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Secure Multi-Party Computation Lecture 15 Must We Trust ? - PowerPoint PPT Presentation

Secure Multi-Party Computation Lecture 15 Must We Trust ? Must We Trust ? Can we have an auction without an auctioneer?! Must We Trust ? Can we have an auction without an auctioneer?! Must We Trust ? Can we


  1. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment)

  2. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment) Also called “Honest-But-Curious” adversary

  3. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment) Also called “Honest-But-Curious” adversary Will require that simulator also corrupts passively

  4. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment) Also called “Honest-But-Curious” adversary Will require that simulator also corrupts passively Simplifies several cases

  5. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment) Also called “Honest-But-Curious” adversary Will require that simulator also corrupts passively Simplifies several cases e.g. coin-tossing [why?], commitment [coming up]

  6. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment) Also called “Honest-But-Curious” adversary Will require that simulator also corrupts passively Simplifies several cases e.g. coin-tossing [why?], commitment [coming up] Oddly, sometimes security against a passive adversary is more demanding than against an active adversary

  7. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment) Also called “Honest-But-Curious” adversary Will require that simulator also corrupts passively Simplifies several cases e.g. coin-tossing [why?], commitment [coming up] Oddly, sometimes security against a passive adversary is more demanding than against an active adversary Active adversary: too pessimistic about what guarantee is available even in the IDEAL world

  8. Passive Adversary Gets only read access to the internal state of the corrupted players (and can use that information in talking to environment) Also called “Honest-But-Curious” adversary Will require that simulator also corrupts passively Simplifies several cases e.g. coin-tossing [why?], commitment [coming up] Oddly, sometimes security against a passive adversary is more demanding than against an active adversary Active adversary: too pessimistic about what guarantee is available even in the IDEAL world e.g. 2-party SFE for OR, with output going to only one party (trivial against active adversary; impossible without computational assumptions against passive adversary)

  9. More Example Functionalities

  10. More Example Functionalities Can consider “arbitrary” functionalities

  11. More Example Functionalities Can consider “arbitrary” functionalities i.e., arbitrary (PPT) program of the trusted party to be emulated

  12. More Example Functionalities Can consider “arbitrary” functionalities i.e., arbitrary (PPT) program of the trusted party to be emulated Some simple (but important) examples:

  13. More Example Functionalities Can consider “arbitrary” functionalities i.e., arbitrary (PPT) program of the trusted party to be emulated Some simple (but important) examples: Secure Function Evaluation

  14. More Example Functionalities Can consider “arbitrary” functionalities i.e., arbitrary (PPT) program of the trusted party to be emulated Some simple (but important) examples: Secure Function Evaluation e.g. Finding max, Oblivious Transfer (coming up)

  15. More Example Functionalities Can consider “arbitrary” functionalities i.e., arbitrary (PPT) program of the trusted party to be emulated Some simple (but important) examples: Secure Function Evaluation e.g. Finding max, Oblivious Transfer (coming up) Can be randomized: e.g. Coin-tossing

  16. More Example Functionalities Can consider “arbitrary” functionalities i.e., arbitrary (PPT) program of the trusted party to be emulated Some simple (but important) examples: Secure Function Evaluation e.g. Finding max, Oblivious Transfer (coming up) Can be randomized: e.g. Coin-tossing “Reactive” functionalities (maintains state over multiple rounds)

  17. More Example Functionalities Can consider “arbitrary” functionalities i.e., arbitrary (PPT) program of the trusted party to be emulated Some simple (but important) examples: Secure Function Evaluation e.g. Finding max, Oblivious Transfer (coming up) Can be randomized: e.g. Coin-tossing “Reactive” functionalities (maintains state over multiple rounds) e.g. Commitment (coming up)

  18. Commitment

  19. Commitment Commit now, reveal later

  20. Commitment Commit now, reveal later Intuitive properties: hiding and binding

  21. Commitment IDEAL World Commit now, reveal later Intuitive properties: hiding and binding

  22. Commitment IDEAL World Commit now, reveal later Intuitive properties: hiding and binding t c i d e r P e W ! ! S K C O T S

  23. Commitment IDEAL World Commit now, reveal later Intuitive properties: hiding and binding t c i d e r P e W ! ! S K C O T S

  24. Commitment IDEAL World Commit now, reveal later Intuitive properties: hiding and binding Really? t c i d e r P e W ! ! S K C O T S

  25. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding Really? t c i d e r P e W ! ! S K C O T S

  26. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding Really? t c i d e r P e W ! ! S K C O T S

  27. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding F COM Really? t c i d e r P e W ! ! S K C O T S

  28. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding up F up Really? t c i d e r P e W ! ! S K C O T S

  29. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding up F “COMMIT” up Really? t c i d e r P e W ! ! S K C O T S

  30. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding up F “COMMIT” up Really? t c i m d commit e r P e W m ! COMMIT: ! S K F C O T S

  31. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding up F Really? t c i m d commit e r P e W m ! COMMIT: ! S K F C O T S Next Day

  32. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding up F up “REVEAL” Really? t c i m d commit e r P e W m ! COMMIT: ! S K F C O T S Next Day

  33. Commitment IDEAL World Commit now, 30 Day Free Trial reveal later Intuitive properties: hiding and binding up F up “REVEAL” Really? t c i m d commit e r P e W m ! COMMIT: ! S K F C O T S Next Day reveal m REVEAL: m F

  34. Oblivious Transfer IDEAL World t c i d e r P e W ! ! S K C O T S

  35. Oblivious Transfer IDEAL World Pick one out of two, without revealing which t c i d e r P e W ! ! S K C O T S

  36. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: transfer partial information t c i d e r P e W “obliviously” ! ! S K C O T S

  37. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: transfer partial information All 2 of t c i d e r P e W them! “obliviously” ! ! S K C O T S

  38. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: transfer partial I need just information All 2 of one t c i d e r P e W them! “obliviously” ! ! S K C O T S

  39. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: transfer partial I need just information All 2 of one t c i d e r P e W them! “obliviously” ! ! S K C O Sure T S

  40. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: transfer partial I need just information All 2 of one t c i d e r P e W them! But can’t “obliviously” ! ! S K C O Sure T tell you S which

  41. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: F OT transfer partial I need just information All 2 of one t c i d e r P e W them! But can’t “obliviously” ! ! S K C O Sure T tell you S which

  42. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: F OT transfer partial A:up, B:down I need just information All 2 of one t c i d e r P e W them! But can’t “obliviously” ! ! S K C O Sure T tell you S which

  43. Oblivious Transfer IDEAL World Pick one out of two, without revealing which Intuitive property: F OT transfer partial A:up, B:down A I need just information All 2 of one t c i d e r P e W them! But can’t “obliviously” ! ! S K C O Sure T tell you S which

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