1 / 26

Secrets in Swarm Computing: Dynamic Membership and Private Computation Strategies

This presentation explores the integration of secret sharing methods and dynamic membership in swarm computing environments. We discuss the roles of adversarial models, including honest-but-curious adversaries, and outline strategies for maintaining privacy in group computations. The focus is on how swarm members can share secrets and engage in private computations despite limitations such as eavesdropping threats. We introduce proactive secret sharing techniques to ensure robustness against members leaving the swarm while preserving the integrity of the shared secrets.

noelle
Télécharger la présentation

Secrets in Swarm Computing: Dynamic Membership and Private Computation Strategies

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Swarming Secrets ShlomiDolev (BGU), Juan Garay (AT&T Labs), NivGilboa (BGU) Vladimir Kolesnikov (Bell Labs) Allerton 2009

  2. Talk Outline • Objectives • Adversary • Secret sharing • Membership and thresholds • Private computation in swarms • Perfectly oblivious TM • Computing transitions

  3. Objectives • Why swarms • Why secrets in a swarm • Dynamic membership in swarms • Computation in a swarm

  4. Adversary • Honest but curious • Adaptive • Controls swarm members • Up to a threshold of t members • What about eavesdropping? • We assume that can eavesdrop on the links (incoming and outgoing) of up to t members

  5. Secret sharing Y Share of Player i Bivariate Polynomial P(x,y) i P(x,i) P(i,y) Share of Player i j P(i,j) X i

  6. Join Hey Guys, can I play with you? I’m J! PA(J,y), PA(x,J) D C PC(J,y), PC(x,J) J PB(J,y), PB(x,J) PA(J,y), PA(x,J) Sure! B A

  7. Leave • Problem: • Member retains share after leaving • Adversary could corrupt leaving member and t current members • Refreshing (Proactive Secret Sharing) • Each member shares random polynomial with free coefficient 0

  8. Additional Operations • Merge • Split • Clone

  9. Increase Threshold • Why do it? • How – simple, add random polynomials of higher degree with P(0,0)=0

  10. Decrease Threshold- t to t* B, C, D, … also share random polynomials D C Choose random, Degree t* QA(x,y) J Share of QA(x,y) Share of QA(x,y) B Share of QA(x,y) Share of QA(x,y) A

  11. Decrease Threshold- t to t* Add local shares Add local shares D C Remove high degree terms Interpolate Add local shares Add local shares J B P(x,y) + QA(x,y) + QB(x,y) +… R(x,y) Add local shares A

  12. Decrease Threshold- t to t* Compute reduced P D C Compute reduced P High mon. Of P High mon. Of P High mon. Of P High mon. Of P Compute reduced P J B Compute reduced P Compute reduced P A

  13. Computation in a Swarm • A distributed system • Computational model • Communication between members • Input – we can consider global and non-global input • Changes to “software” • “Output” of computation when computation time is unbounded

  14. What is Hidden • Current state • Input • Software • Time What is not Hidden? • Space

  15. How is it Hidden? • Secret sharing • Input • State • Universal TM • Software • Perfectly oblivious universal TM • Time

  16. Architecture of a Swarm TM

  17. Perfectly Oblivious TM Perfectly Oblivious TM Tape head     Oblivious TM – Head moves as function of number of steps Perfectly Oblivious TM – Head moves as function of current position

  18. Perfectly Oblivious TM Perfectly Oblivious TM     Tape shifts right, copy  that was in previous cell Tape        Orig. Tape Head N N Y N Transition: (st, )(st3,,left) Transition: (st, )(st1,,left) Transition: (st, )(st2,,right) Tape shifts right, head shifts left, Y stays in place, copy  Insert result of “real” transition, 

  19. TM Transitions States Transition Table st1 1 …  … st2 st1 … ns … … st st ns, … …     … Tape head Tape

  20. Encoding States & Cells States st1 10…0 st2 01…0 … 0…010…0 st 0…010…0 … index  index st    … Tape

  21. Computing a Transition • Goal, Compute transition privately in one communication round • Method, Construct new state/symbol unit vector, ns/n, from • Current state - st • Current symbol -  • ns[k]=st[i] [j], for all i, j such that a transition of (i, j) gives state k • Construct new symbol vector in analogous way n[k]= st[i] [j], for all i, j such that a transition of (i, j) gives symbol k

  22. Encoding State Transitions Current Transition Transition Table 0 … 1 0  …   0 0*0 0*1 0*0 st1 ns, st1, St1, 0*0 0*1 0*0 ns, st1, St1, … … 1 1*0 1*1 1*0 st St2, ns, ns, 1*0 1*1 1*0 St2, ns, ns, 0 0*0 0*0 0*1 0*1 0*0 0*0 st2 ns, ns, St2, St2, st2, st2, 0*0+0*1=0 … 0*0+0*0+1*1+1*0=1 1*0+0*1+0*0=0 0…010…0 New state is ns

  23. Encoding Symbol Transitions Current Transition Transition Table 0 … 1 0  …   0 0*0 0*1 0*0 st1 ns, st1, St1, 0*0 0*1 0*0 ns, st1, St1, … … 1 1*0 1*1 1*0 st ns, ns, 1*0 1*1 1*0 St2, St2, ns, ns, 0 0*0 0*1 0*1 0*0 0*0 st2 ns, ns, St2, St2, st2, st2, 0*0 0*0+0*1=0 … 1*0+0*0+0*0+1*0=0 0*1+1*1+0*0=1 0…01 New symbol is 

  24. What about Privacy? • Goal: compute transitions privately • Method • Compute new shares using the st[i] [j], • Reduce polynomial degree

  25. Sharing States & Symbols • Initially • Encode 1 by P(x,y), P(0,0)=1 • Encode 0 by Q(x,y), Q(0,0)=0 • Share bivariate polynomials for state and symbol • Step • Compute 0*0+ 1*0+ 1*1… by • Multiplying and summing local shares • Running “Decrease” degree protocol

  26. Thank You!!!

More Related