Registre à décalage à rétroaction linéaire

Résumé

Un registre à décalage à rétroaction linéaire, ou LFSR (sigle de l'anglais linear feedback shift register), est un dispositif électronique ou logiciel qui produit une suite de bits qui peut être vue comme une suite récurrente linéaire sur le corps fini F2 à 2 éléments (0 et 1). La notion a été généralisée à n'importe quel corps fini. Réalisé électroniquement, dans le cas particulier d'une suite de 0 et de 1, c'est un registre à décalage avec rétroaction linéaire, ce qui signifie que le bit entrant est le résultat d'un OU exclusif (ou XOR) entre plusieurs bits du registre, cette opération étant également l'addition sur le corps fini F2. Ces dispositifs sont simples, peu coûteux et efficaces. La suite récurrente produite par un LFSR est nécessairement périodique à partir d'un certain rang. Les LFSR sont utilisés en cryptographie pour engendrer des suites de nombres pseudo-aléatoires. La fonction de rétroaction est alors choisie de façon à obtenir une période la plus grande possible.

Source officielle

https://fr.wikipedia.org/wiki/Registre_%C3%A0_d%C3%A9calage_%C3%A0_r%C3%A9troaction_lin%C3%A9aire

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Chargement

Stream ciphers are fast cryptographic primitives to provide confidentiality of electronically transmitted data. They can be very suitable in environments with restricted resources, such as mobile devices or embedded systems. Practical examples are cell phones, RFID transponders, smart cards or devices in sensor networks. Besides efficiency, security is the most important property of a stream cipher. In this thesis, we address cryptanalysis of modern lightweight stream ciphers. We derive and improve cryptanalytic methods for different building blocks and present dedicated attacks on specific proposals, including some eSTREAM candidates. As a result, we elaborate on the design criteria for the development of secure and efficient stream ciphers. The best-known building block is the linear feedback shift register (LFSR), which can be combined with a nonlinear Boolean output function. A powerful type of attacks against LFSR-based stream ciphers are the recent algebraic attacks, these exploit the specific structure by deriving low degree equations for recovering the secret key. We efficiently determine the immunity of existing and newly constructed Boolean functions against fast algebraic attacks. The concept of algebraic immunity is then generalized by investigating the augmented function of the stream cipher. As an application of this framework, we improve the cryptanalysis of a well-known stream cipher with irregularly clocked LFSR's. Algebraic attacks can be avoided by substituting the LFSR with a suitable nonlinear driving device, such as a feedback shift register with carry (FCSR) or the recently proposed class of T-functions. We investigate both replacement schemes in view of their security, and devise different practical attacks (including linear attacks) on a number of specific proposals based on T-functions. Another efficient method to amplify the nonlinear behavior is to use a round-based filter function, where each round consists of simple nonlinear operations. We use differential methods to break a reduced-round version of eSTREAM candidate Salsa20. Similar methods can be used to break a related compression function with a reduced number of rounds. Finally, we investigate the algebraic structure of the initialization function of stream ciphers and provide a framework for key recovery attacks. As an application, a key recovery attack on simplified versions of eSTREAM candidates Trivium and Grain-128 is given.

EPFL2008

Chargement

New slip synthesis and theoretical approach of CVT slip control

Yves Rothenbühler

Today's vehicle must be efficient in terms of gas (CO2, NOx) emissions and fuel consumption. Due to improvements in material and oil, the continuous variable transmission (CVT) is now making a breakthrough in the automotive market. The CVT decouples the engine from the wheel speed. CVT enables significant fuel gains by shifting the engine operating point for specific power demands. This optimization of the operating point enables a reduction of this fuel consumption. A CVT is constituted of two pulley sheaves, one fixed and the other one movable in its axial direction when subjected to an external axial force, in general hydraulic. The transition from the minimum to the maximum speed ratio is continuous and an infinite numbers of ratio is available between these two limits. An intermediate element (a metallic belt or chain) transmits the power from the input (the primary) to the exit (the secondary) of the CVT or variator. Further improvements of the fuel consumption and gas emission are still required for example by improving the variator efficiency. Increasing hydraulic performance or decreasing mechanical losses by reducing the axial forces are some solutions. The latter method is not without risks. The diminution of the clamping forces increases the slip between pulley sheaves and the intermediate element. If the axial forces decrease too much, high slip values can be reached and cause damage to the pulleys and the intermediate element. Control of the slip is an attractive solution to decrease the clamping forces in order to safely improve the variator efficiency. The objective of this thesis is to understand and model the slip of each pulley and establish analytic tools dedicate to the variator control. The slip study and the theoretical approach of the CVT variator is applied to the slip control of the variator with a chain. The contribution of this work is threefold. Firstly, the slip and the traction coefficient are analyzed for each pulley. The slip analysis of each pulley is then used to define a new slip synthesis as the summation of the slip of each pulley. It is demonstrated that the slip and the traction coefficient are different for each pulley and depend on the speed ratio of the variator. In low ratios, both the secondary pulley and the primary pulley slip, but only the primary reaches macro slip. For middle or higher ratios, only the secondary pulley slips and reaches high values of slip. Experiments show that the pulley with the smallest clamping force limits the system. Secondly, based on kinematics, force equilibrium, elastic deformations of the pulleys and the intermediate element, a detail model of the variator is proposed. The principal results are the estimation of the clamping forces, of the traction curve for each pulley and of the chain efficiency. These results are implemented in a simpler model that describes the variator dynamics. This last model considers the two pulleys and the intermediate element as free bodies. The hydraulic circuit and the actuators, which are important to take into account for control, are also modeled. Thirdly, the new slip synthesis and the results of the dynamic models are applied to the slip control of the variator in order to improve the efficiency. A pole placement law is applied to the actuators to control the flow that enters or exits the pulleys. With this law, the actuators are decoupled and the bandwidth is increased sufficiently for actuators dynamics to be neglected. The primary and the secondary pressures are decoupled and linearized by an input-output feedback linearization. The resulting system is linear and linear control theory can be applied to control the two pressures. The speed ratio is controlled by the primary clamping force. The secondary pressure is chosen as a function of the control mode of the variator: standard mode or slip mode. In standard mode, the intermediate element is overclamped by 30%, whereas in slip mode, the secondary clamping force is set as a function of the desired slip. By controlling the slip at 2%, the mechanical efficiency was increased by more than 2% and the clamping forces reduced by more than 30%. For the slip control, a proportional-integrator law and a model reference adaptive control (MRAC) are presented and the performances compared. The MRAC gives slightly better results.

EPFL2009

Chargement

On the use of input-output feedback linearization techniques for the control of nonminimum-phase systems

Kahina Guemghar

The objective of the thesis is to study the possibility of using input-output feedback linearization techniques for controlling nonlinear nonminimum-phase systems. Two methods are developed. The first one is based on an approximate input-output feedback linearization, where a part of the internal dynamics is neglected, while the second method focuses on the stabilization of the internal dynamics. The inverse of a nonminimum-phase system being unstable, standard input-output feedback linearization is not effective to control such systems. In this work, a control scheme is developed, based on an approximate input-output feedback linearization method, where the observability normal form is used in conjunction with input-output feedback linearization. The system is feedback linearized upon neglecting a part of the system dynamics, with the neglected part being considered as a perturbation. Stability analysis is provided based on the vanishing perturbation theory. However, this approximate input-output feedback linearization is only effective for very small values of the perturbation. In the general case, the internal dynamics cannot be crushed and need to be stabilized. On the other hand, predictive control is an effective approach for tackling problems with nonlinear dynamics, especially when analytical computation of the control law is difficult. Therefore, a cascade-control scheme that combines input-output feedback linearization and predictive control is proposed. Therein, inputoutput feedback linearization forms the inner loop that compensates the nonlinearities in the input-output behavior, and predictive control forms the outer loop that is used to stabilize the internal dynamics. With this scheme, predictive control is implemented at a re-optimization rate determined by the internal dynamics rather than the system dynamics, which is particularly advantageous when internal dynamics are slower than the input-output behavior of the controlled system. Exponential stability of the cascade-control scheme is provided using singular perturbation theory. Finally, both the approximate input-output feedback linearization and the cascade-control scheme are implemented successfully, on a polar pendulum 'pendubot' that is available at the Laboratoire d'Automatique of EPFL. The pendubot exhibits all the properties that suit the control methodologies mentioned above. From the approximate input-output feedback linearization point of view, the pendubot is a nonlinear system, not input-state feedback linearizable. Also, the pendubot is nonminimum phase, which prevents the use of standard input-output feedback linearization. From the cascade control point of view, although the pendubot has fast dynamics, the input-output feedback linearization separates the input-output system behavior from the internal dynamics, thus leading to a two-time-scale systems: fast input-output behavior, which is controlled using a linear controller, and slow reduced internal dynamics, which are stabilized using model predictive control. Therefore, the cascade-control scheme is effective, and model predictive control can be implemented at a low frequency compared to the input-output behavior.

EPFL2005

Chargement

On the use of input-output feedback linearization techniques for the control of nonminimum-phase systems

Kahina Guemghar

EPFL2005

New slip synthesis and theoretical approach of CVT slip control

Yves Rothenbühler

EPFL2009

EPFL2008