{"schema_version":"0.1","map_id":"paper-52-map","publication_id":52,"publication_anchor":"paper-52","slug":"paper-52","canonical_path":"/knowledge/papers/paper-52/","machine_path":"/knowledge/papers/paper-52.json","root_node_id":"paper-52","stage":"mapped_draft","contribution_type_vocabulary_version":"0.1","contribution_types":["protocol","scheme"],"title":"Communication-Efficient Proactive Secret Sharing for Dynamic Groups with Dishonest Majorities","year":2020,"status":"Published","venue":"18th International Conference on Applied Cryptography and Network Security (ACNS)","topic":"secure-encrypted-computation","labels":["Theory"],"authors":["Karim Eldefrawy","Tancrède Lepoint","Antonin Leroux"],"keywords":["proactive secret sharing","dynamic groups","dishonest majority","bivariate polynomials"],"research_question":"Can proactive secret sharing simultaneously tolerate a mobile dishonest majority, batch many secrets without a linear threshold loss, reduce communication, and redistribute shares as the participant set changes?","central_answer":"The paper builds a computationally secure dynamic proactive secret-sharing scheme from bivariate-polynomial batching, gradual reconstruction, and dedicated increase/decrease protocols. For batches of up to n minus 2 secrets it reports O(n squared) amortized communication per secret, while preserving mixed-adversary secrecy and fairness under explicitly stated thresholds.","curation":{"drafted_at":"2026-07-11","drafted_by":[{"actor_type":"ai","name":"OpenAI Codex","role":"full-text extraction, formal-claim mapping, and initial assessment"}],"method":"Complete review of the 53-page checked-in manuscript, including its definitions, protocols, theorem statements, supplementary security proofs, and visual inspection of the title page and a protocol/theorem page. Claims below distinguish theorem statements from implementation or deployment evidence, neither of which the paper supplies.","source_scope":"full_source_audit","approval":{"status":"pending","note":"AI-authored source map awaiting full author verification. Threshold transcriptions and interpretations should be checked against the source before approval."}},"sources":[{"id":"source-paper-52-author-pdf","type":"author_hosted_copy","title":"Communication-Efficient Proactive Secret Sharing for Dynamic Groups with Dishonest Majorities","url":"/pubs/2020/pssdgdm_acns2020.pdf","provenance_category":"author","media_type":"application/pdf","sha256":"48669813efeca12ddb68c1996e13e475131660748cfeff3512de42fa37a36a54","page_count":53},{"id":"source-paper-52-official","type":"official_publication_record","title":"ACNS 2020 publisher record","url":"https://doi.org/10.1007/978-3-030-57808-4_1","provenance_category":"official"},{"id":"source-paper-52-archive","type":"public_archive_record","title":"IACR ePrint 2019/1383","url":"https://eprint.iacr.org/2019/1383","provenance_category":"archive"},{"id":"source-paper-52-citations","type":"citation_index_snapshot","title":"OpenAlex work 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change the sharing degree through redistribution protocols when parties join or leave.","source_anchor_ids":["anchor-paper-52-problem","anchor-paper-52-core-protocols","anchor-paper-52-dynamic"]},{"id":"paper-52-scope","kind":"scope","parent_id":"paper-52","order":3,"epistemic_status":"defined","title":"System and adversary model","summary":"The parties operate synchronously over pairwise secure channels and authenticated broadcast. A polynomial-time mixed adversary may passively observe and actively control parties within each phase, and its corrupted set may move between refresh periods.","source_anchor_ids":["anchor-paper-52-model"]},{"id":"paper-52-scope-security","kind":"threat_model","parent_id":"paper-52-scope","order":1,"epistemic_status":"defined","title":"Separate secrecy, correctness, fairness, and robustness thresholds","summary":"The paper assigns distinct multi-thresholds to secrecy, correctness, fairness, and robustness; a claim at one threshold must not be read as establishing the others. Robustness is generally limited to one or two active faults.","source_anchor_ids":["anchor-paper-52-model","anchor-paper-52-boundaries"]},{"id":"paper-52-scope-assumptions","kind":"assumption","parent_id":"paper-52-scope","order":2,"epistemic_status":"computational_assumption","title":"Commitment and erasure assumptions","summary":"Active-fault checking uses Pedersen-style homomorphic commitments and computational security under discrete-log hardness; proactive security also relies on phase separation, reset or recovery, and disposal of obsolete state.","source_anchor_ids":["anchor-paper-52-assumptions","anchor-paper-52-model"]},{"id":"paper-52-construction","kind":"method","parent_id":"paper-52","order":4,"epistemic_status":"specified","title":"Batched bivariate proactive sharing","summary":"A degree-d bivariate polynomial stores secrets at public diagonal points. A party holds a univariate slice, enabling the batch to be refreshed, recovered, reconstructed, and redistributed without exposing the embedded secrets.","source_anchor_ids":["anchor-paper-52-batched-definition","anchor-paper-52-core-protocols"]},{"id":"paper-52-construction-batching","kind":"scheme","parent_id":"paper-52-construction","order":1,"epistemic_status":"specified","title":"Sublinear threshold loss under batching","summary":"The bivariate encoding replaces the usual linear loss in corruption tolerance with a square-root dependence on batch size and supports up to n minus 2 embedded secrets in the maximum batch.","source_anchor_ids":["anchor-paper-52-problem","anchor-paper-52-static-theorems"]},{"id":"paper-52-construction-maintenance","kind":"protocol","parent_id":"paper-52-construction","order":2,"epistemic_status":"specified","title":"Share, Recover, Reconstruct, and Refresh","summary":"Share distributes polynomial slices; Recover replaces a missing slice with blinded assistance; Reconstruct builds a gradual ladder for fair release; and Refresh adds a zero-encoding random bivariate sharing to rerandomize state.","source_anchor_ids":["anchor-paper-52-core-protocols"]},{"id":"paper-52-construction-membership","kind":"protocol","parent_id":"paper-52-construction","order":3,"epistemic_status":"specified","title":"Dynamic membership protocols","summary":"Increase and Decrease adjust the sharing degree as parties join or cooperate in leaving, while DecreaseCorrupt handles one non-participating failed or corrupted departure; Redistribute composes these operations for group changes.","source_anchor_ids":["anchor-paper-52-dynamic"]},{"id":"paper-52-claims","kind":"claim_group","parent_id":"paper-52","order":5,"epistemic_status":"formally_analyzed","title":"Main stated guarantees","summary":"Theorems establish static and dynamic PSS correctness and secrecy under stated mixed-adversary thresholds, together with fairness and amortized communication results.","source_anchor_ids":["anchor-paper-52-static-theorems","anchor-paper-52-dynamic"]},{"id":"paper-52-claim-efficiency","kind":"claim","parent_id":"paper-52-claims","order":1,"epistemic_status":"asymptotic_theorem","title":"O(n squared) amortized communication","summary":"With a maximum-size batch, the paper reports O(n squared) communication per secret overall, versus O(n cubed) for its single-secret specialization and O(n to the fourth) for the compared prior dishonest-majority construction.","source_anchor_ids":["anchor-paper-52-problem","anchor-paper-52-static-theorems","anchor-paper-52-dynamic"]},{"id":"paper-52-claim-security","kind":"claim","parent_id":"paper-52-claims","order":2,"epistemic_status":"proved_under_model","title":"Mixed-adversary security and fairness","summary":"The theorem statements give secrecy and correctness thresholds with a square-root batch-size loss and a separate gradual-reconstruction fairness region; they do not claim robustness at the full dishonest-majority threshold.","source_anchor_ids":["anchor-paper-52-static-theorems","anchor-paper-52-proofs","anchor-paper-52-boundaries"]},{"id":"paper-52-claim-dynamic","kind":"claim","parent_id":"paper-52-claims","order":3,"epistemic_status":"proved_under_model","title":"Dynamic redistribution preserves the shared secret","summary":"Theorem 3 composes the five principal protocols into a dynamic PSS scheme whose new group receives a fresh sharing of the same batch, subject to the old and new phases satisfying the stated thresholds.","source_anchor_ids":["anchor-paper-52-dynamic","anchor-paper-52-proofs"]},{"id":"paper-52-evidence","kind":"evidence_group","parent_id":"paper-52","order":6,"epistemic_status":"proof_documented","title":"Formal evidence","summary":"The source supplies protocol pseudocode, definitions, ideal functionalities, simulators, intermediate lemmas, and proofs for the static and dynamic constructions. This map audits their presence and logical role but does not independently machine-check them.","source_anchor_ids":["anchor-paper-52-core-protocols","anchor-paper-52-proofs"]},{"id":"paper-52-boundaries","kind":"limitation_group","parent_id":"paper-52","order":7,"epistemic_status":"material","title":"Boundaries and costs","summary":"The construction is synchronous and computational, assumes secure channels and authenticated broadcast, loses threshold as the batch grows, is not robust against a general active dishonest majority, and offers asymptotic analysis rather than an implementation or deployment evaluation.","source_anchor_ids":["anchor-paper-52-model","anchor-paper-52-assumptions","anchor-paper-52-boundaries"]},{"id":"paper-52-boundary-membership","kind":"limitation","parent_id":"paper-52-boundaries","order":1,"epistemic_status":"explicitly_scoped","title":"Departure constraints","summary":"Cooperative Decrease requires leaving parties to participate, while DecreaseCorrupt handles only one non-participating departure at a time; broader churn behavior is not established by that subprotocol.","source_anchor_ids":["anchor-paper-52-dynamic"]},{"id":"paper-52-resources","kind":"artifact_group","parent_id":"paper-52","order":8,"epistemic_status":"source_available","title":"Auditable resources","summary":"The complete manuscript is checked into the site with page count and SHA-256, the IACR ePrint supplies an archive identity, and the DOI identifies the ACNS publication. 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