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On Privacy-Preserving Protocols for Smart Metering Systems Defense - Verteidigung - Seminrio de Ps-Graduao Fbio Borges Laboratrio Nacional de Computao Cientfica (LNCC) Coordenao de Sistemas e Redes (CSR) Table of Contents

  1. PPP1 - - SDC-Nets SDC-Nets Using In-Network Aggregation [BM14a] supplier E n c ( m 1 , j ) Enc( m 1 , j ) + Enc( m 2 , j ) + Enc( m 3 , j ) = Enc( m 1 , j + m 2 , j + m 3 , j ) Enc( m 2 , j ) Aggregation Encryption N Enc( m i , j ) = m i , j + H( k i || j ) C = � Enc ( m i , j ) i =1 Decryption N N Dec ( C ) = C − � H( k i || j ) = � m i , j i =1 i =1 August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 22/59

  2. PPP1 PPP1 meets the following requirements Requirement 1 - ✓ Recoverability of consolidated consumption Requirement 2 - ✗ € Recoverability of bill based on dynamic pricing Requirement 3 - ✗ Verification (auditability) Requirement 4 - ✓ Efficiency August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 23/59

  3. € PPP2 - - Commitment Commitment Based on ECC [BM14a] Meters Supplier . . . August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 24/59

  4. € PPP2 - - Commitment Commitment Based on ECC [BM14a] Meters Commit( m Supplier ) || Sign 1 j , 1 j , Commit( m 2 , j ) || Sign 2 , j ) || Sign 3 j , Commit( m 3 j , n i , j g i S | | ) m i , j ( t m i m o j C ) || Sign ˜ , ı j Commit( m ˜ , . ı . . August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 24/59

  5. € PPP2 - - Commitment Commitment Based on ECC [BM14a] Meters Commit( m Supplier ) || Sign 1 j , 1 j , Commit( m 2 , j ) || Sign 2 , j ) || Sign 3 j , Commit( m 3 j , n i , j g i S | | ) m i , j ( t m i m o j C ) || Sign ˜ , ı j Commit( m ˜ , . ı . . Commitment Commit( m i , j ) = k i · H Ω ( j ) + m i , j · P August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 24/59

  6. PPP2 PPP2 meets the following requirements Requirement 1 - ✗ Recoverability of consolidated consumption Requirement 2 - ✓ € Recoverability of bill based on dynamic pricing Requirement 3 - ✓ Verification (auditability) Requirement 4 - ✓ Efficiency August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 25/59

  7. PPP2 - Verification [BDBBM14; BM14b; BM14a; BBM14; BVM15] Supplier Meter i August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 26/59

  8. PPP2 - Verification [BDBBM14; BM14b; BM14a; BBM14; BVM15] Supplier Meter i Enc( m i , j ) , Enc( m i , j +1 ) , . . . August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 26/59

  9. PPP2 - Verification [BDBBM14; BM14b; BM14a; BBM14; BVM15] Supplier Meter i Enc( m i , j ) , Enc( m i , j +1 ) , . . . Q = � j Enc( m i , j ) = � j k i · H Ω ( j ) + m i , j · P August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 26/59

  10. PPP2 - Verification [BDBBM14; BM14b; BM14a; BBM14; BVM15] j k i · H Ω ( j ) j m i , j and V = � v = � Supplier Meter i Enc( m i , j ) , Enc( m i , j +1 ) , . . . Q = � j Enc( m i , j ) = � j k i · H Ω ( j ) + m i , j · P August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 26/59

  11. PPP2 - Verification [BDBBM14; BM14b; BM14a; BBM14; BVM15] j k i · H Ω ( j ) j m i , j and V = � v = � Supplier Meter i Enc( m i , j ) , Enc( m i , j +1 ) , . . . Q = � j Enc( m i , j ) = � j k i · H Ω ( j ) + m i , j · P Verification ? v · P = Q − V August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 26/59

  12. PPP2 - Performance [BM14b; BM14a; BVM15; BDBBM14; LBPN12] � 1 / 3 ��� 64 � � � π o = 2 x = (ln n ) 1 / 3 (ln ln n ) 2 / 3 exp + O (1) 2 , 9 1 . 5 · 10 4 Factorization Elliptic Curves y gives the key bit length y = 506 . 526 exp(0 . 0128886 x ) 1 0 . 5 y = 2 x 0 100 150 200 250 x gives the level of security by brute force August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 27/59

  13. Table of Contents Outline Introduction Privacy-Preserving Protocols (PPPs) PPP1 - Based on SDC-Nets PPP2 - Based on Commitment PPP3 - Based on ADC-Net PPP4 - Based on Quantum Cryptography ADC-Nets Simulation Using Real-World Data Conclusion and Outlook August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 28/59

  14. € PPP3 - - New Concept ADC-Net - [BBM14; BM14b; BVM15] Meters Enc( m Supplier ) || Sign 1 j , 1 j , Enc( m 2 , j ) || Sign 2 , j ) || Sign 3 j , Enc( m 3 j , . . . j ) || Sign ˜ , ı j . ˜ , Enc( m . ı . August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 29/59

  15. € PPP3 - - New Concept ADC-Net - [BBM14; BM14b; BVM15] Meters Encryption Enc( m Enc : Z n × Z n → Z n 2 Supplier ) || Sign 1 j , �→ (1 + n ) m i , j · g h j · k i mod n 2 Enc i ( m i , j ) 1 j , Enc( m 2 , j ) || Sign 2 , j ) || Sign 3 j , Enc( m 3 j , . . . j ) || Sign ˜ , ı j . ˜ , Enc( m . ı . August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 29/59

  16. € PPP3 - - New Concept ADC-Net - [BBM14; BM14b; BVM15] Meters Encryption Enc( m Enc : Z n × Z n → Z n 2 Supplier ) || Sign 1 j , �→ (1 + n ) m i , j · g h j · k i mod n 2 Enc i ( m i , j ) 1 j , Enc( m 2 , j ) || Sign 2 , j Aggregation C j = � ˜ ) || Sign 3 j ı i =1 Enc i ( m i , j ) , Enc( m 3 j , . . . j ) || Sign ˜ , ı j . ˜ , Enc( m . ı . August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 29/59

  17. € PPP3 - - New Concept ADC-Net - [BBM14; BM14b; BVM15] Meters Encryption Enc( m Enc : Z n × Z n → Z n 2 Supplier ) || Sign 1 j , �→ (1 + n ) m i , j · g h j · k i mod n 2 Enc i ( m i , j ) 1 j , Enc( m 2 , j ) || Sign 2 , j Aggregation C j = � ˜ ) || Sign 3 j ı i =1 Enc i ( m i , j ) , Enc( m 3 j , . . . Decryption j ) || Sign ˜ , ı Dec : Z n 2 → Z n j . �→ ( C j · g − ht · s mod n 2 ) − 1 ˜ , Enc( m . ı Dec ( C j ) . n August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 29/59

  18. PPP3 PPP3 meets the following requirements Requirement 1 - ✓ Recoverability of consolidated consumption Requirement 2 - ✓ € Recoverability of bill based on dynamic pricing Requirement 3 - ✓ Verification (auditability) Requirement 4 - ✓ Efficiency August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 30/59

  19. PPP4 - - Quantum Cryptography No Keys [BSM14; BPP12] Meters Supplier . . . August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 31/59

  20. PPP4 - - Quantum Cryptography No Keys [BSM14; BPP12] Meters | ψ � 1 U 1 Supplier | ψ 2 � U 2 . . . ı � U ˜ | ψ ˜ ı August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 31/59

  21. PPP4 - - Quantum Cryptography No Keys [BSM14; BPP12] Meters | ψ � 1 U 1 exp( ı ˆ N U 1 δ 1 ) | ψ 1 � U 1 Supplier | ψ 2 � U 2 � ) | ψ exp( ı ˆ 2 δ U 2 2 N 2 U . . . ı � U ˜ ı ı ) | ψ ˜ ı � U ˜ | ψ ˜ ı δ ˜ ı exp( ı ˆ N U ˜ August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 31/59

  22. PPP4 PPP4 meets the following requirements Requirement 1 - ✓ Recoverability of consolidated consumption Requirement 2 - ✗ € Recoverability of bill based on dynamic pricing Requirement 3 - ✗ Verification (auditability) Requirement 4 - depends on quantum devices Efficiency August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 32/59

  23. Table of Contents Introduction Privacy-Preserving Protocols (PPPs) PPP1 - Based on SDC-Nets PPP2 - Based on Commitment PPP3 - Based on Asymmetric DC-Net (ADC-Net) PPP4 - Based on Quantum Cryptography ADC-Nets Simulation Using Real-World Data Conclusion and Outlook August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 33/59

  24. Symmetric DC-Nets (SDC-Nets) [Cha88] - Dining Cryptographers Problem B Agent A C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 34/59

  25. SDC-Nets [Cha88] - Dining Cryptographers Problem B K AB K BA Agent A C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 34/59

  26. SDC-Nets [Cha88] - Dining Cryptographers Problem B K AB K BA Agent K CB A K BC C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 34/59

  27. SDC-Nets [Cha88] - Dining Cryptographers Problem B K AB K BA Agent K CB A K BC C K CA K AC August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 34/59

  28. SDC-Nets Unconditional Secure [Cha88] B Agent A m 1 , j + k AB + k AC − k BA − k CA C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 35/59

  29. SDC-Nets Unconditional Secure [Cha88] B m + 2 , j k + BA k − Agent BC k − AB k A CB m 1 , j + k AB + k AC − k BA − k CA C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 35/59

  30. SDC-Nets Unconditional Secure [Cha88] B m + 2 , j k + BA k − Agent BC k − AB k A CB m 1 , j + k AB + k AC − k BA − k CA C k − BC k − AC + k CB + k CA m 3 , j August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 35/59

  31. SDC-Nets Unconditional Secure [Cha88] B m + 2 , j k + BA k − Agent BC k − AB k A CB m 1 , j + k AB + k AC − k BA − k CA C k − BC k − AC + k CB + k CA m 3 , j August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 35/59

  32. SDC-Nets Unconditional Secure [Cha88] B m + 2 , j k + BA k − BC k Agent − AB k A CB m 1 , j + k AB + k AC − k BA − k CA C k − BC k − AC + k CB + k CA m 3 , j August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 35/59

  33. SDC-Nets Unconditional Secure [Cha88] B m + 2 , j k + BA k − BC k Agent − AB k A CB m 1 , j + k AB + k AC − k BA − k CA C k − BC k − AC + k CB + k CA m 3 , j August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 35/59

  34. SDC-Nets [GJ04] B Agent A C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 36/59

  35. SDC-Nets [GJ04] B Agent A m 1 , j +H( k AB || j ) +H( k AC || j ) − H( k BA || j ) − H( k CA || j ) C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 36/59

  36. SDC-Nets [GJ04] B m + 2 , j H ( k | | ) BA j + H ( k | | ) BC j − H ( k Agent | | j ) AB − H A ( k | | j ) CB m 1 , j +H( k AB || j ) +H( k AC || j ) − H( k BA || j ) − H( k CA || j ) C August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 36/59

  37. SDC-Nets [GJ04] B m + 2 , j H ( k | | ) BA j + H ( k | | ) BC j − H ( k Agent | | j ) AB − H A ( k | | j ) CB m 1 , j +H( k AB || j ) +H( k AC || j ) − H( k BA || j ) − H( k CA || j ) ) | | j C H ( k BC ) − | j | ( H k AC ) − | | j H ( k + CB ) | | j H ( k + CA m 3 , j August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 36/59

  38. SDC-Net Keys for 10 users August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 37/59

  39. SDC-Net Keys for 10 users August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 37/59

  40. SDC-Net Keys for 10 users August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 37/59

  41. SDC-Nets versus AHEPs Symmetric DC-Nets (SDC-Nets) B m 2 , j + H( k BA || j ) + H( k BC || j ) − H( k AB || j ) − H( k CB || j ) Agent A m 1 , j + H( k AB || j ) + H( k AC || j ) − H( k BA || j ) − H( k CA || j ) m 3 , j + H( k CA || j ) + H( k CB || j ) − H( k AC || j ) − H( k BC || j ) C Additive homomorphic encryption primitives (AHEPs) Agent E n c ( m 1 ) , j Enc( m 1 , j ) · Enc( m 2 , j ) · Enc( m 3 , j ) = Enc( m 1 , j + m 2 , j + m 3 , j ) Enc( m 2 , j ) August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 38/59

  42. ADC-Net Required Properties [BBM14; BM14b; BVM15] Properties SDC-Nets AHEPs ADC-Net Collusion of O (˜ ı ) ✓ ✗ Set of trusted users ✓ ✗ Messages to the counting agent ✓ ✗ Minimum number of messages ✓ ✓ Scalable ✗ ✓ Permanent keys ✓ ✓ Based on trapdoors ✓ ✓ Keys stored per user 2(˜ ı − 1) 1 ı 2 ) Total of keys O (˜ 2 Polynomial time ✓ ✓ One cannot disrupt ✗ ✗ Verification as commitment ✗ ✗ August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 39/59

  43. ADC-Net Required Properties [BBM14; BM14b; BVM15] Properties SDC-Nets AHEPs ADC-Net Collusion of O (˜ ı ) ✓ ✗ ✓ Set of trusted users ✓ ✗ ✓ Messages to the counting agent ✓ ✗ ✓ Minimum number of messages ✓ ✓ ✓ Scalable ✗ ✓ ✓ Permanent keys ✓ ✓ ✓ Based on trapdoors ✓ ✓ ✓ Keys stored per user 2(˜ ı − 1) 1 1 ı 2 ) Total of keys O (˜ 2 O (˜ ı ) Polynomial time ✓ ✓ ✓ One cannot disrupt ✗ ✗ ✓ Verification as commitment ✗ ✗ ✓ August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 40/59

  44. Interesting Results Beyond the State of the Art Result: Asymmetric DC-Nets are abstractions of Symmetric DC-Nets [BBM14] August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 41/59

  45. Interesting Results Beyond the State of the Art Result: Asymmetric DC-Nets are abstractions of Symmetric DC-Nets [BBM14] Result: AHEPs are particular cases of ADC-Nets August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 41/59

  46. Interesting Results Beyond the State of the Art Result: Asymmetric DC-Nets are abstractions of Symmetric DC-Nets [BBM14] Result: AHEPs are particular cases of ADC-Nets Example Paillier is a particular case of an ADC-Net August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 41/59

  47. Table of Contents Introduction Privacy-Preserving Protocols (PPPs) PPP1 - Based on SDC-Nets PPP2 - Based on Commitment PPP3 - Based on Asymmetric DC-Net (ADC-Net) PPP4 - Based on Quantum Cryptography ADC-Nets Simulation Using Real-World Data Conclusion and Outlook August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 42/59

  48. Dataset Raw Dataset ✗ The raw dataset has inconsistencies August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 43/59

  49. Dataset Raw Dataset ✗ The raw dataset has inconsistencies Sanitized Dataset ✓ ◮ 6 435 meters ◮ 25 726 rounds ◮ 165 546 810 measurements August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 43/59

  50. Dataset Raw Dataset ✗ The raw dataset has inconsistencies Sanitized Dataset ✓ ◮ 6 435 meters ◮ 25 726 rounds ◮ 165 546 810 measurements Verification Inconsistencies ⇒ measurements collected without verification August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 43/59

  51. Comparison of requirements between Privacy-Preserving Protocol (PPP) € Protocol Efficiency Enc Agg Dec PPP1 ✓ ✗ ✗ O (1) O (˜ ı ) O (˜ ı ) PPP2 O (log( k )) O (˜ ı ) O ( k ) ✗ ✓ ✓ PPP3 ✓ ✓ ✓ O (log( k )) O (˜ ı ) O (log( k )) EPPP4SMS 2 O (log( k )) O (˜ ı ) O (log( n )) ✓ ✓ ✓ LOP - SDC-Net O (˜ ı ) NA O (˜ ı ) ✓ ✗ ✗ Paillier - AHEP ✓ ✗ ✗ O (log( n )) O (˜ ı ) O (log( n )) IEEE Trans. Smart Grid - Impact Factor: 4.334 “EPPP4SMS: Efficient Privacy-Preserving Protocol for Smart Metering Systems and Its Simulation Using Real-World Data” August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 44/59

  52. Overall Performance Race protocols Smart Grids Telecooperation PPP1 PPP2 PPP3 EPPP4SMS LOP Paillier Smart Meters Efficient Protocols August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 45/59

  53. Overall Performance Race protocols PPP1: the Fastest Horst Görtz Foundation PPP1 PPP2 PPP3 EPPP4SMS LOP Paillier TK Maxx Darmstadt Efficient Protocols August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 46/59

  54. Overall Performance Race protocols PPP3: the Complete PPP3 is the Favorite PPP1 PPP2 PPP3 EPPP4SMS LOP Paillier One Selected Award 10 Selected Papers August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 47/59

  55. Table of Contents Introduction Privacy-Preserving Protocols (PPPs) PPP1 - Based on SDC-Nets PPP2 - Based on Commitment PPP3 - Based on Asymmetric DC-Net (ADC-Net) PPP4 - Based on Quantum Cryptography ADC-Nets Simulation Using Real-World Data Conclusion and Outlook August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 48/59

  56. Conclusion ◮ Privacy-Preserving Protocols (PPPs) only work for large aggregations August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 49/59

  57. Conclusion ◮ PPPs only work for large aggregations ◮ PPP1 has the fastest Enc ( m i , j ) August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 49/59

  58. Conclusion ◮ PPPs only work for large aggregations ◮ PPP1 has the fastest Enc ( m i , j ) ◮ PPP2 and PPP3 are exponentially faster than others August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 49/59

  59. Conclusion ◮ PPPs only work for large aggregations ◮ PPP1 has the fastest Enc ( m i , j ) ◮ PPP2 and PPP3 are exponentially faster than others ◮ PPP4 is resistant against quantum attacks August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 49/59

  60. Conclusion ◮ PPPs only work for large aggregations ◮ PPP1 has the fastest Enc ( m i , j ) ◮ PPP2 and PPP3 are exponentially faster than others ◮ PPP4 is resistant against quantum attacks ◮ The concept of ADC-Nets is introduced August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 49/59

  61. Selected Publications Journal Papers [BM14b] Fábio Borges and Max Mühlhäuser. EPPP4SMS: efficient privacy- preserving protocol for smart metering systems and its simulation using real-world data. IEEE trans. smart grid , 5(6):2701–2708, 2014 Impact Factor 4.334 h5-index 54 [BSM14] Fábio Borges, Raqueline A. M. Santos, and Franklin L. Marquezino. Preserving privacy in a smart grid scenario using quantum mechan- ics. Security and communication networks :n/a–n/a, 2014 Impact Factor 0.433 h5-index 19 [LBPN12] Pedro Lara, Fábio Borges, Renato Portugal, and Nadia Nedjah. Par- allel modular exponentiation using load balancing without precom- putation. Journal of computer and system sciences , 78(2):575– 582, 2012 Impact Factor 1.091 h5-index 30 August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 50/59

  62. Selected Publications Award [BBM14] Fábio Borges, Johannes Buchmann, and Max Mühlhäuser. Introducing asymmetric dc-nets. In Communications and network security (CNS), 2014 IEEE conference on , 2014, pages 508–509 Best Poster Award - IEEE Communications Society August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 51/59

  63. Selected Publications Conference Papers [BBM14] Fábio Borges, Johannes Buchmann, and Max Mühlhäuser. Introducing asymmetric dc-nets. In Communications and network security (CNS), 2014 IEEE conference on , 2014, pages 508–509 [BM14a] Fábio Borges and Leonardo A. Martucci. iKUP keeps users’ privacy in the smart grid. In Communications and network security (CNS), 2014 IEEE conference on , 2014, pages 310–318 [BDBBM14] Fábio Borges, Denise Demirel, Leon Böck, Johannes Buchmann, and Max Mühlhäuser. A privacy- enhancing protocol that provides in-network data aggregation and verifiable smart meter billing. In Computers and communication (ISCC), 2014 IEEE symposium on , 2014, pages 1–6 [BMBM14] Fábio Borges, Leonardo A. Martucci, Filipe Beato, and Max Mühlhäuser. Secure and privacy- friendly public key generation and certification. In Trust, security and privacy in computing and communications (TrustCom), 2014 IEEE 13th international conference on , 2014, pages 114–121 [BMM12] Fábio Borges, Leonardo A. Martucci, and Max Mühlhäuser. Analysis of privacy-enhancing pro- tocols based on anonymity networks. In Smart grid communications (SmartGridComm), 2012 IEEE third international conference on , 2012, pages 378–383 [BPP12] Fábio Borges, Albrecht Petzoldt, and Renato Portugal. Small private keys for systems of mul- tivariate quadratic equations using symmetric cryptography. In XXXIV CNMAC - congrasso nacional de matemática aplicada e computacional . Águas de Lindóia - SP, 2012, pages 1085– 1091 [BVM15] Fábio Borges, Florian Volk, and Max Mühlhäuser. Efficient, verifiable, secure, and privacy-friendly computations for the smart grid. In Innovative smart grid technologies conference (ISGT), 2015 IEEE power energy society , 2015, pages 1–5 August 31, 2015 – LNCC – CSR – Pós – TU Darmstadt – FB – 52/59

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