{"schema_version":"0.1","map_id":"paper-65-map","publication_id":65,"publication_anchor":"paper-65","slug":"paper-65","canonical_path":"/knowledge/papers/paper-65/","machine_path":"/knowledge/papers/paper-65.json","root_node_id":"paper-65","stage":"mapped_draft","contribution_type_vocabulary_version":"0.1","contribution_types":[],"title":"On the Hardness of Scheme-Switching Between SIMD FHE Schemes","short_title":"Hardness of SIMD FHE Scheme Switching","year":2023,"venue":"14th International Conference on Post-Quantum Cryptography (PQCrypto)","publication_status":"Published","topic":"secure-encrypted-computation","labels":["Theory"],"authors":["Karim Eldefrawy","Nicholas Genise","Nathan Manohar"],"keywords":["fully homomorphic encryption","scheme switching","BGV and BFV","CKKS","bootstrapping","oracle reduction"],"research_question":"Can exact SIMD ciphertexts from BGV or BFV be efficiently converted to approximate CKKS ciphertexts, and back, without making expensive FHE capabilities such as bootstrapping unexpectedly cheap?","central_answer":"The paper gives conditional reductions rather than an unconditional lower bound: sufficiently capable scheme-switching oracles imply bootstrapping for the target schemes with little additional homomorphic work. It also relates comparison access to bootstrapping and nonlinear functions, supplying barrier evidence for general-purpose switching across exact and approximate encodings.","curation":{"drafted_at":"2026-07-11","drafted_by":[{"actor_type":"ai","name":"OpenAI Codex","role":"full-text theorem extraction, assumption mapping, and initial assessment"}],"method":"Source-grounded review of the complete IACR ePrint body, cross-checked against the PQCrypto DOI and IBM author record. The map distinguishes oracle reductions from unconditional impossibility or concrete security lower bounds.","source_scope":"full_source_audit","approval":{"status":"pending","note":"AI-authored source map awaiting author verification; theorem readings, reduction boundaries, and ratings should be checked before approval."}},"sources":[{"id":"source-paper-65-eprint","type":"public_preprint","title":"On the Hardness of Scheme-Switching Between SIMD FHE Schemes","url":"https://eprint.iacr.org/2023/988","provenance_category":"archive"},{"id":"source-paper-65-official","type":"official_publication_record","title":"PQCrypto 2023 publication record","url":"https://doi.org/10.1007/978-3-031-40003-2_8","provenance_category":"official"},{"id":"source-paper-65-author","type":"author_record","title":"IBM Research author page","url":"https://research.ibm.com/publications/on-the-hardness-of-scheme-switching-between-simd-fhe-schemes","provenance_category":"author"},{"id":"source-paper-65-citations","type":"citation_index_snapshot","title":"OpenAlex record W4385698748","url":"https://api.openalex.org/works/W4385698748","accessed_at":"2026-07-11"}],"source_anchors":[{"id":"anchor-paper-65-problem","source_id":"source-paper-65-eprint","label":"Problem statement, contributions, and interpretation","locator":"Abstract and Section 1","url":"https://eprint.iacr.org/2023/988.pdf"},{"id":"anchor-paper-65-preliminaries","source_id":"source-paper-65-eprint","label":"BGV, BFV, CKKS, SIMD encodings, and oracle notation","locator":"Section 2","url":"https://eprint.iacr.org/2023/988.pdf"},{"id":"anchor-paper-65-switch-definitions","source_id":"source-paper-65-eprint","label":"Weak and strong scheme-switch definitions","locator":"Section 3, including Lemmas 3.1-3.2 and Theorems 3-4","url":"https://eprint.iacr.org/2023/988.pdf"},{"id":"anchor-paper-65-exact-to-approx","source_id":"source-paper-65-eprint","label":"BGV-to-CKKS switching implies CKKS bootstrapping","locator":"Section 4, Theorem 5","url":"https://eprint.iacr.org/2023/988.pdf"},{"id":"anchor-paper-65-approx-to-exact","source_id":"source-paper-65-eprint","label":"CKKS-to-BGV switching implies BGV bootstrapping","locator":"Section 4, Theorem 6 and BFV extension","url":"https://eprint.iacr.org/2023/988.pdf"},{"id":"anchor-paper-65-comparison","source_id":"source-paper-65-eprint","label":"Comparison-oracle consequences","locator":"Section 5","url":"https://eprint.iacr.org/2023/988.pdf"},{"id":"anchor-paper-65-conclusion","source_id":"source-paper-65-eprint","label":"Interpretation and open scope","locator":"Conclusion","url":"https://eprint.iacr.org/2023/988.pdf"},{"id":"anchor-paper-65-publication","source_id":"source-paper-65-official","label":"Official publication identity","locator":"PQCrypto 2023, DOI 10.1007/978-3-031-40003-2_8","url":"https://doi.org/10.1007/978-3-031-40003-2_8"},{"id":"anchor-paper-65-citation-count","source_id":"source-paper-65-citations","label":"Dated citation-count snapshot","locator":"OpenAlex cited_by_count was 1 when accessed 2026-07-11","url":"https://api.openalex.org/works/W4385698748"}],"nodes":[{"id":"paper-65","kind":"paper","parent_id":null,"order":1,"epistemic_status":"published","title":"Hardness of SIMD FHE scheme switching","summary":"A theory paper that studies exact-to-approximate and approximate-to-exact SIMD FHE conversion through oracle reductions, showing that broadly useful switching would subsume costly refresh capabilities.","source_anchor_ids":["anchor-paper-65-problem"]},{"id":"paper-65-question","kind":"question","parent_id":"paper-65","order":1,"epistemic_status":"research_question","title":"Research question","summary":"Is generic, efficient switching between BGV/BFV exact SIMD encodings and CKKS approximate SIMD encodings substantially easier than bootstrapping?","source_anchor_ids":["anchor-paper-65-problem"]},{"id":"paper-65-answer","kind":"contribution","parent_id":"paper-65","order":2,"epistemic_status":"proved_conditionally","title":"Conditional barrier answer","summary":"Under the formal oracle interfaces, switching in either direction yields bootstrapping for the destination scheme with small additional work. Thus an efficient switching primitive of the modeled strength would also solve a capability usually regarded as expensive.","source_anchor_ids":["anchor-paper-65-exact-to-approx","anchor-paper-65-approx-to-exact"]},{"id":"paper-65-model","kind":"model","parent_id":"paper-65","order":3,"epistemic_status":"defined","title":"Exact and approximate SIMD model","summary":"BGV and BFV represent exact modular plaintext slots, whereas CKKS represents approximate complex or real slots with scale and error; switching must address both ciphertext semantics and plaintext encoding.","source_anchor_ids":["anchor-paper-65-preliminaries"]},{"id":"paper-65-model-oracle","kind":"definition","parent_id":"paper-65-model","order":1,"epistemic_status":"formalized","title":"Weak versus strong switching","summary":"A weak oracle preserves a compatible underlying ring-polynomial representation without performing the full slot-encoding conversion. A strong oracle includes the encoding transformation expected by an application-facing scheme switch.","source_anchor_ids":["anchor-paper-65-switch-definitions"]},{"id":"paper-65-model-encoding","kind":"theorem","parent_id":"paper-65-model","order":2,"epistemic_status":"proved","title":"Weak-to-strong lifting","summary":"The Section 3 lemmas and theorems connect the weak oracle formulations to strong switching by accounting for the relevant BGV and CKKS encoding transformations.","source_anchor_ids":["anchor-paper-65-switch-definitions"]},{"id":"paper-65-results","kind":"claim_group","parent_id":"paper-65","order":4,"epistemic_status":"proved","title":"Reduction results","summary":"The central results are black-box consequences of possessing the specified switching oracle; they are not constructions of a cheap switching implementation.","source_anchor_ids":["anchor-paper-65-exact-to-approx","anchor-paper-65-approx-to-exact"]},{"id":"paper-65-result-bgv-ckks","kind":"theorem","parent_id":"paper-65-results","order":1,"epistemic_status":"proved","title":"Exact-to-approximate switch bootstraps CKKS","summary":"Theorem 5 shows that a weak BGV-to-CKKS switching oracle can be used to bootstrap CKKS with one oracle call and one rescaling step, subject to the theorem's parameter and noise conditions.","source_anchor_ids":["anchor-paper-65-exact-to-approx"]},{"id":"paper-65-result-ckks-bgv","kind":"theorem","parent_id":"paper-65-results","order":2,"epistemic_status":"proved","title":"Approximate-to-exact switch bootstraps BGV","summary":"The reverse reduction uses one CKKS-to-BGV oracle call followed by a homomorphic inner-product style computation, plaintext multiplication and addition, and modulus switching to obtain a refreshed BGV ciphertext; the treatment extends to BFV through the stated conversion.","source_anchor_ids":["anchor-paper-65-approx-to-exact"]},{"id":"paper-65-result-comparison","kind":"theorem","parent_id":"paper-65-results","order":3,"epistemic_status":"proved_conditionally","title":"Comparison access also carries refresh power","summary":"The comparison analysis shows how a suitable comparison oracle can support bootstrapping with few calls for typical parameter regimes and connects the mechanism to nonlinear operations such as minimum, maximum, and ReLU.","source_anchor_ids":["anchor-paper-65-comparison"]},{"id":"paper-65-evidence","kind":"evidence_group","parent_id":"paper-65","order":5,"epistemic_status":"formal","title":"Formal evidence","summary":"The paper's evidence consists of definitions, encoding lemmas, constructive oracle reductions, and explicit noise or parameter accounting rather than implementation benchmarks.","source_anchor_ids":["anchor-paper-65-switch-definitions","anchor-paper-65-exact-to-approx","anchor-paper-65-approx-to-exact"]},{"id":"paper-65-boundaries","kind":"limitation_group","parent_id":"paper-65","order":6,"epistemic_status":"explicitly_bounded","title":"What the reductions do not establish","summary":"The reductions delimit the consequences of modeled switching capabilities but do not prove an unconditional complexity lower bound or impossibility theorem.","source_anchor_ids":["anchor-paper-65-problem","anchor-paper-65-conclusion"]},{"id":"paper-65-boundary-conditional","kind":"limitation","parent_id":"paper-65-boundaries","order":1,"epistemic_status":"logical_boundary","title":"Conditional, not unconditional, hardness","summary":"Showing that A implies B does not prove that A is impossible or as hard as B under every implementation model; the result becomes a hardness barrier only together with an external belief or lower bound about bootstrapping cost.","source_anchor_ids":["anchor-paper-65-exact-to-approx","anchor-paper-65-approx-to-exact"]},{"id":"paper-65-boundary-interface","kind":"limitation","parent_id":"paper-65-boundaries","order":2,"epistemic_status":"model_bounded","title":"Oracle-interface dependence","summary":"A specialized converter outside the weak or strong oracle semantics, a restricted plaintext domain, amortization, or changed correctness and precision requirements may fall outside a theorem's conclusion.","source_anchor_ids":["anchor-paper-65-switch-definitions","anchor-paper-65-conclusion"]},{"id":"paper-65-boundary-empirical","kind":"limitation","parent_id":"paper-65-boundaries","order":3,"epistemic_status":"not_evaluated","title":"No implementation comparison","summary":"The work does not implement a switch, benchmark bootstrapping, or measure engineering tradeoffs; it establishes relative capability, not concrete runtime cost.","source_anchor_ids":["anchor-paper-65-problem","anchor-paper-65-conclusion"]},{"id":"paper-65-resources","kind":"artifact_group","parent_id":"paper-65","order":7,"epistemic_status":"source_available","title":"Auditable resources","summary":"The full IACR manuscript, official DOI, and IBM author record expose the definitions and proof arguments; no code or experimental artifact is claimed.","source_anchor_ids":["anchor-paper-65-problem","anchor-paper-65-publication"]},{"id":"paper-65-scrutiny","kind":"scrutiny","parent_id":"paper-65","order":8,"epistemic_status":"venue_reviewed","title":"External scrutiny","summary":"PQCrypto publication establishes venue review. No public proof review, correction, independent formalization, or subsequent technical critique was located in this audit.","source_anchor_ids":["anchor-paper-65-publication"]},{"id":"paper-65-lineage","kind":"lineage","parent_id":"paper-65","order":9,"epistemic_status":"documented","title":"Place in the FHE design space","summary":"The paper reframes scheme switching as a relative-capability question linking exact and approximate SIMD schemes to bootstrapping and comparison, rather than proposing another FHE scheme.","source_anchor_ids":["anchor-paper-65-problem","anchor-paper-65-conclusion"]}],"relations":[{"id":"paper-65-rel-answer-question","type":"addresses","from_id":"paper-65-answer","to_id":"paper-65-question"},{"id":"paper-65-rel-model-answer","type":"scopes","from_id":"paper-65-model","to_id":"paper-65-answer"},{"id":"paper-65-rel-lifting-model","type":"connects","from_id":"paper-65-model-encoding","to_id":"paper-65-model-oracle"},{"id":"paper-65-rel-forward-answer","type":"supports","from_id":"paper-65-result-bgv-ckks","to_id":"paper-65-answer"},{"id":"paper-65-rel-reverse-answer","type":"supports","from_id":"paper-65-result-ckks-bgv","to_id":"paper-65-answer"},{"id":"paper-65-rel-comparison-results","type":"extends","from_id":"paper-65-result-comparison","to_id":"paper-65-results"},{"id":"paper-65-rel-evidence-results","type":"supports","from_id":"paper-65-evidence","to_id":"paper-65-results"},{"id":"paper-65-rel-boundaries-results","type":"qualifies","from_id":"paper-65-boundaries","to_id":"paper-65-results"},{"id":"paper-65-rel-conditional-answer","type":"qualifies","from_id":"paper-65-boundary-conditional","to_id":"paper-65-answer"},{"id":"paper-65-rel-resources-evidence","type":"enables_audit_of","from_id":"paper-65-resources","to_id":"paper-65-evidence"},{"id":"paper-65-rel-lineage-paper","type":"contextualizes","from_id":"paper-65-lineage","to_id":"paper-65"}],"assessment":{"id":"paper-65-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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