Universally composable mpc using tamper proof hardware
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Universally Composable MPC using Tamper-Proof Hardware. Jonathan Katz. What to do??!. Overview I. Goal : construct protocols that are secure when run concurrently alongside arbitrary other protocols Specifically, within the UC framework [C01]

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Universally Composable MPC using Tamper-Proof Hardware

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Universally composable mpc using tamper proof hardware

Universally Composable MPC using Tamper-Proof Hardware

Jonathan Katz


Overview i

What to do??!

Overview I

  • Goal: construct protocols that are secure when run concurrently alongside arbitrary other protocols

    • Specifically, within the UC framework [C01]

  • Unfortunately…this is impossible in the “plain” network model[CF01]


Overview ii

Overview II

  • One idea: introduce setup assumptions

  • Previous suggestions seem to require some trusted parties (think: CRS)

    • Is this inherent?

  • This talk: physical assumptions as a possible alternative to trusted setup

    • Specifically, the existence of tamper-proof hardware


Outline of the talk

Outline of the talk

  • MPC, UC framework, impossibility results, existing setup assumptions, …

  • Physical assumptions (e.g., tamper-proof hardware) as a new direction

    • Potential advantages

  • Quick intuition as to why tamper-proof hardware helps

  • UC-MPC from tamper-proof hardware


A brief review

A (brief) review


Secure multi party computation

Secure multi-party computation

  • Parties P1, …, Pn holding x1, …, xn

  • Want to compute f = (f1(x1, …, xn), …, fn(x1, …, xn)), while maintaining

    • Privacy

    • Correctness

    • Independence of inputs

  • Formalize using simulation paradigm


Settings

Settings

  • Stand-alone setting

    • Major results from mid-80s establish that secure computation of any function is possible [Y82,GMW87,RB89,…]

  • Concurrent setting

    • Situation is less clear…

    • Focus of much recent research

    • Let’s see the problem


Zero knowledge stand alone

(prover)

transcript

x  Lwitness w

(simulator)

com

c

c’

open

x  L

Zero knowledge, stand-alone

(verifier)


Zero knowledge concurrent

open

com

com

c

c

c

c’

c’

open

com

Zero knowledge, concurrent

Exponential blowup!


Handling concurrent executions

UC framework [C01]

Handling concurrent executions

  • For ZK, security in a concurrent setting is possible [RK99,KP01,PRS02]

  • What about other functions?

  • How to manage the complexity of this setting, in general?


Simplified overview

Simplified overview

Interactive distinguisher

(aka “environment”)

(real world)

(ideal world)


Simplified overview1

(Simplified) overview

  • A key feature of the model is that the environment cannot be rewound

  • A protocol proven secure in the UC framework remains secure under general concurrent composition

    • Analyze a protocol in isolation; conclude that it is secure in a concurrent setting


Impossibility results

Impossibility results

  • In the “plain model” with no honest majority, UC-computation of any “interesting” function is impossible [CF01,CKL03]

  • In some sense, this is an inherent limitation of concurrency

    • I.e., not just an artifact of the UC framework [L03,L04]


What to do

What to do?


Setup assumptions

“Setup assumptions”

  • That is, augment the plain model

  • E.g., a common reference/random string (CRS) available to all parties

    • This idea has a long history [BFM88], and was the first setup assumption proposed in the UC setting [CF01]

    • Most commonly-used setup assumption

    • All feasibility results recovered [CLOS02]


How to generate a crs

How to generate a CRS?

  • Rely on a trusted party to generate it?

    • What if we are unwilling to assume any trusted parties?

    • Anyone who generates the CRS can potentially “attack” any protocol.

  • Use naturally-occurring random sources?

    • Unclear… (need correct distribution, synchronization, “privacy”[CDPW07])


Other setup assumptions

Other setup assumptions?

  • Public-key registration services [BCNP04,CDPW07]:

    • Very strong requirements

    • E.g., must check all parties’ secret keys to make sure keys are well-formed

  • Again, requires a high degree of trust


Other setup assumptions1

Other setup assumptions?

  • “Signature cards” [HM-QU05]:

    • Government issued cards carrying out a specific functionality

  • Again, requires trust


An alternative

An alternative?

  • Existing setup assumptions all appear to require some set of trusted parties

  • Perhaps physical assumptions can be used to circumvent existing impossibility results?

    • This might potentially lead to an approach that entirely avoids the need for trust!


Physical assumptions

Physical assumptions?!

  • Not as crazy as it might (at first) sound:

    • IT bounds on secret communication can be circumvented if noisy channels are assumed [Wyner75, CK78, Maurer93]

    • Quantum key exchange [BB84]

    • Broadcast with dishonest majority using physical multicast channels [FM00]

    • Network timing [DNS98, KLP05]


This talk tamper proof hardware

This talk: tamper-proof hardware

  • Assume the existence of tamper-proof hardware tokens

    • Users can create tokens implementing any functionality

      • No guarantee for tokens created by dishonest users

    • Dishonest users can do no more than observe input/output of honest tokens

  • Given the above, what can be done?


Possible advantages

(Possible) advantages?

  • Elimination of trust

    • Users can produce their own tokens…

  • Reduction or distribution of trust

    • Each user can choose their own hardware vendor (not possible with other setup assumptions)

  • Accountability/falsifiability

    • Demonstrate hardware not tamper proof


Two philosophical caveats

Two (philosophical) caveats

  • Is the assumption reasonable?

    • Perhaps not today, perhaps someday…

    • Weaker assumptions (tamper-evident hardware?) may suffice…

  • Has the assumption been modeled appropriately?

    • You tell me 

    • This is always a concern…


Inspiration from prior work

Inspiration from prior work

  • Using tamper-proof hardware to obtain more efficient/more secure protocols is not new

    • Inspired by the work on “observers” in the context of e-cash [CP, Brands, CP]

  • This is the first time it has been suggested for concurrent security or general MPC


Concurrent zero knowledge

com

com

Dependency

eliminated!

x

x

x

open

com

Concurrent zero knowledge

(verifier)

Problem: dependence of the different executions


Details

Details…

  • Functionality of token:

    • Run ZK protocol; sign statement being proven plus a bit indicating acceptance

  • Protocol (for prover):

    • Obtain token; run ZK protocol with the token; upon completion, send the final output of the token to the verifier


Security analysis informal

Security analysis (informal)

  • When the verifier is honest

    • Soundness of ZK proof system + security of signature scheme imply soundness

  • When the prover is honest

    • Zero knowledge of each proof system (in stand-alone sense) means that the view of each token can be simulated

    • Does not matter if the token runs incorrect protocol, or if there is a covert channel


Note on the proof

Note on the proof…

  • The token can be rewound

    • (Intuition:) rewinding token ok since it is “isolated” from the network

    • This will follow from the formal model

  • Parties still cannot be rewound

    • In particular, MPC not trivial to achieve

    • (Think ZK proofs of knowledge…)


Modeling tamper proof hardware simplified

Modeling tamper-proof hardware(simplified)

  • On input (create, P, P’, M) from P (where M is an interactive Turing machine) do:

    • Send (create, P, P’) to P’

    • Store (P, P’, M)

  • On input (run, P, msg) from P’, do:

    • As expected…

    • Chose random coins for M and run an execution of M with incoming message msg

    • (Maintain state)

Fwrap


Observation

Observation

  • Implicit in Fwrap are the following assumptions:

    • A party creating a token “knows” the code the token will run

    • An token is completely tamper-proof, and has access to a source of randomness (this can be relaxed to some extent with a PRG)

    • Token cannot communicate directly with external network


Uc computation using f wrap

UC computation using Fwrap

  • Using results of [CLOS02], it suffices to realize the (multiple) commitment functionality

  • Notation: (g, h, G, H)

    • Is a Diffie-Hellman tuple if loggG = loghH

    • Is a random tuple otherwise

  • Com(g,h,G,H)(b) = (gxhy, GxHygb)

    • Perfectly hiding if (g,h,G,H) is a random tuple

    • Extractable if it is a DH tuple and loggG is known


The protocol i

The protocol I

  • S creates the following token:

    • Receive (g, h)

    • Choose random G1, H1 and commit to them using a perfectly-hiding scheme

    • Receive (G2, H2); set G=G1G2 and H=H1H2

    • Decommit to G1, H1 and set tSR=(g,h,G,H)

    • Output a signature on tSR

  • R creates a token symmetrically, and the parties exchange tokens


The protocol ii

The protocol II

  • S and R each interact with the token sent by the other party, and then exchange tSR/tRS and signatures

    • At the end of this step, both parties hold tSR and tRS

    • (or abort)


Proof intuition i

Proof intuition I

  • Say P honest and P’ malicious

  • What can we argue about tPP’?

    • Since rewinding of P’ is not allowed, there is no way for a simulator to “force” the value of tPP’

    • Nevertheless, with all but negligible probability tPP’ will be a random tuple


Proof intuition ii

Proof intuition II

  • (P honest and P’ malicious)

  • What about tP’P?

    • When P’ sends M to Fwrap, the simulator obtains it

    • Although we cannot rewind P’, we can rewind the extracted M (i.e., the token)

    • Can “force” tP’P to be a Diffie-Hellman tuple with known discrete logarithm

      • (Indistinguishable from a random tuple)


The protocol iii

The protocol III

  • To commit to b, S does:

    • Commit to b using standard commitment C

    • Compute commitment Com to b using tSR

    • Send both commitments to R and give witness indistinguishable proof that either

      • Commitments are to same value

      • Or, tRS is a Diffie-Hellman tuple


The protocol iv

The protocol IV

  • To decommit, S does:

    • Send b

    • Give witness indistinguishable proof that either

      • Commitments C and Com were to b

      • Or, tRS is a Diffie-Hellman tuple


Proof intuition iii

  • Crucial that Com is perfectly hiding

    • (since impossible to “force” the value of tSR)

Proof intuition III

  • Proof is now straightforward…

  • Say S is honest

    • tSR random tuple; tRS Diffie-Hellman tuple

    • Simulation:

      • Commit to garbage; give WI proof using tRS

      • Send correct bit b; give WI proof using tRS


Proof intuition iv

Proof intuition IV

  • Say R is honest

    • tRS random tuple; tSR Diffie-Hellman tuple

    • S sends C and Com + WI proof

      • Since tRS random tuple, this means that C and Com are commitments to the same value

      • Extract from Com using known discrete logarithm of tSR

    • In decommitment phase, WI proof can only be given successfully for the same bit


Conclusions and future directions

Conclusions and future directions

  • UC multi-party computation is impossible without extending the “plain model”

  • A natural goal is to find extensions that are both useful and realistic

    • Here, we suggest physical assumptions and tamper resistance in particular

  • Future work

    • General assumptions, more efficient protocols

    • Weaker models of tamper resistance

    • Other setup assumptions? Characterization?


Thank you

Thank you!


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