{"title":"Generic constructions of PoRs from codes and instantiations","authors":"Julien Lavauzelle, F. Levy-dit-Vehel","doi":"10.1515/jmc-2018-0018","DOIUrl":null,"url":null,"abstract":"Abstract In this paper, we show how to construct – from any linear code – a Proof of Retrievability ( 𝖯𝗈𝖱 {\\mathsf{PoR}} ) which features very low computation complexity on both the client ( 𝖵𝖾𝗋𝗂𝖿𝗂𝖾𝗋 {\\mathsf{Verifier}} ) and the server ( 𝖯𝗋𝗈𝗏𝖾𝗋 {\\mathsf{Prover}} ) sides, as well as small client storage (typically 512 bits). We adapt the security model initiated by Juels and Kaliski [PoRs: Proofs of retrievability for large files, Proceedings of the 2007 ACM Conference on Computer and Communications Security—CCS 2007, ACM, New York 2007, 584–597] to fit into the framework of Paterson, Stinson and Upadhyay [A coding theory foundation for the analysis of general unconditionally secure proof-of-retrievability schemes for cloud storage, J. Math. Cryptol. 7 2013, 3, 183–216], from which our construction evolves. We thus provide a rigorous treatment of the security of our generic design; more precisely, we sharply bound the extraction failure of our protocol according to this security model. Next we instantiate our formal construction with codes built from tensor-products as well as with Reed–Muller codes and lifted codes, yielding 𝖯𝗈𝖱 {\\mathsf{PoR}} s with moderate communication complexity and (server) storage overhead, in addition to the aforementioned features.","PeriodicalId":43866,"journal":{"name":"Journal of Mathematical Cryptology","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/jmc-2018-0018","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Cryptology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/jmc-2018-0018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract In this paper, we show how to construct – from any linear code – a Proof of Retrievability ( 𝖯𝗈𝖱 {\mathsf{PoR}} ) which features very low computation complexity on both the client ( 𝖵𝖾𝗋𝗂𝖿𝗂𝖾𝗋 {\mathsf{Verifier}} ) and the server ( 𝖯𝗋𝗈𝗏𝖾𝗋 {\mathsf{Prover}} ) sides, as well as small client storage (typically 512 bits). We adapt the security model initiated by Juels and Kaliski [PoRs: Proofs of retrievability for large files, Proceedings of the 2007 ACM Conference on Computer and Communications Security—CCS 2007, ACM, New York 2007, 584–597] to fit into the framework of Paterson, Stinson and Upadhyay [A coding theory foundation for the analysis of general unconditionally secure proof-of-retrievability schemes for cloud storage, J. Math. Cryptol. 7 2013, 3, 183–216], from which our construction evolves. We thus provide a rigorous treatment of the security of our generic design; more precisely, we sharply bound the extraction failure of our protocol according to this security model. Next we instantiate our formal construction with codes built from tensor-products as well as with Reed–Muller codes and lifted codes, yielding 𝖯𝗈𝖱 {\mathsf{PoR}} s with moderate communication complexity and (server) storage overhead, in addition to the aforementioned features.