{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T15:34:03Z","timestamp":1780068843252,"version":"3.54.0"},"reference-count":24,"publisher":"International Association for Cryptologic Research","issue":"3","license":[{"start":{"date-parts":[[2025,7,8]],"date-time":"2025-07-08T00:00:00Z","timestamp":1751932800000},"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":[[2025,9,2]]},"abstract":"<jats:p>The Cheon-Kim-Kim-Song (CKKS) homomorphic encryption scheme is widely adopted for securely evaluating circuits over real numbers, such as those arising in privacy-preserving machine learning (PPML), because it efficiently supports approximate floating-point arithmetic of messages. A CKKS ciphertext has a finite level, which corresponds to the budget for how many multiplicative operations can be applied. Once these levels are consumed, the ciphertext must be refreshed through a bootstrapping procedure to restore its capacity for further computation. The CKKS bootstrapping procedure consists of four main steps: 1) ModRaise, which raises the ciphertext coefficient modulus; 2) C2S, which homomorphically evaluates the inverse-DFT (iDFT) to enable further operations on the ciphertext coefficients; 3) EvalMod, which homomorphically removes the unintended coefficients introduced by ModRaise and shifted to the message side by C2S; and 4) S2C, which homomorphically evaluates the DFT to map the ciphertext back from the iDFT domain. However, these bootstrapping procedures also consume a significant number of levels, leaving fewer levels after each bootstrapping.<\/jats:p>\n          <jats:p>In this work, we introduce three techniques\u2014OverModRaise1, OverModRaise2, and Tuple-C2S\/S2C\u2014that target reductions in the modulus consumption of C2S\/S2C among the CKKS bootstrapping procedures, without introducing substantial overhead or compromising security. By combining these techniques, our implementation demonstrates at most 41% throughput improvement compared to the state-of-the-art bootstrapping. <\/jats:p>","DOI":"10.62056\/a3n5qjp10","type":"journal-article","created":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T18:49:52Z","timestamp":1759776592000},"update-policy":"https:\/\/doi.org\/10.62056\/adfjwm02dj","source":"Crossref","is-referenced-by-count":1,"title":["OverModRaise: Reducing Modulus Consumption of CKKS Bootstrapping"],"prefix":"10.62056","volume":"2","author":[{"ORCID":"https:\/\/orcid.org\/0009-0005-9832-5480","authenticated-orcid":false,"given":"Jihwan","family":"Kim","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04h9pn542","id-type":"ROR","asserted-by":"publisher"}],"name":"Seoul National University","place":["Seoul, Korea"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7085-2220","authenticated-orcid":false,"given":"Jung","family":"Cheon","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04h9pn542","id-type":"ROR","asserted-by":"publisher"}],"name":"Seoul National University","place":["Seoul, Korea"]},{"name":"CryptoLab Inc.","place":["Seoul, Korea"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0009-0006-3826-4636","authenticated-orcid":false,"given":"Yongdong","family":"Yeo","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/04h9pn542","id-type":"ROR","asserted-by":"publisher"}],"name":"Seoul National University","place":["Seoul, Korea"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"48349","published-online":{"date-parts":[[2025,10,6]]},"reference":[{"key":"ref1:AC:CKKS17","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"409","DOI":"10.1007\/978-3-319-70694-8_15","article-title":"Homomorphic Encryption for Arithmetic of Approximate\n  Numbers","volume":"10624","author":"Jung Hee Cheon","year":"2017"},{"key":"ref2:EC:CHKKS18","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"360","DOI":"10.1007\/978-3-319-78381-9_14","article-title":"Bootstrapping for Approximate Homomorphic Encryption","volume":"10820","author":"Jung Hee Cheon","year":"2018"},{"key":"ref3:CCS:CCKS23","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1145\/3576915.3623086","article-title":"Homomorphic Multiple Precision Multiplication for CKKS and\n  Reduced Modulus Consumption","author":"Jung Hee Cheon","year":"2023"},{"key":"ref4:IEEEAccess:SSKM25","doi-asserted-by":"publisher","first-page":"140847","DOI":"10.1109\/ACCESS.2025.3595177","article-title":"EvalRound+ Bootstrapping and Its Rigorous Analysis for CKKS\n  Scheme","volume":"13","author":"Hyewon Sung","year":"2025","journal-title":"IEEE Access"},{"key":"ref5:C:HalSho14","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"554","DOI":"10.1007\/978-3-662-44371-2_31","article-title":"Algorithms in HElib","volume":"8616","author":"Shai Halevi","year":"2014"},{"key":"ref6:IEEEAccess:HHC19","doi-asserted-by":"publisher","first-page":"57361","DOI":"10.1109\/ACCESS.2019.2913850","article-title":"Improved Homomorphic Discrete Fourier Transforms and FHE\n  Bootstrapping","volume":"7","author":"Kyoohyung Han","year":"2019","journal-title":"IEEE Access"},{"key":"ref7:EC:BMTH21","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1007\/978-3-030-77870-5_21","article-title":"Efficient Bootstrapping for Approximate Homomorphic\n  Encryption with Non-sparse Keys","volume":"12696","author":"Jean-Philippe Bossuat","year":"2021"},{"key":"ref8:MICRO:KLKSRKA22","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1109\/MICRO56248.2022.00086","article-title":"ARK: Fully Homomorphic Encryption Accelerator with Runtime\n  Data Generation and Inter-Operation Key Reuse","author":"Jongmin Kim","year":"2022"},{"key":"ref9:C:HalSho18","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"93","DOI":"10.1007\/978-3-319-96884-1_4","article-title":"Faster Homomorphic Linear Transformations in HElib","volume":"10991","author":"Shai Halevi","year":"2018"},{"key":"ref10:JC:HalSho21","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1007\/s00145-020-09368-7","article-title":"Bootstrapping for HElib","volume":"34","author":"Shai Halevi","year":"2021","journal-title":"Journal of Cryptology"},{"key":"ref11:EC:CheChiSon19","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"34","DOI":"10.1007\/978-3-030-17656-3_2","article-title":"Improved Bootstrapping for Approximate Homomorphic\n  Encryption","volume":"11477","author":"Hao Chen","year":"2019"},{"key":"ref12:EC:LLLKN21","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"618","DOI":"10.1007\/978-3-030-77870-5_22","article-title":"High-Precision Bootstrapping of RNS-CKKS Homomorphic\n  Encryption Using Optimal Minimax Polynomial Approximation and Inverse Sine\n  Function","volume":"12696","author":"Joon-Woo Lee","year":"2021"},{"key":"ref13:EPRINT:JutMan20","volume-title":"Modular Lagrange Interpolation of the Mod Function for\n  Bootstrapping for Approximate HE","author":"Charanjit S. Jutla","year":"2020"},{"key":"ref14:EC:LLKKNK22","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"551","DOI":"10.1007\/978-3-031-06944-4_19","article-title":"High-Precision Bootstrapping for Approximate Homomorphic\n  Encryption by Error Variance Minimization","volume":"13275","author":"Yongwoo Lee","year":"2022"},{"key":"ref15:AC:KPKKM22","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/978-3-031-22966-4_6","article-title":"EvalRound Algorithm in CKKS Bootstrapping","volume":"13792","author":"Seonghak Kim","year":"2022"},{"key":"ref16:EC:CHKS25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1007\/978-3-031-91131-6_14","article-title":"SHIP: A Shallow and Highly Parallelizable CKKS\n  Bootstrapping Algorithm","volume":"15603","author":"Jung Hee Cheon","year":"2025"},{"key":"ref17:Eprint:2024\/1014","volume-title":"Grafting: Decoupled Scale Factors and Modulus in\n  RNS-CKKS","author":"Jung Hee Cheon","year":"2024"},{"key":"ref18:CCS:BCCKK22","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1145\/3548606.3560696","article-title":"META-BTS: Bootstrapping Precision Beyond the Limit","author":"Youngjin Bae","year":"2022"},{"key":"ref19:WAHC:MBTPH20","first-page":"64","article-title":"Lattigo: A multiparty homomorphic encryption library in go","author":"Christian Vincent Mouchet","year":"2020"},{"key":"ref20:evalroundgithub","volume-title":"EvalRound: GitHub repository","author":"CryptoLabInc","year":"2024"},{"key":"ref21:RSA:HanKi20","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1007\/978-3-030-40186-3_16","article-title":"Better Bootstrapping for Approximate Homomorphic\n  Encryption","volume":"12006","author":"Kyoohyung Han","year":"2020"},{"key":"ref22:ACNS:BosTroHub22","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"521","DOI":"10.1007\/978-3-031-09234-3_26","article-title":"Bootstrapping for Approximate Homomorphic Encryption with\n  Negligible Failure-Probability by Using Sparse-Secret Encapsulation","volume":"13269","author":"Jean-Philippe Bossuat","year":"2022"},{"key":"ref23:SAC:CHKKS18","series-title":"LNCS","doi-asserted-by":"publisher","first-page":"347","DOI":"10.1007\/978-3-030-10970-7_16","article-title":"A Full RNS Variant of Approximate Homomorphic Encryption","volume":"11349","author":"Jung Hee Cheon","year":"2019"},{"key":"ref24:TDSC:CKKJY25","doi-asserted-by":"publisher","first-page":"1674","DOI":"10.1109\/TDSC.2024.3448406","article-title":"Batch Inference on Deep Convolutional Neural Networks With\n  Fully Homomorphic Encryption Using Channel-By-Channel Convolutions","volume":"22","author":"Jung Hee Cheon","year":"2025","journal-title":"IEEE Transactions on Dependable and Secure Computing"}],"container-title":["IACR Communications in Cryptology"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T20:23:25Z","timestamp":1759782205000},"score":1,"resource":{"primary":{"URL":"https:\/\/cic.iacr.org\/p\/2\/3\/32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,6]]},"references-count":24,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2025,10,6]]}},"URL":"https:\/\/doi.org\/10.62056\/a3n5qjp10","archive":["Internet Archive","Internet Archive"],"relation":{},"ISSN":["3006-5496"],"issn-type":[{"value":"3006-5496","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,6]]},"assertion":[{"value":"2025-07-08","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2025-09-02","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"cc2-3-72"}}