, not optimal in general. We also analyse the possibility of obtaining truly optimal solutions for single input linear systems with input constraints and uncertainty related to output feedback and stochastic disturbances.We first find the optimal solution for the case of horizon N = 1, and then we indicate the complications that arise in the case of horizon N = 2. Our conclusion is that, for the case of linear constrained systems, the extra effort involved in the optimal feedback policy is probably not justified in practice. Indeed, we show by example that CE can give near optimal performance. We thus advocate this approach in real applications.