Privacy-friendly Forecasting for the Smart Grid using Homomorphic - PowerPoint PPT Presentation

Privacy-friendly Forecasting for the Smart Grid using Homomorphic Encryption J. Bos 1 , W. Castryck 2 , 3 , I. Iliashenko 2 and F . Vercauteren 2 , 4 1 NXP Semiconductors 2 COSIC, KU Leuven and imec 3 Université de Lille-1 4 Open Security Research AfricaCrypt 2017 Dakar, Senegal

The Smart-Grid 1 / 24

The Smart-Grid load consumption weather conditions bills structure of a local utility grid . . . 1 / 24

The Smart-Grid Benefits control of consumption optimization of utility production improved logistics source of research data 1 European Commission. Benchmarking smart metering deployment in the EU-27 with a focus on electricity. Technical report 365, June 2014. 2 / 24

The Smart-Grid Benefits control of consumption optimization of utility production improved logistics source of research data “The Third Energy Package requires Member States to ensure implementa- tion of intelligent metering systems for the long-term benefit of consumers. [. . . ] For electricity, there is a target of rolling out at least 80 % by 2020, of the positively assessed cases. 1 ” 1 European Commission. Benchmarking smart metering deployment in the EU-27 with a focus on electricity. Technical report 365, June 2014. 2 / 24

Privacy Concerns in the Smart-Grid Update rate of smart-meters: ≤ 15 min (EU recommendation) 3 / 24

Privacy Concerns in the Smart-Grid Update rate of smart-meters: ≤ 15 min (EU recommendation) Power step changes due to individual appliance events. G.W. Hart. Nonintrusive appliance load monitoring. Proceedings of the IEEE , 80(12):1870-1891, 1992 3 / 24

Homomorphic Encryption Enc ( x ) Enc ( f ( x )) 4 / 24

Homomorphic Encryption Enc ( x ) Enc ( f ( x )) + or × Partially HE: + and up to some consecutive × Somewhat HE: + and × Fully HE: 4 / 24

Homomorphic Encryption Enc ( x ) Enc ( f ( x )) + or × Partially HE: Complexity + and up to some consecutive × Somewhat HE: + and × Fully HE: 4 / 24

Prediction for the Smart-Grid actual load 3 load demand , kW 2 1 0 0 1 , 000 2 , 000 3 , 000 4 , 000 time , min 5 / 24

Prediction for the Smart-Grid actual load fitting function 3 load demand , kW 2 1 0 0 1 , 000 2 , 000 3 , 000 4 , 000 time , min 5 / 24

Prediction for the Smart-Grid actual load fitting function 3 load demand , kW 2 1 0 0 1 , 000 2 , 000 3 , 000 4 , 000 time , min n n � y forecast − y actual � MSE = 1 ( y forecast − y actual ) 2 , MAPE = 100 � � i i � � n i i n y actual � � i i = 1 i = 1 5 / 24

Prediction for the Smart-Grid Time period ARIMA BATS NNET PERSIST TBATS 30 min 91 57 49 75 72 60 min 51 59 52 60 63 MAPE for varying periods and algorithms Source: Veit et al. Household electricity demand forecasting: benchmarking state-of-the-art methods. In Proceedings of e-Energy ’14. 2014. ANNs are the best choice, but . . . 6 / 24

Prediction for the Smart-Grid Time period ARIMA BATS NNET PERSIST TBATS 30 min 91 57 49 75 72 60 min 51 59 52 60 63 MAPE for varying periods and algorithms Source: Veit et al. Household electricity demand forecasting: benchmarking state-of-the-art methods. In Proceedings of e-Energy ’14. 2014. ANNs are the best choice, but . . . . . . they contain highly non-linear sigmoids as activation functions. 6 / 24

Prediction for the Smart-Grid 1 − 1 . 5 − 1 − 0 . 5 0 . 5 1 1 . 5 − 1 7 / 24

Prediction for the Smart-Grid 1 − 1 . 5 − 1 − 0 . 5 0 . 5 1 1 . 5 − 1 tanh x − 1 3 x 3 3 x 3 + x − 1 15 x 5 2 3 x 3 + x − 1 15 x 5 − 2 315 x 7 17 7 / 24

Prediction for the Smart-Grid 1 − 1 . 5 − 1 − 0 . 5 0 . 5 1 1 . 5 − 1 tanh x − 1 3 x 3 3 x 3 + x − 1 15 x 5 2 3 x 3 + x − 1 15 x 5 − 2 315 x 7 17 7 / 24

Polynomial Neural Networks ANNs with polynomial activation functions: x 2 pattern recognition (Microsoft’s CryptoNets) GMDH forecasting 8 / 24

Polynomial Neural Networks ANNs with polynomial activation functions: x 2 pattern recognition (Microsoft’s CryptoNets) GMDH forecasting Published by Alexei Ivakhnenko in 1970. Originally used for wheat harvest prediction in Ukraine. 8 / 24

Polynomial Neural Networks ANNs with polynomial activation functions: x 2 pattern recognition (Microsoft’s CryptoNets) GMDH forecasting Published by Alexei Ivakhnenko in 1970. Originally used for wheat harvest prediction in Ukraine. Applied for load forecasting: comparable with conventional ANNs MAPE ≈ 2 % 8 / 24

Polynomial Neural Networks ANNs with polynomial activation functions: x 2 pattern recognition (Microsoft’s CryptoNets) GMDH forecasting Published by Alexei Ivakhnenko in 1970. Originally used for wheat harvest prediction in Ukraine. Applied for load forecasting: comparable with conventional ANNs MAPE ≈ 2 % over a town, a big city district or a region 8 / 24

Group Method of Data Handling Approximation by truncated Wiener series n n n n n n � � � � � � a 0 + a i x i + a ij x i x j + a ijk x i x j x k + . . . i = 1 i = 1 j = i i = 1 j = i k = j n is the number of previous states of a system. 9 / 24

Group Method of Data Handling Approximation by truncated Wiener series n n n n n n � � � � � � a 0 + a i x i + a ij x i x j + a ijk x i x j x k + . . . i = 1 i = 1 j = i i = 1 j = i k = j n is the number of previous states of a system. Find coefficients { a i } , { a ij } , { a ijk } , . . . 9 / 24

Group Method of Data Handling Approximation by truncated Wiener series n n n n n n � � � � � � a 0 + a i x i + a ij x i x j + a ijk x i x j x k + . . . i = 1 i = 1 j = i i = 1 j = i k = j n is the number of previous states of a system. Find coefficients { a i } , { a ij } , { a ijk } , . . . Can be replaced by a composition of quadratic polynomials { b ij 0 + b ij 1 x i + b ij 2 x j + b ij 3 x i x j + b ij 4 x 2 i + b ij 5 x 2 j } . 9 / 24

Group Method of Data Handling A neural network with the structure 4 – 4 – 3 – 2 – 1. Input variables Output value 10 / 24

Group Method of Data Handling x i Neuron output b ij 0 + b ij 1 x i + b ij 2 x j + b ij 3 x i x j + b ij 4 x 2 i + b ij 5 x 2 j x j 11 / 24

Group Method of Data Handling x i Neuron output b ij 0 + b ij 1 x i + b ij 2 x j + b ij 3 x i x j + b ij 4 x 2 i + b ij 5 x 2 j x j Learning Define coefficients of a quadratic polynomial from Y = bX + e , where X = ( 1 , x i , x j , x i x j , x 2 i , x 2 j ) ⊺ , b = ( b ij 0 , b ij 1 , b ij 2 , b ij 3 , b ij 4 , b ij 5 ) , Y is the expected output, e is a random noise. Can be done by the least-squares method. 11 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables 12 / 24

Group Method of Data Handling Input variables Output value 12 / 24

Sample data Source: Commission for Energy Regulation (CER) is the regulator for the electricity and natural gas sectors in Ireland. Over 5,000 Irish homes and businesses observed. Electricity consumed during 30 minutes intervals. Time frame: July 14 2009 to Dec. 31 2010. Data splits: training set (1 year), test set (half a year). 13 / 24

Structure of the GMDH-network Input layer (51 nodes): previous 48 half-hour load measures, day of the week, month, temperature. Hidden layers: 3 hidden layers of sizes 8 , 4 , 2. Output node: predicted consumption during the next 30 minutes. Resulting polynomial is of degree 2 4 = 16. 14 / 24

Implementation in the Plain Mode: Floating Point Floating point experiments 80 MAPE , % 60 40 20 0 0 20 40 60 80 100 number of houses # houses 1 2 5 10 20 50 100 avg. MAPE(%) 90 55 33 23 15 9 7 15 / 24

Implementation in the Plain Mode: Floating Point Floating point experiments 80 MAPE , % 60 40 20 0 0 20 40 60 80 100 number of houses # houses 1 2 5 10 20 50 100 avg. MAPE(%) 90 55 33 23 15 9 7 15 / 24

Fan-Vercauteren SHE Ring-LWE based SHE (2012). Parameters: ring R = Z [ X ] / ( f ( X )) with f ( X ) = X d + 1, d = 2 n moduli t , q ∈ Z : q ≫ t , plaintext and ciphertext spaces R t = R / ( t ) , R q = R / ( q ) , key and error distributions over R : χ key , χ err discrete Gaussian with small σ . 16 / 24

Fan-Vercauteren SHE Ring-LWE based SHE (2012). Parameters: ring R = Z [ X ] / ( f ( X )) with f ( X ) = X d + 1, d = 2 n moduli t , q ∈ Z : q ≫ t , plaintext and ciphertext spaces R t = R / ( t ) , R q = R / ( q ) , key and error distributions over R : χ key , χ err discrete Gaussian with small σ . Key generation s ← χ key , a ← U ( R q ) , e ← χ err b = [ − ( a · s + e )] q pk = ( a , b ) 16 / 24