{"title":"A digit-serial algorithm for the discrete logarithm modulo 2/sup k/","authors":"A. Fit-Florea, D. Matula","doi":"10.1109/ASAP.2004.1","DOIUrl":null,"url":null,"abstract":"We introduce as our main result a digit-serial residue arithmetic algorithm for computing the discrete logarithm modulo 2/sup k/ (dlg). \"Digit inheritance\" is presented as a fundamental property common to the primitive operations modulo 2/sup k/ of addition, multiplication, multiplicative inverse, exponentiation and discrete logarithm. Our main algorithm computes dlg using binary arithmetic with 3 as the logarithmic base and has a critical path containing one modulo 2/sup k/ multiplication operation for each of its k iterations. Extensions of the algorithm to other logarithmic bases and computations using digits in a higher radix 2/sup r/ are also described.","PeriodicalId":120245,"journal":{"name":"Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004.","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2004-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"10","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings. 15th IEEE International Conference on Application-Specific Systems, Architectures and Processors, 2004.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ASAP.2004.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 10
Abstract
We introduce as our main result a digit-serial residue arithmetic algorithm for computing the discrete logarithm modulo 2/sup k/ (dlg). "Digit inheritance" is presented as a fundamental property common to the primitive operations modulo 2/sup k/ of addition, multiplication, multiplicative inverse, exponentiation and discrete logarithm. Our main algorithm computes dlg using binary arithmetic with 3 as the logarithmic base and has a critical path containing one modulo 2/sup k/ multiplication operation for each of its k iterations. Extensions of the algorithm to other logarithmic bases and computations using digits in a higher radix 2/sup r/ are also described.
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