Abstract. Since Gentry's breakthrough work in 2009, homomorphic cryptography has received a widespread attention. Implementation of a fully homomorphic cryptographic scheme is however still highly expensive. Somewhat Homomorphic Encryption (SHE) schemes, on the other hand, allow only a limited number of arithmetical operations in the encrypted domain, but are more practical. Many SHE schemes have been proposed, among which the most competitive ones rely on (Ring-) Learning With Error (RLWE) and operations occur on high-degree polynomials with large coe cients. This work focuses in particular on the Chinese Remainder Theorem representation (a.k.a. Residue Number Systems) applied to large coe cients. In SHE schemes like that of Fan and Vercauteren (FV), such a representation remains hardly compatible with procedures involving coe cient-wise division and rounding required in decryption and homomorphic multiplication. This paper suggests a way to entirely eliminate the need for multi-precision arithmetic, and presents techniques to enable a full RNS implementation of FV-like schemes. For dimensions between 2 11 and 2 15 , we report speed-ups from 5⇥ to 20⇥ for decryption, and from 2⇥ to 4⇥ for multiplication.

because of both the global energy crisis and the necessary improvement of energy efficiency in buildings, one of the largest sectors of energy consumption and greenhouse gases emissions, a strategy allowing managing energy resources is proposed. Its aim is reducing energy consumption and promoting the use of renewable energy, while ensuring thermal comfort, when heating "multi-energy" buildings, thanks to indoor temperature control schemes. Three schemes (based on a commonly-used PID controller and on the combination of PID and model predictive or fuzzy controllers) were tested in simulation, using dynamic models describing the thermal behavior of a building, and fully met the management strategy's requirements, especially reducing the consumption of fossil energy. Three criteria describing the way energy is used and controlled in real-time were defined with the aim of evaluating the control schemes performance and adapting the strategy to the specific use of a building. The PID-MPC provided the best results while the PID-FLC proved to be a very good compromise, thanks to both the flexibility and the adaptability offered by fuzzy logic, between the easy-todevelop but not-very-efficient PID and the efficient but hard-to-develop PID-MPC.

To cite this version:Julien Eynard, Stéphane Grieu, Monique Polit. Wavelet-based multi-resolution analysis and artificial neural networks for forecasting temperature and thermal power consumption. Engineering Applications of Artificial Intelligence, Elsevier, 2011, 24 (3) Domitia, 52 Av. Paul Alduy, 66860, Perpignan, Abstract: as part of the OptiEnR research project, the present paper deals with outdoor temperature and thermal power consumption forecasting. This project focuses on optimizing the functioning of a multi-energy district boiler (La Rochelle, west coast of France), adding to the plant a thermal storage unit and implementing a model-based predictive controller. The proposed short-term forecast method is based on the concept of time series and uses both a wavelet-based multi-resolution analysis and multi-layer artificial neural networks. One could speak of "MRA-ANN" methodology. The discrete wavelet transform allows decomposing sequences of past data in subsequences (named coefficients) according to different frequency domains, while preserving their temporal characteristics. From these coefficients, multi-layer Perceptrons are used to estimate future subsequences of 4 hours and 30 minutes. Future values of outdoor temperature and thermal power consumption are then obtained by simply summing up the estimated coefficients. Substituting the prediction task of an original time series of high variability by the estimation of its wavelet coefficients on different levels of lower variability is the main idea of the present work. In addition, the sequences of past data are completed, for each of their components, by both the minute of the day and the day of the year to place the developed model in time. The present paper mainly focuses on the impact on forecast accuracy of various parameters, related with the discrete wavelet transform, such as both the wavelet order and the decomposition level, and the topology of the neural networks used. The number of past sequences to take into account and the chosen time step were also major concerns. The optimal configuration for the tools used leads to very good forecasting results and validates the proposed MRA-ANN methodology.

both indoor temperature regulation and energy resources management in buildings require the design and the implementation of efficient and readily adaptable control schemes. One can use standard schemes, such as "on/off" and PID, or "advanced" schemes, such as MPC (Model Predictive Control). Another approach would be considering artificial intelligence tools. In this sense, fuzzy logic allows controlling temperature and managing energy sources, taking advantage of the flexibility offered by linguistic reasoning. With this kind of approaches, both the specific use of a building and the specificities of a proposed energy management strategy can be easily taken into account when designing or adjusting the control scheme, without having to model the process to be controlled. PID controllers being commonly used in buildings engineering, the proposed control scheme is built on the basis of a PID controller. This allows implementing the scheme even if a control system based on such a controller is already in use. So, a hybrid PID-fuzzy scheme is proposed for managing energy resources in buildings, as the combination of two usual control structures based on PID and fuzzy controllers: the "parallel" structure (according to the current dynamical state of the considered process, either the PID or the fuzzy controller is selected) and the "fuzzy supervision" of a PID controller. To test the scheme in simulation, a building mock-up has been built, instrumented and modeled. Finally, criteria describing the way energy is used and controlled in real-time have been defined with the aim of evaluating both the proposed strategy and the control scheme performance.

International audienceIn France, buildings account for a large part of the energy consumption and carbon emissions. Both are mainly due to Heating, Ventilation and AirConditioning (HVAC) systems. Because older, oversized or poorly maintained systems may be using more energy and costing more to operate than necessary, new management approaches are needed. In addition, energy efficiency can be improved in central heating and cooling systems by introducing zoned operation. So, the present work deals with the predictive control of multizone HVAC systems in non-residential buildings. First, a real non-residential building located in Perpignan (south of France) has been modelled using the EnergyPlus software. We used the Predicted Mean Vote (PMV) index as a thermal comfort indicator and developed low-order ANN-based models to be used as controller's internal models. A genetic algorithm allowed the optimization problem to be solved. Using the proposed strategy, the operation of all the HVAC subsystems is optimized by computing the right time to turn them on and off, in both heating and cooling modes. Energy consumption is minimized and thermal comfort requirements are met. In order to appraise the proposed management strategy, it has been compared to basic scheduling techniques. The simulation results highlight the pertinence of a predicitive approach for multizone HVAC systems management

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Recent studies have demonstrated the importance of protecting the hardware implementations of cryptographic functions against side channel and fault attacks. In last years, very efficient implementations of modular arithmetic have been done in RNS (RSA, ECC, pairings) as well on FPGA as on GPU. Thus the protection of RNS Montgomery modular multiplication is a crucial issue. For that purpose, some techniques have been proposed to protect this RNS operation against side channel analysis. Nevertheless, there are still no effective and generic approaches for the detection of fault injection, which would be additionnally compatible with a leak resistant arithmetic. This paper proposes a new RNS Montgomery multiplication algorithm with fault detection capability. A mathematical analysis demonstrates the validity of the proposed approach. Moreover, an architecture that implements the proposed algorithm is presented. A comparative analysis shows that the introduction of the proposed fault detection technique requires only a limited increase in area.

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