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Information Set Decoding in the Lee Metric with Applications to Cryptography [article]

Anna-Lena Horlemann-Trautmann, Violetta Weger
2020 arXiv   pre-print
We convert Stern's information set decoding (ISD) algorithm to the ring Z/4 Z equipped with the Lee metric.  ...  We show that using Lee metric codes can drastically decrease the key size, compared to Hamming metric codes. In the end we explain how our results can be generalized to other Galois rings Z/p^sZ.  ...  Acknowledgments We would like to thank Karan Khathuria for fruitful discussions and technical support.  ... 
arXiv:1903.07692v2 fatcat:g5bvb6qaanayfdalll7jc5zone

Information set decoding in the lee metric with applications to cryptography

Anna-Lena Horlemann-Trautmann, ,Faculty of Mathematics and Statistics, University of St. Gallen, Bodanstr. 6, St. Gallen, Switzerland, Violetta Weger, ,Institute of Mathematics, University of Zurich, Winterthurerstrasse 190, 8057 Zurich, Switzerland
2019 Advances in Mathematics of Communications  
We convert Stern's information set decoding (ISD) algorithm to the ring Z/4Z equipped with the Lee metric.  ...  We show that using Lee metric codes can substantially decrease the key size, compared to Hamming metric codes. In the end we explain how our results can be generalized to other Galois rings Z/p s Z.  ...  Acknowledgments We would like to thank Karan Khathuria for fruitful discussions and technical support.  ... 
doi:10.3934/amc.2020089 fatcat:nlnyopxblffcnn2ngpdlqdfrjq

Post-Quantum and Code-Based Cryptography—Some Prospective Research Directions

Chithralekha Balamurugan, Kalpana Singh, Ganeshvani Ganesan, Muttukrishnan Rajarajan
2021 Cryptography  
Cryptography has been used from time immemorial for preserving the confidentiality of data/information in storage or transit.  ...  Some potential research directions that are yet to be explored in code-based cryptography research from the perspective of codes is a key contribution of this paper.  ...  Acknowledgments: This research work has been carried out under the leadership of the Institute for Technological Research SystemX, and therefore granted within the scope of the program "Recherche Exploratoire  ... 
doi:10.3390/cryptography5040038 fatcat:wkb43zunwjagbnljc6brfou4ty

McNie: A code-based public-key cryptosystem [article]

Jon-Lark Kim, Young-Sik Kim, Lucky Galvez, Myeong Jae Kim, Nari Lee
2019 arXiv   pre-print
In particular, we apply rank-metric codes to McNie.  ...  McNie is a hybrid version of the McEliece and Niederreiter cryptosystems and its security is reduced to the hard problem of syndrome decoding.  ...  .: Decoding random binary linear codes in 2n/20: How 1+1 = 0 improves information set decoding.  ... 
arXiv:1812.05008v2 fatcat:wsagwr4tofd3fdn2cxpp3vogte

Information Set Decoding for Lee-Metric Codes using Restricted Balls [article]

Jessica Bariffi, Karan Khathuria, Violetta Weger
2022 arXiv   pre-print
The observation that such decoders come with a larger cost than their Hamming metric counterparts make the Lee metric a promising alternative for classical code-based cryptography.  ...  Unlike in the Hamming metric, an error vector that is chosen uniform at random of a given Lee weight is expected to have only few entries with large Lee weight.  ...  The second author is supported by the Estonian Research Council grant number PRG49. The third author is supported by the Swiss National Science Foundation grant number 195290.  ... 
arXiv:2205.12903v1 fatcat:cs7zwbm3xjexplhqxoiuy4tv2m

Information set decoding of Lee-metric codes over finite rings [article]

Violetta Weger, Massimo Battaglioni, Paolo Santini, Franco Chiaraluce, Marco Baldi, Edoardo Persichetti
2021 arXiv   pre-print
In this paper we switch from the Hamming metric to the Lee metric, and study ISD algorithms and their complexity for codes measured with the Lee metric over finite rings.  ...  Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes.  ...  In particular, our study can be useful to address potential applicability of the Lee metric to design new code-based cryptosystems.  ... 
arXiv:2001.08425v2 fatcat:fevcgoge6vaujhafzjnqswtklm

On the Properties of Error Patterns in the Constant Lee Weight Channel [article]

Jessica Bariffi, Hannes Bartz, Gianluigi Liva, Joachim Rosenthal
2022 arXiv   pre-print
The problem of scalar multiplication applied to vectors is considered in the Lee metric.  ...  Unlike in other metrics, the Lee weight of a vector may be increased or decreased by the product with a nonzero, nontrivial scalar.  ...  New families of error correcting codes endowed with the Lee metric together with an iterative decoding algorithm were proposed [12] while information set decoding (ISD) in the Lee metric has been analyzed  ... 
arXiv:2110.01878v2 fatcat:pezyaqdxwrgxra5vvqziorvo7i

Page 2659 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
Inform. Theory 28 (1982), no. 1, 111-113. Author’s summary: “The classical Elias bound for the Lee metric is weak when the size of the alphabet is larger than the minimum distance.  ...  ISBN 0-471-08132-9 This book has two parts: Foundations of cryptography and Applications of cryptography.  ... 

Classical and Quantum algorithms for generic Syndrome Decoding problems and applications to the Lee metric [article]

André Chailloux, Thomas Debris-Alazard, Simona Etinski
2021 arXiv   pre-print
By providing the parameters of SD for which decoding in the Lee weight seems to be the hardest, our study could have several applications for designing code-based cryptosystems and their security analysis  ...  We then apply our results to the Lee metric, which currently receives a significant amount of attention.  ...  The authors want to thank Nicolas Sendrier and Anthony Leverrier for helpful discussions.  ... 
arXiv:2104.12810v2 fatcat:olihfyyyszazhfp32qjza4y6sq

On the Hardness of the Lee Syndrome Decoding Problem [article]

Violetta Weger, Karan Khathuria, Anna-Lena Horlemann, Massimo Battaglioni, Paolo Santini, Edoardo Persichetti
2022 arXiv   pre-print
In this paper we study the hardness of the syndrome decoding problem over finite rings endowed with the Lee metric.  ...  Then, we study the complexity of solving the problem, by translating the best known solvers in the Hamming metric over finite fields to the Lee metric over finite rings, as well as proposing some novel  ...  Acknowledgments The first author is supported by the Swiss National Science Foundation grant number 195290. The second author is supported by the Estonian Research Council grant number PRG49.  ... 
arXiv:2002.12785v5 fatcat:xrtv6beys5h4hl5k7rmc5smfuu

Recent Progress in Code-Based Cryptography [chapter]

Pierre-Louis Cayrel, Sidi Mohamed El Yousfi Alaoui, Gerhard Hoffmann, Mohammed Meziani, Robert Niebuhr
2011 Communications in Computer and Information Science  
Section 3 deals with the new improvements of code-based signature schemes and Section 4 presents the new results in code-based secret-key cryptography.  ...  In contrast to number-theoretic problems typically used in cryptography, the underlying problems have so far resisted subexponential time attacks as well as quantum algorithms.  ...  Decoding attacks Information-set decoding (ISD) and the generalized birthday algorithm (GBA) are the two most important types of generic attacks against code-based cryptosystems.  ... 
doi:10.1007/978-3-642-23141-4_3 fatcat:tydg6d5zunhbplpchcnozoaanm

Frequency Speech Scrambler Based on the Hartley Transform and the Insertion of Random Frequency Components

Francisco Nascimento, Ricardo Toscano
2012 The International Journal of Forensic Computer Science  
Speech scrambler applications in the time domain may be found in literature (Mitchell and Piper, 1985 ; Lee and Chou, 1984; Huang and Stansfield, 1993) .  ...  This paper presents a voice cryptography system based on a scrambler that lends itself to this purpose, providing: significant resistance to the breach of information, the ability to reconfigure internal  ... 
doi:10.5769/j201201001 fatcat:dqffyxrtbbc3tojv3rureh3dxq

Decoding permutation arrays with ternary vectors

Chia-Jung Lee, Te-Tsung Lin, Min-Zheng Shieh, Shi-Chun Tsai, Hsin-Lung Wu
2010 Designs, Codes and Cryptography  
We give an explicit decoding scheme for the permutation arrays under Hamming distance metric, where the encoding is constructed via a distance-preserving mapping from ternary vectors to permutations (3  ...  Acknowledgments The work was supported in part by the National Science Council of Taiwan under contract NSC 97-2221-E-009-064-MY3 and NSC-98-2221-E-009-078-MY3.  ...  In this paper, we investigate the same problem but with the Hamming distance metric, which is widely used in coding theory and related areas [2] . Meanwhile, Lin et al.  ... 
doi:10.1007/s10623-010-9435-3 fatcat:7qekmgs5urhsndf4zxrzs3ckxy

A Survey on Code-Based Cryptography [article]

Violetta Weger, Niklas Gassner, Joachim Rosenthal
2022 arXiv   pre-print
We provide the mathematical background in a lecture notes style, with the intention of reaching a wider audience.  ...  We cover the main frameworks introduced in code-based cryptography and analyze their security assumptions.  ...  Acknowledgement The first author is supported by the Swiss National Science Foundation grant number 195290.  ... 
arXiv:2201.07119v3 fatcat:oo53emg22jdxtmsevemlit7hlm

Page 2299 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
Lee metric is appropriate.”  ...  The codes are considered with respect to a Mannheim metric, which is a Manhattan metric modulo a two-dimensional grid.  ... 
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