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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

Arabic

في CRYPTO 2007، قدمت Damgård وNielsen نهجًا متكاملًا لتنفيذ الحسابات متعددة الأطراف لتحقيق تعقيدات الاتصالات الخطية. تم طرح نهجًا آخر لتقليل تعقيدات الاتصالات من قبل Cramer، Damgård، وde Haan في EUROCRYPT 2007، الذي كان يتناول استخدام خطط التبادل الضوئي المباشر للتبادل المباشر بين المكونات الأساسية من الضوابط من المجال التوسعي. في هذه المقالة، نجمع بين هذه الأفكار لإنجاز خفض تكلفة الاتصالات غير المباشر في إعدادات MPC متعددة الأطراف. قدمنا تعديلًا جديدًا لخطط التبادل الضوئي المباشر المباشر، والذي يسمى التبادل الضوئي المباشر، وحرص

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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