{"schema_version":"0.1","map_id":"paper-61-map","publication_id":61,"publication_anchor":"paper-61","slug":"paper-61","canonical_path":"/knowledge/papers/paper-61/","machine_path":"/knowledge/papers/paper-61.json","root_node_id":"paper-61","stage":"mapped_draft","contribution_type_vocabulary_version":"0.1","contribution_types":["protocol"],"title":"Communication-Efficient Proactive MPC for Dynamic Groups with Dishonest Majorities","year":2022,"status":"Published","venue":"20th International Conference on Applied Cryptography and Network Security (ACNS)","topic":"secure-encrypted-computation","labels":["Theory"],"authors":["Karim Eldefrawy","Tancrède Lepoint","Antonin Leroux"],"keywords":["secure multiparty computation","proactive security","dynamic groups","dishonest majority"],"research_question":"Can a full proactive MPC protocol evaluate arithmetic circuits efficiently when a mobile adversary may control a dishonest majority and the participant group changes between computation layers?","central_answer":"The paper extends batched bivariate proactive secret sharing with multi-dealer input sharing, addition, permutation, and a new no-precomputation multiplication pipeline. It proves conditional proactive security and fair reconstruction and reports O(n squared) amortized communication per secret for maximum-size batches.","curation":{"drafted_at":"2026-07-11","drafted_by":[{"actor_type":"ai","name":"OpenAI Codex","role":"full-text extraction, protocol-and-proof mapping, and initial assessment"}],"method":"Complete review of the 44-page IACR ePrint PDF through the public archive, including the adversary model, multi-dealer sharing, eight-operation PMPC, multiplication subprotocols, thresholds, ideal functionalities, and appendical proofs. Direct local download was blocked by an archive anti-bot challenge, so no local hash is claimed.","source_scope":"full_source_audit","approval":{"status":"pending","note":"AI-authored source map awaiting full author verification. Thresholds, proof-composition wording, and asymptotic expressions require author checking."}},"sources":[{"id":"source-paper-61-archive-pdf","type":"public_archive_copy","title":"Communication-Efficient Proactive MPC for Dynamic Groups with Dishonest Majorities","url":"https://eprint.iacr.org/2021/1564.pdf","provenance_category":"archive","media_type":"application/pdf","page_count":44},{"id":"source-paper-61-official","type":"official_publication_record","title":"ACNS 2022 publisher record","url":"https://doi.org/10.1007/978-3-031-09234-3_28","provenance_category":"official"},{"id":"source-paper-61-citations","type":"citation_index_snapshot","title":"OpenAlex work W3214757571","url":"https://api.openalex.org/works/W3214757571","accessed_at":"2026-07-11"}],"source_anchors":[{"id":"anchor-paper-61-problem","source_id":"source-paper-61-archive-pdf","label":"Problem, contributions, and headline thresholds","locator":"Abstract and Section 1.1, PDF pages 1-3","url":"https://eprint.iacr.org/2021/1564.pdf#page=1"},{"id":"anchor-paper-61-overview","source_id":"source-paper-61-archive-pdf","label":"Bivariate multiplication overview","locator":"Section 1.2, PDF pages 3-5","url":"https://eprint.iacr.org/2021/1564.pdf#page=3"},{"id":"anchor-paper-61-model","source_id":"source-paper-61-archive-pdf","label":"Mobile mixed adversary and cryptographic assumptions","locator":"Sections 2.1-2.3, PDF pages 5-8","url":"https://eprint.iacr.org/2021/1564.pdf#page=5"},{"id":"anchor-paper-61-share","source_id":"source-paper-61-archive-pdf","label":"Multi-dealer batched proactive sharing","locator":"Section 3 and Protocol 1, PDF pages 8-10","url":"https://eprint.iacr.org/2021/1564.pdf#page=8"},{"id":"anchor-paper-61-pmpc","source_id":"source-paper-61-archive-pdf","label":"Eight-subprotocol dynamic PMPC","locator":"Section 4 and Protocol 2, PDF pages 10-13","url":"https://eprint.iacr.org/2021/1564.pdf#page=10"},{"id":"anchor-paper-61-main-theorem","source_id":"source-paper-61-archive-pdf","label":"Full PMPC security and fairness theorem","locator":"Theorem 1, PDF page 13, with proof in Appendix D, PDF pages 39-41","url":"https://eprint.iacr.org/2021/1564.pdf#page=13"},{"id":"anchor-paper-61-multiplication","source_id":"source-paper-61-archive-pdf","label":"Resharing, masking, product, verification, and Mult","locator":"Sections 5.1-5.5 and Protocols 3-7, PDF pages 13-20","url":"https://eprint.iacr.org/2021/1564.pdf#page=13"},{"id":"anchor-paper-61-mult-theorem","source_id":"source-paper-61-archive-pdf","label":"Multiplication security and communication","locator":"Theorem 2, PDF page 20","url":"https://eprint.iacr.org/2021/1564.pdf#page=20"},{"id":"anchor-paper-61-proofs","source_id":"source-paper-61-archive-pdf","label":"Updated PSS proofs, multiplication proofs, permutation, and full composition","locator":"Appendices A-E, PDF pages 21-44","url":"https://eprint.iacr.org/2021/1564.pdf#page=21"},{"id":"anchor-paper-61-boundaries","source_id":"source-paper-61-archive-pdf","label":"Scheduling, planned membership, fairness, and evidence boundaries","locator":"Sections 2.1 and 4 and Appendix D, PDF pages 5-6, 10-13, and 39-41","url":"https://eprint.iacr.org/2021/1564.pdf#page=5"},{"id":"anchor-paper-61-publication","source_id":"source-paper-61-official","label":"Official ACNS publication identity","locator":"DOI 10.1007/978-3-031-09234-3_28","url":"https://doi.org/10.1007/978-3-031-09234-3_28"},{"id":"anchor-paper-61-citations","source_id":"source-paper-61-citations","label":"Dated citation-count snapshot","locator":"OpenAlex reported 3 citations when accessed 2026-07-11","url":"https://api.openalex.org/works/W3214757571"}],"nodes":[{"id":"paper-61","kind":"paper","parent_id":null,"order":1,"epistemic_status":"published","title":"Communication-Efficient Proactive MPC for Dynamic Groups with Dishonest Majorities","summary":"A formal batched proactive MPC protocol for arithmetic circuits, dynamic groups, mobile mixed adversaries, and dishonest-majority thresholds.","source_anchor_ids":["anchor-paper-61-problem"]},{"id":"paper-61-question","kind":"question","parent_id":"paper-61","order":1,"epistemic_status":"research_question","title":"Research question","summary":"Can the efficient dynamic dishonest-majority PSS of paper #52 be extended to multiplication and full circuit evaluation without returning to quartic communication?","source_anchor_ids":["anchor-paper-61-problem"]},{"id":"paper-61-answer","kind":"contribution","parent_id":"paper-61","order":2,"epistemic_status":"theorem_supported","title":"Central answer","summary":"Add a multi-dealer Share, local Add, batched Permute, and a new verified bivariate multiplication pipeline to the existing refresh, recover, redistribute, and reconstruct protocols.","source_anchor_ids":["anchor-paper-61-share","anchor-paper-61-pmpc","anchor-paper-61-multiplication"]},{"id":"paper-61-scope","kind":"threat_model","parent_id":"paper-61","order":3,"epistemic_status":"defined","title":"Mobile mixed adversary","summary":"A computationally bounded adversary adaptively chooses passive and active corruptions between predefined refresh phases and may eventually visit every party, while the within-phase multi-threshold remains satisfied.","source_anchor_ids":["anchor-paper-61-model"]},{"id":"paper-61-scope-network","kind":"assumption","parent_id":"paper-61-scope","order":1,"epistemic_status":"assumed","title":"Network, reset, and cryptographic assumptions","summary":"Parties use synchronous pairwise secure channels and authenticated broadcast, reset parties return to a pristine state, old shares are not retained, and proofs rely on DDH-based homomorphic commitments plus Paillier and zero-knowledge multiplication components.","source_anchor_ids":["anchor-paper-61-model","anchor-paper-61-multiplication"]},{"id":"paper-61-pmpc","kind":"protocol","parent_id":"paper-61","order":4,"epistemic_status":"specified","title":"Layered dynamic PMPC","summary":"Inputs are batched and shared, then each arithmetic-circuit layer permutes operands, applies Add or Mult, redistributes shares for planned departures and arrivals, optionally refreshes, and finally reconstructs designated outputs.","source_anchor_ids":["anchor-paper-61-pmpc"]},{"id":"paper-61-pmpc-maintenance","kind":"protocol","parent_id":"paper-61-pmpc","order":1,"epistemic_status":"reused_and_adapted","title":"Proactive and dynamic maintenance","summary":"Refresh rerandomizes current batches, Recover restores reset parties, Redistribute changes membership, and gradual Reconstruct releases outputs fairly within a separate threshold region.","source_anchor_ids":["anchor-paper-61-pmpc","anchor-paper-61-proofs"]},{"id":"paper-61-share","kind":"protocol","parent_id":"paper-61-pmpc","order":2,"epistemic_status":"specified","title":"Multi-dealer batched Share","summary":"Multiple input owners first Shamir-share their values and the parties combine those univariate sharings into a common bivariate batch, removing the earlier requirement that every batched secret originate from one dealer.","source_anchor_ids":["anchor-paper-61-share"]},{"id":"paper-61-mult","kind":"protocol","parent_id":"paper-61-pmpc","order":3,"epistemic_status":"specified","title":"Bivariate batched multiplication","summary":"The protocol splits each batch into roughly square-root-sized univariate groups, creates bivariate zero masks, computes blinded cross-products with pairwise zero-knowledge multiplication, verifies random evaluations, and recombines product sharings.","source_anchor_ids":["anchor-paper-61-overview","anchor-paper-61-multiplication"]},{"id":"paper-61-mult-verification","kind":"mechanism","parent_id":"paper-61-mult","order":1,"epistemic_status":"cryptographically_checked","title":"Commitment and random-evaluation checks","summary":"Homomorphic commitments check local algebra, Paillier-based ZK-Mult protects pairwise products, and a jointly sampled random evaluation detects malformed bivariate commitments except with the theorem's bounded probability.","source_anchor_ids":["anchor-paper-61-model","anchor-paper-61-multiplication","anchor-paper-61-proofs"]},{"id":"paper-61-claims","kind":"claim_group","parent_id":"paper-61","order":5,"epistemic_status":"formally_analyzed","title":"Main guarantees","summary":"Theorems separately state multiplication security, full PMPC secrecy and correctness, conditional fairness, and amortized communication; the thresholds and ideal functionalities must be read together.","source_anchor_ids":["anchor-paper-61-main-theorem","anchor-paper-61-mult-theorem"]},{"id":"paper-61-claim-efficiency","kind":"claim","parent_id":"paper-61-claims","order":1,"epistemic_status":"asymptotic_theorem","title":"Quadratic amortized communication","summary":"For batches of size n minus 2, the complete PMPC reports O(n squared) amortized communication per secret; the new multiplication and permutation procedures report O(n times square root of n) amortized communication.","source_anchor_ids":["anchor-paper-61-problem","anchor-paper-61-mult-theorem","anchor-paper-61-proofs"]},{"id":"paper-61-claim-security","kind":"claim","parent_id":"paper-61-claims","order":2,"epistemic_status":"proved_under_model","title":"Dishonest-majority proactive security","summary":"Under DDH and the formal model, Theorem 1 gives a secrecy and correctness region with a square-root batch-size loss from n minus 3, plus a distinct mixed active/passive threshold for fair reconstruction.","source_anchor_ids":["anchor-paper-61-main-theorem","anchor-paper-61-proofs"]},{"id":"paper-61-claim-mult","kind":"claim","parent_id":"paper-61-claims","order":3,"epistemic_status":"proved_under_model","title":"No-precomputation multiplication","summary":"Theorem 2 realizes the multiplication ideal functionality for batches within the degree bound and a square-root-loss corruption threshold, without a preprocessing phase.","source_anchor_ids":["anchor-paper-61-mult-theorem","anchor-paper-61-proofs"]},{"id":"paper-61-evidence","kind":"evidence_group","parent_id":"paper-61","order":6,"epistemic_status":"proof_documented","title":"Formal evidence","summary":"The source contains detailed pseudocode, commitment checks, ideal functionalities, subprotocol simulators, permutation constructions, and an appendical composition argument. This map audits their presence, not every proof step independently.","source_anchor_ids":["anchor-paper-61-multiplication","anchor-paper-61-proofs"]},{"id":"paper-61-boundaries","kind":"limitation_group","parent_id":"paper-61","order":7,"epistemic_status":"material","title":"Boundaries","summary":"Membership changes are assumed planned before execution and occur between circuit layers; corruption sets change only during refresh; fairness holds only in its narrower region; the protocol assumes synchrony, secure channels, reset and erasure; and evidence is formal rather than implemented or benchmarked.","source_anchor_ids":["anchor-paper-61-model","anchor-paper-61-pmpc","anchor-paper-61-boundaries"]},{"id":"paper-61-boundary-refresh","kind":"limitation","parent_id":"paper-61-boundaries","order":1,"epistemic_status":"deployment_tradeoff","title":"Refresh frequency is a policy input","summary":"More frequent refresh permits the adversary less time within a corruption set but costs more communication; the protocol accepts a set of refresh layers rather than deriving an operational schedule.","source_anchor_ids":["anchor-paper-61-pmpc","anchor-paper-61-boundaries"]},{"id":"paper-61-resources","kind":"artifact_group","parent_id":"paper-61","order":8,"epistemic_status":"full_text_available","title":"Publication resources","summary":"The complete IACR ePrint exposes all proofs and the DOI fixes the ACNS identity. No public implementation artifact or local byte copy is represented in this map.","source_anchor_ids":["anchor-paper-61-problem","anchor-paper-61-publication"]},{"id":"paper-61-scrutiny","kind":"scrutiny","parent_id":"paper-61","order":9,"epistemic_status":"venue_reviewed","title":"External scrutiny","summary":"The work appeared at ACNS 2022. Public reviews, independent proof checking, and reproductions are not linked.","source_anchor_ids":["anchor-paper-61-publication"]},{"id":"paper-61-lineage","kind":"lineage","parent_id":"paper-61","order":10,"epistemic_status":"documented","title":"Builds full PMPC on paper","summary":"The paper reuses the dynamic bivariate PSS from paper #52, adapts its proof to multi-dealer batches, and adds the missing arithmetic-circuit multiplication and permutation layers.","source_anchor_ids":["anchor-paper-61-problem","anchor-paper-61-share","anchor-paper-61-multiplication"]}],"relations":[{"id":"paper-61-relation-answer-question","type":"addresses","from_id":"paper-61-answer","to_id":"paper-61-question"},{"id":"paper-61-relation-maintenance-pmpc","type":"component_of","from_id":"paper-61-pmpc-maintenance","to_id":"paper-61-pmpc"},{"id":"paper-61-relation-share-pmpc","type":"component_of","from_id":"paper-61-share","to_id":"paper-61-pmpc"},{"id":"paper-61-relation-mult-pmpc","type":"component_of","from_id":"paper-61-mult","to_id":"paper-61-pmpc"},{"id":"paper-61-relation-verification-mult","type":"supports","from_id":"paper-61-mult-verification","to_id":"paper-61-mult"},{"id":"paper-61-relation-pmpc-answer","type":"realizes","from_id":"paper-61-pmpc","to_id":"paper-61-answer"},{"id":"paper-61-relation-evidence-claims","type":"supports","from_id":"paper-61-evidence","to_id":"paper-61-claims"},{"id":"paper-61-relation-scope-security","type":"qualifies","from_id":"paper-61-scope","to_id":"paper-61-claim-security"},{"id":"paper-61-relation-boundaries-claims","type":"qualifies","from_id":"paper-61-boundaries","to_id":"paper-61-claims"},{"id":"paper-61-relation-lineage-paper","type":"contextualizes","from_id":"paper-61-lineage","to_id":"paper-61"}],"assessment":{"id":"paper-61-assessment-2026-07-11","rubric_version":"0.2","assessed_at":"2026-07-11","status":"ai_draft_author_review_pending","note":"These dimensions describe documented support and process, not truth, correctness, or a universal ranking. No composite score is calculated.","axes":[{"id":"epistemic_evidence","level":"high","rationale":"The complete source defines the model, specifies all subprotocols, states exact thresholds and ideal functionalities, and supplies appendical proofs and a composition argument. It provides no implementation evidence.","basis_source_anchor_ids":["anchor-paper-61-main-theorem","anchor-paper-61-multiplication","anchor-paper-61-mult-theorem","anchor-paper-61-proofs"]},{"id":"auditability","level":"high","rationale":"The complete IACR archive PDF and official DOI expose assumptions, protocols, and proofs. Archive anti-bot controls prevented recording local byte fixity, and no author-hosted copy is represented.","basis_source_anchor_ids":["anchor-paper-61-problem","anchor-paper-61-publication"]},{"id":"production_provenance","level":"medium","rationale":"Authorship, date, archive identity, venue, and DOI are documented; revision history, roles, tool use, and artifact lineage are not.","basis_source_anchor_ids":["anchor-paper-61-publication","anchor-paper-61-problem"]},{"id":"external_scrutiny","level":"medium","rationale":"ACNS publication establishes venue review, but public reports, independent proof checks, and implementation review are unavailable.","basis_source_anchor_ids":["anchor-paper-61-publication"]},{"id":"reception","level":"low","rationale":"The dated exact-DOI OpenAlex record located 3 citations. Under the author-defined rule, 0 through 8 located citations is Low; counts vary by index and date.","basis_source_anchor_ids":["anchor-paper-61-citations"]},{"id":"contribution_significance","level":"medium","rationale":"The work closes the full-MPC gap in its bivariate dishonest-majority line and reports a large asymptotic improvement, but priority and downstream impact remain to be independently assessed.","basis_source_anchor_ids":["anchor-paper-61-problem","anchor-paper-61-share","anchor-paper-61-multiplication"]}]},"reception_snapshot":{"as_of":"2026-07-11","method":"OpenAlex exact DOI lookup","citation_count":3,"source_url":"https://api.openalex.org/works/W3214757571","signals":["The exact DOI-matched OpenAlex work reported three citing works."],"limitation":"Citation counts are index- and date-dependent and may merge or split ePrint and proceedings versions differently."}}