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Wysteria: A Programming Language for Generic, Mixed-Mode Multiparty Computations Aseem Rastogi Matthew Hammer, Michael Hicks (University of Maryland, College Park)

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What is Secure Multiparty Computation (SMC) A B Compute f(A, B) Without revealing A to Bob and B to Alice

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Using a Trusted Third Party A B A B f(A, B) Compute f(A, B) Without revealing A to Bob and B to Alice

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SMC Eliminates Trusted Third Party A B Compute f(A, B) Without revealing A to Bob and B to Alice Cryptographic Protocol

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SMC Examples Private Data Nearest neighborLocations AuctionBids Private set intersectionSets Statistical computationNumbers

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Beyond Toy SMC Examples Online card games SMC to deal cards Dice-based games SMC to roll dice

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Monolithic Secure Multiparty Computation f(A, B) A B Not Enough !

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Mixed-Mode Secure Multiparty Computation f(A, B) A B g(A 1, B 1 ) A 1 B 1 g(A 1, B 1 ) … … h(A 2, B 2 ) A 2 B 2 h(A 2, B 2 ) … Local … Secure State

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State Of The Art: Existing SMC Languages Fairplay, FairplayMP, CBMC-GC – Only “circuit compilers” – No mixed-mode – No secure state L1 – Only 2-party, low level – No formal guarantees FastGC – Circuit library, only 2-party None supports generic programs (parametric in number of parties) None supports generic programs (parametric in number of parties)

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Our Goal Push SMC beyond toy applications

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Design an SMC Language Local and secure computations High-level support for secure state Mixed-Mode Code parametric in number of parties Generic Single specification Runtime compilation to circuits High-level Statically typed, sound Compositional Guarantees

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A High-level Functional Language to write Mixed-Mode Generic SMCs Implementation and examples available at: http://ter.ps/wysteria Developing Online Poker using Wysteria (almost there …) Goes Without Saying, Wysteria Has It All ! Demo (coming up) Demo (coming up)

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Wysteria by Examples: Two-party Millionaire’s * let a = read() in let b = read() in let o = a > b in o par(A) par(B) sec(A,B) *The example in this form does not type check in Wysteria. Single specification A and B run the same program Compute who is richer among A and B

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Wysteria by Examples: Two-party Millionaire’s let a = read() in let b = read() in let o = a > b in o par(A) par(B) sec(A,B) A’s Local Computation (Skipped by B) Computation modes

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Wysteria by Examples: Two-party Millionaire’s let a = read() in let b = read() in let o = a > b in o par(A) par(B) sec(A,B) A’s Local Computation B’s Local Computation (Skipped by A)

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Wysteria by Examples: Two-party Millionaire’s let a = read() in let b = read() in let o = a > b in o par(A) par(B) sec(A,B) A’s Local Computation B’s Local Computation Secure Computation by (A,B)

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let a = read() in let b = read() in let o = a > b in o par(A) par(B) sec(A,B) A’s Local Computation B’s Local Computation Secure Computation by (A,B) Runtime compiles it to boolean circuit, and evaluates using secure computation No communication primitives ! Wysteria by Examples: Two-party Millionaire’s

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Key Ideas Mixed-Mode Computations via Mode Annotations

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Wysteria by Examples: Asymmetric Output let a = read() in let b = read() in let o = a > b in o par(A) par(B) sec(A,B) What if only A is allowed to know the output ?

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Wysteria by Examples: Asymmetric Output let a = read() in let b = read() in let o = wire A:(a > b) in o par(A) par(B) sec(A,B) What if only A is allowed to know the output ? Wire Bundle

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Wire Bundles in Wysteria Maps from parties to values Each party sees only its own component in the bundle – Or nothing if it’s not in the domain Wire bundles are dependently typed Create wire A:0 : W {A} nat Concat (wire A:0)++(wire B:1) : W {A U B} nat Project (wire A:0)[A] : nat

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Wysteria by Examples: Inputs Via Wire Bundles let a = read() in let b = read() in let w1 = wire A:a in let w2 = wire B:b in let w3 = w1 ++ w2 in let o = wire A:(w3[A] > w3[B]) in o par(A) par(B) sec(A,B)

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let a = read() in let b = read() in let w1 = wire A:a in let w2 = wire B:b in let w3 = w1 ++ w2 in let o = wire A:(w3[A] > w3[B]) in o Wysteria by Examples: Wire Bundle Views A’s ViewB’s Viewsec(A,B)’s View w1{A:a}{}{A:a} w2{}{B:b} w3{A:a}{B:b}{A:a,B:b} par(A) par(B) sec(A,B)

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Key Ideas Wire Bundle Abstraction for Private Inputs/Outputs Mixed-Mode Computations via Place Annotations

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let mill = λx:W {A U B} nat. let o = x[A] > x[B] in o in let a = read () in let b = read () in mill (wire A:a ++ wire B:b) sec(A,B) Wysteria by Examples: Functions par(A) par(B)

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So Far We Have Seen … Mixed-Mode support via mode annotations Wire Bundles abstraction for private data Now: Writing Generic Code in Wysteria

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Parties As First Class Values Parties are values of type ps φ Refinement types for more precise invariants {A} : ps {ν = A} {A} : ps {ν A U B}

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Wysteria by Examples: Generic Millionaire’s sec(x) let comb = λx:ps. λy:W x nat. λa:ps option. λp:ps. λn:nat match a with | None => Some(p) | Some(q) => if y[q] > n then a else Some(p) in let mill = λx:ps. λy:W x nat. let o = wfold(y, None, comb x y) in o in … sec(x)

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Wysteria by Examples: Generic Millionaire’s sec(x) let comb = λx:ps. λy:W x nat. λa:ps option. λp:ps. λn:nat match a with | None => Some(p) | Some(q) => if y[q] > n then a else Some(p) in let mill = λx:ps. λy:W x nat. let o = wfold(y, None, comb x y) in o in … sec(x)

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Wysteria by Examples: Generic Millionaire’s sec(x) let comb = λx:ps. λy:W x nat. λa:ps{ν x} option.λp:ps{ν x}.λn:nat match a with | None => Some(p) | Some(q) => if y[q] > n then a else Some(p) in let mill = λx:ps. λy:W x nat. let o = wfold(y, None, comb x y) in o in … sec(x)

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Key Ideas Generic Code: 1. Parties as First Class Values 2. Wire Bundle Combinators (e.g. wfold ) Wire Bundle Abstraction for Private Inputs/Outputs Mixed-Mode Computations via Place Annotations

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Wysteria Metatheory Formalized using λ -calculus with extensions Dependent type system Two operational semantics: – Single-threaded (SIMD style specification) – Multi-threaded (actual protocol runs) – Slicing judgment from single- to multi-threaded

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Wysteria Theorems* Type soundness (progress and preservation) in single-threaded semantics Sound simulation: C1C1 C2 π1π1 π2π2 … * Single-threaded Multi-threaded slice operation *Proofs in Technical Report

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Wysteria Implementation We use GMW Implementation from Choi et. al.

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Wysteria Evaluation Applicationn-Party ?Mixed-Mode ?Secure state ? Millionaire’sYesNo 2 nd Price auctionYesNo PSI2-partyYesNo Nearest neighborYesNo Median2-partyYesNo PSI count2-partyYes 2-round biddingYes Online pokerYes

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Wysteria Code for Card Dealing let retryloop = fix retryloop: (tmp5:unit) -> W tgt nat. (tmp5:unit). let myrand = \(z:unit).rand () in let rs = wapp x [wire x:(); wire x:myrand] in let res = check rs in if res.#success then let nd = select ndealt[0] in let _ = update dealt [nd] <- res.#sum in let _ = update ndealt [0] <- nd + 1 in let card @ sec(x) = let s = combsh (res.#sum) in wire tgt:s in card else retryloop () in retryloop () in wcopy as x from w in { #deal : deal } in Secure computation Local computation Secret shares let rand = \(myunit:unit). sysop rand 52 in let mkdeal = \(x:ps{true}). let zerosh @ par(x) = let zerosh1 @ sec(x) = makesh 0 in zerosh1 in let dealt @ par(x) = array [ 52 ] of zerosh in let ndealt @ par(x) = array [ 1 ] of 0 in let deal = \(tgt:ps{singl and subeq x}). let w @ par(x) = let check = \(rs:W x nat). let nd = select ndealt[0] in let sum @ sec(x) = let s = wfold x [rs; 0; \(n1:nat).\(p:ps{true}).\(n2:nat). n1 + n2 ] in let s1 = wfold x [wire x:(); s; \(n1:nat).\(p:ps{true}).\(n2:unit). if n1 > 51 then n1 - 51 else n1 ] in makesh s1 in let checkloop = fix checkloop:(i:nat) -> {#sum:Sh x nat, #success: bool}. (i:nat). if i = nd then {#sum:sum, #success:true} else l2et sd = select dealt[i] in let cmp @ sec(x) = let t1 = combsh sd in let t2 = combsh sum in t1 = t2 in if cmp then {#sum:sum, #success:false} else checkloop (i + 1) n checkloop 0 in

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Demo (Card dealing using Wysteria) Future Work: Integrate with bitcoin for betting (c.f. Secure Multiparty Computation on BitCoin, Andrychowicz et. al.)

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Also In The Paper … Support for secure state More language features – Mutable state (interesting interaction with mixed- mode) – Additional wire bundle combinators Performance evaluation Complete proofs in TR

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Wysteria Summary http://ter.ps/wysteria Implementation and examples available at: A High-level Functional Language to write Mixed-Mode Generic SMCs

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