{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T04:15:44Z","timestamp":1778040944475,"version":"3.51.4"},"reference-count":26,"publisher":"International Association for Cryptologic Research","issue":"1","license":[{"start":{"date-parts":[[2025,12,14]],"date-time":"2025-12-14T00:00:00Z","timestamp":1765670400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IACR CiC"],"accepted":{"date-parts":[[2026,4,20]]},"abstract":"<jats:p>We examine the relationship between correctness definitions for Fully Homomorphic Encryption (FHE) and the associated security definitions. We show that reactive notions of correctness imply IND-CPA-D and sIND-CPA-D security. But that to obtain both IND-CPA-D and sIND-CPA-D security we need to use a randomized version of the evaluation procedure. Such randomized evaluation procedures cause problems in real life deployments of FHE solutions, so we then go on to show how one can de-randomize the evaluation procedure and still obtain sIND-CPA-D security in the random oracle model for the specific FHE scheme of TFHE.<\/jats:p>","DOI":"10.62056\/aksdkmol","type":"journal-article","created":{"date-parts":[[2026,5,4]],"date-time":"2026-05-04T18:09:08Z","timestamp":1777918148000},"update-policy":"https:\/\/doi.org\/10.62056\/adfjwm02dj","source":"Crossref","is-referenced-by-count":0,"title":["Reactive Correctness, sIND-CPAD-Security and Deterministic Evaluation for TFHE"],"prefix":"10.62056","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3567-3304","authenticated-orcid":false,"given":"Nigel","family":"Smart","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05f950310","id-type":"ROR","asserted-by":"publisher"}],"name":"KU Leuven","place":["Kasteelpark Arenberg 10, box 2452, Leuven, Vlaams-Brabant, 3001, Belgium"],"department":["Computer Security and Industrial Cryptography"]},{"id":[{"id":"https:\/\/ror.org\/0036vvb62","id-type":"ROR","asserted-by":"publisher"}],"name":"Zama","place":["Paris, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3186-2482","authenticated-orcid":false,"given":"Michael","family":"Walter","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/0036vvb62","id-type":"ROR","asserted-by":"publisher"}],"name":"Zama","place":["Paris, France"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"48349","published-online":{"date-parts":[[2026,5,4]]},"reference":[{"key":"ref1:GentryThesis","volume-title":"A fully homomorphic encryption scheme","author":"Craig Gentry","year":"2009"},{"key":"ref2:EC:LiMic21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"648","DOI":"10.1007\/978-3-030-77870-5_23","article-title":"On the Security of Homomorphic Encryption on Approximate\n  Numbers","volume":"12696","author":"Baiyu Li","year":"2021"},{"key":"ref3:C:CSBB24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1007\/978-3-031-68382-4_1","article-title":"On the Practical $\\text{CPA}^{D}$ Security of \u201cexact\u201d and\n  Threshold FHE Schemes and Libraries","volume":"14922","author":"Marina Checri","year":"2024"},{"key":"ref4:CCS:CCPSS24","doi-asserted-by":"publisher","first-page":"2505","DOI":"10.1145\/3658644.3690341","article-title":"Attacks Against the IND-CPA$^{\\text{D}}$ Security of\n  Exact FHE Schemes","author":"Jung Hee Cheon","year":"2024"},{"key":"ref5:EC:BJSW25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/978-3-031-91101-9_7","article-title":"Drifting Towards Better Error Probabilities in Fully\n  Homomorphic Encryption Schemes","volume":"15608","author":"Olivier Bernard","year":"2025"},{"key":"ref6:CiC:ABMP25","doi-asserted-by":"publisher","first-page":"3","DOI":"10.62056\/ayl83z10k","article-title":"Application-Aware Approximate Homomorphic Encryption:\n  Configuring FHE for Practical Use","volume":"2","author":"Andreea Alexandru","year":"2026","journal-title":"IACR Communications in Cryptology (CiC)"},{"key":"ref7:AC:ACGS24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"302","DOI":"10.1007\/978-981-96-0935-2_10","article-title":"HELIOPOLIS: Verifiable Computation over Homomorphically\n  Encrypted Data from Interactive Oracle Proofs is Practical","volume":"15488","author":"Diego F. Aranha","year":"2024"},{"key":"ref8:C:GarGoeWan24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"449","DOI":"10.1007\/978-3-031-68403-6_14","article-title":"How to Prove Statements Obliviously?","volume":"14929","author":"Sanjam Garg","year":"2024"},{"key":"ref9:KVMH24","doi-asserted-by":"publisher","first-page":"11","DOI":"10.1145\/3689945.3694806","article-title":"vFHE: Verifiable Fully Homomorphic Encryption","author":"Christian Knabenhans","year":"2024"},{"key":"ref10:EPRINT:LLZHXT25","volume-title":"HasteBoots: Proving FHE Bootstrapping in Seconds","author":"Fengrun Liu","year":"2025"},{"key":"ref11:CCS:ThiWal25","doi-asserted-by":"publisher","first-page":"1113","DOI":"10.1145\/3719027.3765097","article-title":"Towards Verifiable FHE in Practice: Proving Correct\n  Execution of TFHE's Bootstrapping using plonky2","author":"Louis Tremblay Thibault","year":"2025"},{"key":"ref12:C:CCCFGS25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"643","DOI":"10.1007\/978-3-032-01907-3_21","article-title":"Verifiable Computation for Approximate Homomorphic\n  Encryption Schemes","volume":"16006","author":"Ignacio Cascudo","year":"2025"},{"key":"ref13:IMA:Smart23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"263","DOI":"10.1007\/978-3-031-47818-5_14","article-title":"Practical and Efficient FHE-Based MPC","volume":"14421","author":"Nigel P. 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Smart","year":"2025","journal-title":"IACR Communications in Cryptology (CiC)"},{"key":"ref26:C:KLSS23b","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1007\/978-3-031-38554-4_18","article-title":"Toward Practical Lattice-Based Proof of Knowledge from\n  Hint-MLWE","volume":"14085","author":"Duhyeong Kim","year":"2023"}],"container-title":["IACR Communications in Cryptology"],"original-title":[],"language":"en","deposited":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T04:01:44Z","timestamp":1778040104000},"score":1,"resource":{"primary":{"URL":"https:\/\/cic.iacr.org\/p\/3\/1\/8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,5,4]]},"references-count":26,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,5,4]]}},"URL":"https:\/\/doi.org\/10.62056\/aksdkmol","archive":["Internet Archive","Internet Archive"],"relation":{},"ISSN":["3006-5496"],"issn-type":[{"value":"3006-5496","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,5,4]]},"assertion":[{"value":"2025-12-14","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2026-04-20","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"cc3-1-3"}}