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Big Secrets Small Shares: Revisiting Secure Multi-Party Computation

Wilton Kim, Van Long Phuoc Pham, Stanislav Kruglik, Han Mao Kiah · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27609 · cited by 0 works (OpenAlex) · open-access PDF

Indonesian

Pada CRYPTO 2007, Damgård dan Nielsen memperkenalkan pendekatan preprocessing untuk multi-party computing (MPC) untuk mencapai kompleksitas komunikasi linear. Pendekatan lain untuk mengurangi kompleksitas komunikasi diusulkan oleh Cramer, Damgård, dan de Haan di EUROCRYPT 2007, yang melibatkan menggunakan skema berbagi rahsia ramp untuk bersama-sama berbagi komponen basis-field rahsia dari bidang ekstensi. Dalam makalah ini, kami menggabungkan dua ide ini untuk mencapai pengurangan biaya komunikasi non-asymptotic dalam pengaturan MPC multi-fase. Kami memperkenalkan modifikasi baru dari skema berbagi rahsia ramp, yang disebut berbagi rahsia, dan menyesuaikan protokol MPC untuk menampung modifikasi ini. Pembagian rahsia kompak menutupi koefisien polynomial yang akan bocor selama pengurangan derajat.

Machine translation (Meta M2M100); the English original follows.

Abstract

At CRYPTO 2007, Damgård and Nielsen introduced a preprocessing approach to multi-party computation (MPC) to achieve linear communication complexity. Another approach to reduce communication complexity was proposed by Cramer, Damgård, and de Haan at EUROCRYPT 2007, which involved using ramp-secret sharing schemes to jointly share base-field components of secrets from the extension field. In this paper, we combine these two ideas to achieve a non-asymptotic reduction of communication cost in a multi-phase MPC setup. We introduce a new modification of the ramp secret sharing scheme, called compact sharing, and tailor the MPC protocol to accommodate this modification. Compact sharing masks the polynomial coefficients that would otherwise leak during degree reduction. The protocol provides perfect security against static semi-honest adversaries under an explicit tradeoff between the corruption threshold and the extension degree. When the extension degree scales linearly with the number of parties, the gate-evaluation core achieves constant communication overhead relative to an extension-field element, amortized over full preprocessing batches; input and output communication is counted separately.

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Topics: Secret sharing, Secure multi-party computation, Extension (predicate logic), Overhead (engineering), Computer science, Theoretical computer science

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