Generalizing the SPDZ Compiler For Other Protocols

Araki, Toshinori; Barak, Assi; Furukawa, Yoshihiro; Keller, Marcel; Lindell, Yehuda; Ohara, Kazuma; Tsuchida, Hikaru

doi:10.1145/3243734.3243854

Cited by 35 publications

(36 citation statements)

References 22 publications

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“…For the setting where t < n/2 and broadcast is given, we develop a way to reduce the soundness error when checking whether values are secret-shared correctly. 1 We also show a packing technique that allows us to reduce the overhead to obtain a total communication complexity O(|C|n 2 log n) ring elements, plus some term that does not depend on the size of the circuit. Finally, to get MPC over Z/p k Z rather than R, we show how to efficiently sample R-sharings of random elements of Z/p k Z with statistical security.…”

Section: Our Contributionsmentioning

confidence: 99%

“…, rL) ∈R L and broadcasts this value using protocol DCBroadcast. L+V ) ]R towards PV , who then checks correctness of the shares, i.e., PV checks that these shares lie on a polynomial of degree at most t. If no verifier PV complained in the previous step, the output is defined to be [a (1)…”

Section: Vss1dmentioning

confidence: 99%

“…The goal of this protocol is to upgrade a 1D-sharing [a] of a ∈ R to a 2D-sharing [[a]]. In fact, several values a (1) , . .…”

Section: Generating Randommentioning

confidence: 99%

“…-Letd be such that d •d ≥ κ. let L = /d, and assume thatd is large enough so p κ ≥ L + κ + 1, i.e.d ≥ /(p κ − κ − 1). -PS partitions m (1) , . .…”

Section: Ic-distrmentioning

confidence: 99%

“…Closely matching the data format used by CPUs is an advantage since one expects that when programming secure computation one can reuse some of the techniques that CPUs use to run efficiently. Additionally, bitwise operations like comparison or bit decomposition are expressed more naturally modulo powers of 2, and are very fast when computed over these rings [1].…”

Section: Introductionmentioning

confidence: 99%

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Efficient Information-Theoretic Secure Multiparty Computation over $$\mathbb {Z}/p^k\mathbb {Z}$$ via Galois Rings

Abspoel

Cramer

Damgård

et al. 2019

Lecture Notes in Computer Science

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At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPDZ 2 k that allows for secure multiparty computation (MPC) in the dishonest majority setting over the ring of integers modulo 2 k , thus solving a long-standing open question in MPC about secure computation over rings in this setting. In this paper we study this problem in the information-theoretic scenario. More specifically, we ask the following question: Can we obtain information-theoretic MPC protocols that work over rings with comparable efficiency to corresponding protocols over fields? We answer this question in the affirmative by presenting an efficient protocol for robust Secure Multiparty Computation over Z/p k Z (for any prime p and positive integer k) that is perfectly secure against active adversaries corrupting a fraction of at most 1/3 players, and a robust protocol that is statistically secure against an active adversary corrupting a fraction of at most 1/2 players.

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Section: Our Contributionsmentioning

confidence: 99%

Section: Vss1dmentioning

confidence: 99%

“…The goal of this protocol is to upgrade a 1D-sharing [a] of a ∈ R to a 2D-sharing [[a]]. In fact, several values a (1) , . .…”

Section: Generating Randommentioning

confidence: 99%

“…-Letd be such that d •d ≥ κ. let L = /d, and assume thatd is large enough so p κ ≥ L + κ + 1, i.e.d ≥ /(p κ − κ − 1). -PS partitions m (1) , . .…”

Section: Ic-distrmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Efficient Information-Theoretic Secure Multiparty Computation over $$\mathbb {Z}/p^k\mathbb {Z}$$ via Galois Rings

Abspoel

Cramer

Damgård

et al. 2019

Lecture Notes in Computer Science

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$$\textsc {Wys}^\star $$ : A DSL for Verified Secure Multi-party Computations

Rastogi

Swamy

Hicks

2019

Lecture Notes in Computer Science

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Secure multi-party computation (MPC) enables a set of mutually distrusting parties to cooperatively compute, using a cryptographic protocol, a function over their private data. This paper presents Wys , a new domain-specific language (DSL) for writing mixed-mode MPCs. Wys is an embedded DSL hosted in F , a verification-oriented, effectful programming language. Wys source programs are essentially F programs written in a custom MPC effect, meaning that the programmers can use F 's logic to verify the correctness and security properties of their programs. To reason about the distributed runtime semantics of these programs, we formalize a deep embedding of Wys , also in F . We mechanize the necessary metatheory to prove that the properties verified for the Wys source programs carry over to the distributed, multi-party semantics. Finally, we use F 's extraction to extract an interpreter that we have proved matches this semantics, yielding a partially verified implementation. Wys is the first DSL to enable formal verification of MPC programs. We have implemented several MPC protocols in Wys , including private set intersection, joint median, and an MPC-based card dealing application, and have verified their correctness and security.

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