{"title":"Finding Enumerators for Generalized (L, G)-Code","authors":"I. K. Noskov, S. V. Bezzateev","doi":"10.3103/S0146411623080187","DOIUrl":null,"url":null,"abstract":"<p>The algorithm for finding the enumerators of degree 2 and higher for the generalized (<i>L</i>, <i>G</i>)‑code is presented. This algorithm makes it possible to enhance the rate of finding enumerators as distinct from the exhaustive search algorithm. It can be used to construct a modern variant of the McEliece cryptosystem. The presented solution is based on using the representation of the Galois field element via the function containing the coefficients of a smaller field. In addition, the results of comparison of the modern McEliece cryptosystem constructed based on the Goppa codes and generalized (<i>L</i>, <i>G</i>)-codes are presented.</p>","PeriodicalId":46238,"journal":{"name":"AUTOMATIC CONTROL AND COMPUTER SCIENCES","volume":"57 8","pages":"922 - 927"},"PeriodicalIF":0.6000,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"AUTOMATIC CONTROL AND COMPUTER SCIENCES","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.3103/S0146411623080187","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
The algorithm for finding the enumerators of degree 2 and higher for the generalized (L, G)‑code is presented. This algorithm makes it possible to enhance the rate of finding enumerators as distinct from the exhaustive search algorithm. It can be used to construct a modern variant of the McEliece cryptosystem. The presented solution is based on using the representation of the Galois field element via the function containing the coefficients of a smaller field. In addition, the results of comparison of the modern McEliece cryptosystem constructed based on the Goppa codes and generalized (L, G)-codes are presented.
期刊介绍：
Automatic Control and Computer Sciences is a peer reviewed journal that publishes articles on• Control systems, cyber-physical system, real-time systems, robotics, smart sensors, embedded intelligence • Network information technologies, information security, statistical methods of data processing, distributed artificial intelligence, complex systems modeling, knowledge representation, processing and management • Signal and image processing, machine learning, machine perception, computer vision
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