{"schema_version":"0.1","map_id":"paper-57-map","publication_id":57,"publication_anchor":"paper-57","slug":"paper-57","canonical_path":"/knowledge/papers/paper-57/","machine_path":"/knowledge/papers/paper-57.json","root_node_id":"paper-57","stage":"mapped_draft","contribution_type_vocabulary_version":"0.1","contribution_types":[],"title":"On Regenerating Codes and Proactive Secret Sharing: Relationships and Implications","year":2021,"status":"Published","venue":"23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)","topic":"secure-encrypted-computation","labels":["Theory"],"authors":["Karim Eldefrawy","Nicholas Genise","Rutuja Kshirsagar","Moti Yung"],"keywords":["proactive secret sharing","regenerating codes","leakage","generalized decoding"],"research_question":"What formal relationships connect proactive secret sharing and regenerating codes, and what new efficiency opportunities, leakage risks, and coding notions follow from those relationships?","central_answer":"The paper gives conditional translations in both directions, uses Reed-Solomon repair methods to expose partial-leakage attacks and an alternative recovery procedure, and transfers general adversary structures into a new generalized-decoding regenerating-code definition with an existence theorem.","curation":{"drafted_at":"2026-07-11","drafted_by":[{"actor_type":"ai","name":"OpenAI Codex","role":"full-text extraction, theorem mapping, and initial assessment"}],"method":"Complete review of the 19-page IACR ePrint PDF through the public archive and author-uploaded full text, including definitions, propositions, theorems, proofs, and future-work boundaries. Direct local download was blocked by archive anti-bot controls, so no local hash is claimed.","source_scope":"full_source_audit","approval":{"status":"pending","note":"AI-authored source map awaiting full author verification. Parameter correspondences and leakage interpretations should be checked before approval."}},"sources":[{"id":"source-paper-57-archive-pdf","type":"public_archive_copy","title":"On Regenerating Codes and Proactive Secret Sharing: Relationships and Implications","url":"https://eprint.iacr.org/2022/096.pdf","provenance_category":"archive","media_type":"application/pdf","page_count":19},{"id":"source-paper-57-author-copy","type":"author_hosted_copy","title":"ResearchGate author-uploaded full text","url":"https://www.researchgate.net/publication/356008654_On_Regenerating_Codes_and_Proactive_Secret_Sharing_Relationships_and_Implications","provenance_category":"author"},{"id":"source-paper-57-official","type":"official_publication_record","title":"SSS 2021 publisher record","url":"https://doi.org/10.1007/978-3-030-91081-5_23","provenance_category":"official"},{"id":"source-paper-57-citations","type":"citation_index_snapshot","title":"OpenAlex work W3211377169","url":"https://api.openalex.org/works/W3211377169","accessed_at":"2026-07-11"}],"source_anchors":[{"id":"anchor-paper-57-problem","source_id":"source-paper-57-archive-pdf","label":"Motivation, contributions, and claimed relationships","locator":"Abstract and Section 1, PDF pages 1-4","url":"https://eprint.iacr.org/2022/096.pdf#page=1"},{"id":"anchor-paper-57-author-copy","source_id":"source-paper-57-author-copy","label":"Author-uploaded full text","locator":"ResearchGate public full-text record","url":"https://www.researchgate.net/publication/356008654_On_Regenerating_Codes_and_Proactive_Secret_Sharing_Relationships_and_Implications"},{"id":"anchor-paper-57-models","source_id":"source-paper-57-archive-pdf","label":"Reed-Solomon repair, regenerating codes, and PSS definitions","locator":"Sections 2.1-2.3, PDF pages 4-6","url":"https://eprint.iacr.org/2022/096.pdf#page=4"},{"id":"anchor-paper-57-leakage-model","source_id":"source-paper-57-archive-pdf","label":"Full-field and subfield leakage model","locator":"Section 2.4, PDF pages 6-7","url":"https://eprint.iacr.org/2022/096.pdf#page=6"},{"id":"anchor-paper-57-leakage-results","source_id":"source-paper-57-archive-pdf","label":"Static and dynamic leakage attacks","locator":"Section 4 and Propositions 1-2, PDF pages 8-10","url":"https://eprint.iacr.org/2022/096.pdf#page=8"},{"id":"anchor-paper-57-equivalence","source_id":"source-paper-57-archive-pdf","label":"PSS-to-RC and RC-to-PSS translations","locator":"Section 5, Theorems 1-2 and Corollary 1, PDF pages 10-11","url":"https://eprint.iacr.org/2022/096.pdf#page=10"},{"id":"anchor-paper-57-grc","source_id":"source-paper-57-archive-pdf","label":"Generalized-decoding regenerating codes","locator":"Section 6, Definition 10 and Theorem 3, PDF pages 11-14","url":"https://eprint.iacr.org/2022/096.pdf#page=11"},{"id":"anchor-paper-57-conclusion","source_id":"source-paper-57-archive-pdf","label":"Conclusions and open directions","locator":"Section 7, PDF page 14","url":"https://eprint.iacr.org/2022/096.pdf#page=14"},{"id":"anchor-paper-57-proofs","source_id":"source-paper-57-archive-pdf","label":"Repair background and missing proofs","locator":"Appendices A-B, PDF pages 16-19","url":"https://eprint.iacr.org/2022/096.pdf#page=16"},{"id":"anchor-paper-57-publication","source_id":"source-paper-57-official","label":"Official SSS publication identity","locator":"DOI 10.1007/978-3-030-91081-5_23","url":"https://doi.org/10.1007/978-3-030-91081-5_23"},{"id":"anchor-paper-57-citations","source_id":"source-paper-57-citations","label":"Dated citation-count snapshot","locator":"OpenAlex reported 2 citations when accessed 2026-07-11","url":"https://api.openalex.org/works/W3211377169"}],"nodes":[{"id":"paper-57","kind":"paper","parent_id":null,"order":1,"epistemic_status":"published","title":"On Regenerating Codes and Proactive Secret Sharing: Relationships and Implications","summary":"A theory paper relating two self-repairing representations, deriving leakage implications and conditional translations, and defining generalized-decoding regenerating codes.","source_anchor_ids":["anchor-paper-57-problem"]},{"id":"paper-57-question","kind":"question","parent_id":"paper-57","order":1,"epistemic_status":"research_question","title":"Research question","summary":"When do PSS recovery and regenerating-code repair represent the same mathematical capability, and what transfers across the two domains?","source_anchor_ids":["anchor-paper-57-problem"]},{"id":"paper-57-answer","kind":"contribution","parent_id":"paper-57","order":2,"epistemic_status":"theorem_supported","title":"Central answer","summary":"Match PSS sharing, reconstruction, recovery, and refresh to coding encode, decode, and repair; under additional linear-MDS conditions the mapping reverses, enabling repair-bandwidth insights and general adversary structures to cross domains.","source_anchor_ids":["anchor-paper-57-equivalence","anchor-paper-57-grc"]},{"id":"paper-57-scope","kind":"scope","parent_id":"paper-57","order":3,"epistemic_status":"defined","title":"Mathematical setting","summary":"The central comparison uses finite-field secret sharing, Shamir-based proactive protocols, Reed-Solomon repair, and regenerating-code parameters for storage per node, contacted helpers, and repair bandwidth.","source_anchor_ids":["anchor-paper-57-models"]},{"id":"paper-57-leakage","kind":"threat_model","parent_id":"paper-57","order":4,"epistemic_status":"defined","title":"Partial leakage across epochs","summary":"Nodes may leak whole field elements or collections of smaller-subfield elements. Static leakage repeats one linear view, while dynamic leakage can change transformations between refresh epochs, including through incomplete erasure of intermediate state.","source_anchor_ids":["anchor-paper-57-leakage-model","anchor-paper-57-leakage-results"]},{"id":"paper-57-claim-static-leakage","kind":"claim","parent_id":"paper-57-leakage","order":1,"epistemic_status":"proved_under_model","title":"Static partial leakage defeats a whole-share threshold","summary":"Proposition 1 quantifies how full-share and subfield leakage reduce the remaining Reed-Solomon repair information needed to reconstruct the secret, even when fewer than the nominal threshold of whole shares leak in an epoch.","source_anchor_ids":["anchor-paper-57-leakage-results","anchor-paper-57-proofs"]},{"id":"paper-57-claim-dynamic-leakage","kind":"claim","parent_id":"paper-57-leakage","order":2,"epistemic_status":"proved_under_strong_model","title":"Dynamic leakage accumulates across epochs","summary":"Proposition 2 gives an efficient adversary that gathers enough subfield information across epochs to reconstruct the secret when leakage functions vary and affected nodes store nonzero values; the paper labels this a strong but plausible implementation model.","source_anchor_ids":["anchor-paper-57-leakage-results","anchor-paper-57-proofs"]},{"id":"paper-57-equivalence","kind":"claim_group","parent_id":"paper-57","order":5,"epistemic_status":"proved_with_conditions","title":"Conditional PSS-RC correspondence","summary":"Two theorems preserve storage and repair parameters across translations, but the reverse direction requires a linear MDS regenerating code and the baseline forward encoding has a low rate unless linearity or batching is exploited.","source_anchor_ids":["anchor-paper-57-equivalence"]},{"id":"paper-57-equivalence-forward","kind":"claim","parent_id":"paper-57-equivalence","order":1,"epistemic_status":"proved","title":"PSS implies an erasure regenerating code","summary":"A (t,n) PSS storing alpha bits per node and recovering through d helpers sending beta bits yields an erasure regenerating code with n nodes, reconstruction dimension t plus 1, and the same storage and repair parameters.","source_anchor_ids":["anchor-paper-57-equivalence","anchor-paper-57-proofs"]},{"id":"paper-57-equivalence-reverse","kind":"claim","parent_id":"paper-57-equivalence","order":2,"epistemic_status":"proved_with_conditions","title":"Linear MDS RC implies PSS","summary":"Every specified linear MDS regenerating code with n plus 1 nodes and dimension k plus 1 yields a (k,n) PSS whose recovery contacts the same d helpers for beta bits each.","source_anchor_ids":["anchor-paper-57-equivalence","anchor-paper-57-proofs"]},{"id":"paper-57-recovery","kind":"analytical_result","parent_id":"paper-57","order":6,"epistemic_status":"corollary","title":"Subfield-based Shamir recovery","summary":"Combining the reverse translation with Guruswami-Wootters repair yields an alternative Shamir recovery that contacts n minus 1 nodes and receives smaller-subfield symbols, under the corollary's field-degree conditions and without leakage.","source_anchor_ids":["anchor-paper-57-equivalence"]},{"id":"paper-57-grc","kind":"definition","parent_id":"paper-57","order":7,"epistemic_status":"introduced","title":"Generalized-decoding regenerating code","summary":"GRC replaces one uniform threshold with monotone decoding sets and allowed error patterns, requiring Decode to correct every permitted error set and every erasure pattern leaving some decoding set intact.","source_anchor_ids":["anchor-paper-57-grc"]},{"id":"paper-57-claim-grc","kind":"claim","parent_id":"paper-57-grc","order":1,"epistemic_status":"existence_theorem","title":"Linear GRC existence for Q2 error structures","summary":"Theorem 3 maps a Q2 general adversary structure into a linear GRC over a finite field, while explicitly leaving parameter optimization and achievable rates open.","source_anchor_ids":["anchor-paper-57-grc"]},{"id":"paper-57-evidence","kind":"evidence_group","parent_id":"paper-57","order":8,"epistemic_status":"proof_documented","title":"Formal evidence","summary":"Definitions, propositions, parameter-preserving reductions, an existence theorem, and appendical proofs support the analysis. There is no prototype, benchmark, or deployed storage-system evaluation.","source_anchor_ids":["anchor-paper-57-equivalence","anchor-paper-57-grc","anchor-paper-57-proofs"]},{"id":"paper-57-boundaries","kind":"limitation_group","parent_id":"paper-57","order":9,"epistemic_status":"material","title":"Boundaries and open problems","summary":"The equivalence is conditional, the basic PSS-to-RC rate can be only 1/n, the dynamic leakage attack uses a strong model, and GRC is an unoptimized existence result. Efficient GRCs, generalized repair sets, dynamic groups, and verifiable RC remain future work.","source_anchor_ids":["anchor-paper-57-leakage-results","anchor-paper-57-equivalence","anchor-paper-57-grc","anchor-paper-57-conclusion"]},{"id":"paper-57-resources","kind":"artifact_group","parent_id":"paper-57","order":10,"epistemic_status":"full_text_available","title":"Publication resources","summary":"Archive and author-uploaded full texts expose the proofs, and the DOI identifies the SSS chapter. No code or data artifact is claimed.","source_anchor_ids":["anchor-paper-57-problem","anchor-paper-57-publication"]},{"id":"paper-57-scrutiny","kind":"scrutiny","parent_id":"paper-57","order":11,"epistemic_status":"venue_reviewed","title":"External scrutiny","summary":"The work appeared at SSS 2021. Public review reports and independent theorem checking are not represented.","source_anchor_ids":["anchor-paper-57-publication"]},{"id":"paper-57-lineage","kind":"lineage","parent_id":"paper-57","order":12,"epistemic_status":"documented","title":"Bridge between cryptography and coding theory","summary":"The paper imports repair-bandwidth methods into proactive sharing and exports general adversary structures into regenerating codes, framing a bidirectional research program rather than a deployed system.","source_anchor_ids":["anchor-paper-57-problem","anchor-paper-57-conclusion"]}],"relations":[{"id":"paper-57-relation-answer-question","type":"addresses","from_id":"paper-57-answer","to_id":"paper-57-question"},{"id":"paper-57-relation-forward-equivalence","type":"component_of","from_id":"paper-57-equivalence-forward","to_id":"paper-57-equivalence"},{"id":"paper-57-relation-reverse-equivalence","type":"component_of","from_id":"paper-57-equivalence-reverse","to_id":"paper-57-equivalence"},{"id":"paper-57-relation-equivalence-answer","type":"supports","from_id":"paper-57-equivalence","to_id":"paper-57-answer"},{"id":"paper-57-relation-equivalence-recovery","type":"enables","from_id":"paper-57-equivalence","to_id":"paper-57-recovery"},{"id":"paper-57-relation-equivalence-grc","type":"motivates","from_id":"paper-57-equivalence","to_id":"paper-57-grc"},{"id":"paper-57-relation-evidence-equivalence","type":"supports","from_id":"paper-57-evidence","to_id":"paper-57-equivalence"},{"id":"paper-57-relation-leakage-recovery","type":"qualifies","from_id":"paper-57-leakage","to_id":"paper-57-recovery"},{"id":"paper-57-relation-boundaries-answer","type":"qualifies","from_id":"paper-57-boundaries","to_id":"paper-57-answer"}],"assessment":{"id":"paper-57-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. 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