{"title":"Shamir's shared secret scheme in GF(p/sup m/)","authors":"Leong Peng Chor, Tan Peng Chong","doi":"10.1109/TENCON.1999.818451","DOIUrl":null,"url":null,"abstract":"A. Shamir's (1979) shared secret scheme is adapted to operate over an extension field GF(p)[x]/x/sup m/-/spl omega/ where p is an odd prime p. Both multiplication and multiplicative inverse in such a field can be efficiently computed on 8-bit microcontrollers with appropriate choice of p and exploiting the built-in byte-multiply instruction. In applications with fixed p, m, and /spl omega/ further acceleration can be achieved via a small set of pre-computed values. Pre-computation also eliminates the necessity for division at the sub-field level. A brief discussion on efficiency and memory trade-off is provided. It is found that reconstruction of a 128-bit secret under a (2,3) threshold scheme on a low-end smart card is not impractical.","PeriodicalId":121142,"journal":{"name":"Proceedings of IEEE. IEEE Region 10 Conference. TENCON 99. 'Multimedia Technology for Asia-Pacific Information Infrastructure' (Cat. No.99CH37030)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1999-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of IEEE. IEEE Region 10 Conference. TENCON 99. 'Multimedia Technology for Asia-Pacific Information Infrastructure' (Cat. No.99CH37030)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/TENCON.1999.818451","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
A. Shamir's (1979) shared secret scheme is adapted to operate over an extension field GF(p)[x]/x/sup m/-/spl omega/ where p is an odd prime p. Both multiplication and multiplicative inverse in such a field can be efficiently computed on 8-bit microcontrollers with appropriate choice of p and exploiting the built-in byte-multiply instruction. In applications with fixed p, m, and /spl omega/ further acceleration can be achieved via a small set of pre-computed values. Pre-computation also eliminates the necessity for division at the sub-field level. A brief discussion on efficiency and memory trade-off is provided. It is found that reconstruction of a 128-bit secret under a (2,3) threshold scheme on a low-end smart card is not impractical.