MPF – Sergio Demian Lerner 1/83 MPF (Mental Poker Framework) A new family of practical and secure Mental Poker protocols Tesis de Licenciatura Autor: Sergio Demian Lerner Director: Dr. Hugo D. Scolnik Departamento de Computación Facultad de Ciencias Exactas y Naturales Universidad de Buenos Aires Noviembre de 2010 MPF – Sergio Demian Lerner 2/83 Agradecimientos A mi esposa Alush, que me alentó siempre a seguir mi camino. A mi hijo Ariel, por su infinita impaciencia. A mis padres, por enseñarme a aprender. A mi director, Dr. Hugo Scolnik, por darme la oportunidad y ayudarme. A los profesores de Exactas, que dan lo mejor de sí para engrandecer día a día la facultad. A mis amigos y en especial a Diego Bursztyn, por el puntapié inicial. Por último a Bruce Schneier, autor del primer libro sobre criptografía que cayó en mis manos. MPF – Sergio Demian Lerner 3/83 Table of Contents Abstract....................................................................................................................................................... 6 List of Figures.............................................................................................................................................. 7 List of Tables................................................................................................................................................ 7 1. Introduction.............................................................................................................................................. 8 1.1. Background...................................................................................................................................... 9 1.2. Mental Protocol Requirements.........................................................................................................9 1.2.1. Basic Requirements.................................................................................................................9 1.2.2. Extended Requirements.........................................................................................................11 1.2.3. Unreal Requirements.............................................................................................................12 1.3. Measuring Performance................................................................................................................13 1.4. Delayed Verifications.....................................................................................................................13 1.5. Non-interactive vs. Interactive Proofs............................................................................................13 1.6. External on-line Auditing ...............................................................................................................14 1.7. Hash Chains.................................................................................................................................. 14 1.8. Theoretical Security in Mental Poker Protocols.............................................................................14 1.9. Kinds of Proofs..............................................................................................................................14 2. MPF base concepts .............................................................................................................................. 16 2.1. MPF base protocols ...................................................................................................................... 18 2.2. MPF instantiation........................................................................................................................... 18 2.3. Verification Protocols.....................................................................................................................18 2.4. Unified Verification protocol (UniVP)..............................................................................................20 2.5. Ad-hoc Verification protocols and malleability................................................................................22 2.6. MPF compared to SRA..................................................................................................................23 2.7. MPF compared to Barnett-Smart...................................................................................................23 2.8. Keys Lifetime................................................................................................................................. 23 2.9. Open Cards Lifetime......................................................................................................................23 2.10. Encoding of Open-Cards.............................................................................................................24 2.10.1. VRF-based CO-PRNGP......................................................................................................24 2.10.2. Hash-based CO-PRNGP.....................................................................................................24 2.11. MPF Rounds................................................................................................................................ 26 2.12. Free Cards................................................................................................................................... 27 2.13. Card Keys.................................................................................................................................... 28 2.14. Card Dealing ...............................................................................................................................28 2.15. Master Card Keys........................................................................................................................ 29 2.16. Unverified Computations .............................................................................................................29 2.17. Card Transfers............................................................................................................................. 29 2.18. Suicide Cheaters.........................................................................................................................29 2.19. VSM-VPUM trick.......................................................................................................................... 30 2.20. VSM-L-OL, The Fastest Dealing Protocol....................................................................................30 2.21. Card Deal Preparation Phase .....................................................................................................31 2.22. Card showdowns......................................................................................................................... 31 2.23. Advanced Card Operations..........................................................................................................31 2.24. Abrupt Drop-out tolerance............................................................................................................31 2.25. Duplicated Cards......................................................................................................................... 33 2.26. Some known CGCs ....................................................................................................................34 3. MPF formal definition............................................................................................................................. 35 3.1. Definitions...................................................................................................................................... 35 3.2. Types............................................................................................................................................. 35 3.3. Private Data Structures..................................................................................................................35 3.4. Miscellaneous Operations..............................................................................................................36 3.5. Operations on Cards...................................................................................................................... 37 3.6. Introduction to MPF base protocols...............................................................................................37 3.6.1. VSM-L-OL..............................................................................................................................38 3.6.2. VSM-VL................................................................................................................................. 39 3.6.3. VSM-VPUM........................................................................................................................... 40 3.6.4. VSM-VL-VUM........................................................................................................................ 41 MPF – Sergio Demian Lerner 4/83 3.7. Card Protocols ..............................................................................................................................42 3.7.1. Create-Deck (CO-PRNGP)....................................................................................................43 3.7.2. Create-Deck (Locking)...........................................................................................................44 3.7.3. Shuffle-Deck.......................................................................................................................... 44 3.7.4. Prepare-Cards-To-Deal