{"title":"Multivariate correlation attacks and the cryptanalysis of LFSR-based stream ciphers","authors":"Isaac A. Canales-Martínez, Igor Semaev","doi":"10.1007/s10623-024-01444-4","DOIUrl":null,"url":null,"abstract":"<p>Cryptanalysis of modern symmetric ciphers may be done by using linear equation systems with multiple right hand sides, which describe the encryption process. The tool was introduced by Raddum and Semaev (Des Codes Cryptogr 49(1):147–160, 2008) where several solving methods were developed. In this work, the probabilities are ascribed to the right hand sides and a statistical attack is then applied. The new approach is a multivariate generalisation of the correlation attack by Siegenthaler (IEEE Trans Comput C 49(1):81–85, 1985). A fast version of the attack is provided too. It may be viewed as an extension of the fast correlation attack in Meier and Staffelbach (J Cryptol 1(3):159–176, 1989), based on exploiting so called parity-checks for linear recurrences. Parity-checks are a particular case of the relations that we introduce in the present work. The notion of a relation is irrelevant to linear recurrences. We show how to apply the method to some LFSR-based stream ciphers including those from the Grain family. The new method generally requires a lower number of the keystream bits to recover the initial states than other techniques reported in the literature.</p>","PeriodicalId":11130,"journal":{"name":"Designs, Codes and Cryptography","volume":"13 1","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Designs, Codes and Cryptography","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10623-024-01444-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
Cryptanalysis of modern symmetric ciphers may be done by using linear equation systems with multiple right hand sides, which describe the encryption process. The tool was introduced by Raddum and Semaev (Des Codes Cryptogr 49(1):147–160, 2008) where several solving methods were developed. In this work, the probabilities are ascribed to the right hand sides and a statistical attack is then applied. The new approach is a multivariate generalisation of the correlation attack by Siegenthaler (IEEE Trans Comput C 49(1):81–85, 1985). A fast version of the attack is provided too. It may be viewed as an extension of the fast correlation attack in Meier and Staffelbach (J Cryptol 1(3):159–176, 1989), based on exploiting so called parity-checks for linear recurrences. Parity-checks are a particular case of the relations that we introduce in the present work. The notion of a relation is irrelevant to linear recurrences. We show how to apply the method to some LFSR-based stream ciphers including those from the Grain family. The new method generally requires a lower number of the keystream bits to recover the initial states than other techniques reported in the literature.
期刊介绍:
Designs, Codes and Cryptography is an archival peer-reviewed technical journal publishing original research papers in the designated areas. There is a great deal of activity in design theory, coding theory and cryptography, including a substantial amount of research which brings together more than one of the subjects. While many journals exist for each of the individual areas, few encourage the interaction of the disciplines.
The journal was founded to meet the needs of mathematicians, engineers and computer scientists working in these areas, whose interests extend beyond the bounds of any one of the individual disciplines. The journal provides a forum for high quality research in its three areas, with papers touching more than one of the areas especially welcome.
The journal also considers high quality submissions in the closely related areas of finite fields and finite geometries, which provide important tools for both the construction and the actual application of designs, codes and cryptographic systems. In particular, it includes (mostly theoretical) papers on computational aspects of finite fields. It also considers topics in sequence design, which frequently admit equivalent formulations in the journal’s main areas.
Designs, Codes and Cryptography is mathematically oriented, emphasizing the algebraic and geometric aspects of the areas it covers. The journal considers high quality papers of both a theoretical and a practical nature, provided they contain a substantial amount of mathematics.