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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
The security of code-based cryptography usually relies on the hardness of the syndrome decoding (SD) problem for the Hamming weight.  ...  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  ...  The authors want to thank Nicolas Sendrier and Anthony Leverrier for helpful discussions.  ... 
arXiv:2104.12810v2 fatcat:olihfyyyszazhfp32qjza4y6sq

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

Chithralekha Balamurugan, Kalpana Singh, Ganeshvani Ganesan, Muttukrishnan Rajarajan
2021 Cryptography  
This threat triggered post-quantum cryptography research to design and develop post-quantum algorithms that can withstand quantum computing attacks.  ...  Thus, cryptography research has also been evolving from the classical Caesar cipher to the modern cryptosystems, based on modular arithmetic to the contemporary cryptosystems based on quantum computing  ...  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

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
Information set decoding (ISD) algorithms are the best known procedures to solve the decoding problem for general linear codes.  ...  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.  ...  The rationale of this work is to introduce techniques to solve the SDP for general codes in the Lee metric.  ... 
arXiv:2001.08425v2 fatcat:fevcgoge6vaujhafzjnqswtklm

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.  ...  Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring.  ...  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.  ...  Moreover, we set up the general framework for a McEliece and a Niederreiter cryptosystem over this ring.  ...  Acknowledgments We would like to thank Karan Khathuria for fruitful discussions and technical support.  ... 
doi:10.3934/amc.2020089 fatcat:nlnyopxblffcnn2ngpdlqdfrjq

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
McNie is a hybrid version of the McEliece and Niederreiter cryptosystems and its security is reduced to the hard problem of syndrome decoding.  ...  In particular, we apply rank-metric codes to McNie.  ...  This problem is generalized in the case of rank metric as follows: Rank Syndrome Decoding (RSD) Problem Let H be a (n − k) × n matrix over Fqm with k ≤ n, s ∈ Fkqm and r an integer.  ... 
arXiv:1812.05008v2 fatcat:wsagwr4tofd3fdn2cxpp3vogte

Decoding of (Interleaved) Generalized Goppa Codes [article]

Hedongliang Liu, Sabine Pircher, Alexander Zeh, Antonia Wachter-Zeh
2021 arXiv   pre-print
Finally, some code parameters and how they apply to the Classic McEliece post-quantum cryptosystem are shown.  ...  A quadratic-time decoding algorithm is presented which can decode errors up to half of the minimum distance.  ...  To deal with burst errors, we introduce interleaved generalized Goppa codes in Section V. We provide an explicit decoding algorithm and derive the new maximum decoding radius for GGCs.  ... 
arXiv:2102.02831v2 fatcat:7ez4td6awfhghes2tviksfyiw4

The Art of Signaling: Fifty Years of Coding Theory [chapter]

2009 Information Theory  
It is in fact tempting to ask a slightly different question; to fix the complexity of decoding and to ask for the maximum transmission rate that is possible.  ...  There is a sense in which the journey is more important than the goal, for the challenge of coming close to capacity has generated many important coding techniques.  ...  in Table I on soft-decision decoding, and to Walter Willinger for education on data network traffic.  ... 
doi:10.1109/9780470544907.ch20 fatcat:eeuyqk35orhmdleeiktamxgv6u

Code based Cryptography: Classic McEliece [article]

Harshdeep Singh
2020 arXiv   pre-print
We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD).  ...  Successful implementation of the ISD attack on McEliece cryptosystem for some small parameters set is executed and the code for the same is provided in the Appendix.  ...  Applications must extend using each public key for long enough to handle the costs of generating and distributing the key.  ... 
arXiv:1907.12754v2 fatcat:gt4rleeorba6zjtvol6qmwfyle

The art of signaling: fifty years of coding theory

A.R. Calderbank
1998 IEEE Transactions on Information Theory  
It is in fact tempting to ask a slightly different question; to fix the complexity of decoding and to ask for the maximum transmission rate that is possible.  ...  There is a sense in which the journey is more important than the goal, for the challenge of coming close to capacity has generated many important coding techniques.  ...  in Table I on soft-decision decoding, and to Walter Willinger for education on data network traffic.  ... 
doi:10.1109/18.720549 fatcat:utsr3jz3frexjezv3bznqkaxie

A code-based hybrid signcryption scheme [article]

Jean Belo Klamti, M. Anwar Hasan
2021 arXiv   pre-print
The proposed scheme uses an equivalent subcode as a public code for the receiver, making the NP-completeness of the equivalent subcode problem be one of our main security assumptions.  ...  We then base the signcryption tag-KEM to design a code-based hybrid signcryption scheme. A hybrid scheme deploys an asymmetric- as well as a symmetric-key encryption.  ...  The syndrome decoding problem was proven to be NP-complete in 1978 by Berlekamp et al. [13]. It is equivalent to the following problem.  ... 
arXiv:2112.07130v1 fatcat:mxx3zwiax5hgticy4llun2pepa

Modified pqsigRM: RM Code-based Signature Scheme

Yongwoo Lee, Wijik Lee, Young-Sik Kim, Jong-Seon No
2020 IEEE Access  
The proposed decoder samples from coset elements with small Hamming weight for any given syndrome and efficiently finds such an element.  ...  For 128 bits of classical security, the signature size is 4096 bits, and the public key size is less than 1 MB.  ...  However, there is currently no algorithm for solving the syndrome decoding problem by taking advantage of the hull.  ... 
doi:10.1109/access.2020.3026989 fatcat:ozlmqazvojeznh5zh3mwcny2aq

Coding Theory

Joachim Rosenthal, Mohammad Amin Shokrollahi
2007 Oberwolfach Reports  
Coding theory lies naturally at the intersection of a large number of disciplines in pure and applied mathematics: algebra and number theory, probability theory and statistics, communication theory, discrete  ...  The workshop on coding theory covered many facets of the recent research advances.  ...  a (generalized) decoding problem for rank-metric codes, allowing many of the tools from the theory of rank-metric codes to be applied to random network coding.  ... 
doi:10.4171/owr/2007/56 fatcat:ac2rttsrn5g2rn5la72nudiyum

Decoding Random Binary Linear Codes in 2 n/20: How 1 + 1 = 0 Improves Information Set Decoding [chapter]

Anja Becker, Antoine Joux, Alexander May, Alexander Meurer
2012 Lecture Notes in Computer Science  
Decoding random linear codes is a well studied problem with many applications in complexity theory and cryptography.  ...  Recently, there has been progress in improving the running time of the best decoding algorithms for binary random codes.  ...  We would like to thank Dan Bernstein for several excellent comments, in particular he proposed to use random partitions for generating the base lists in the COLUMNMATCH algorithm.  ... 
doi:10.1007/978-3-642-29011-4_31 fatcat:cb6j4fzr4jf3tgraodugauvkbe

Post-Quantum Cryptography [chapter]

Qijun Gu, Pascal Paillier, Tanja Lange, Edlyn Teske, Darrel Hankerson, Alfred Menezes, David Zhang, Feng Yue, Wangmeng Zuo, Jean-Jacques Quisquater, Gildas Avoine, Gerald Brose (+73 others)
2011 Encyclopedia of Cryptography and Security  
laws and regulations and therefore free for general use.  ...  The first editor would like to additionally thank Tanja Lange for many illuminating discussions regarding post-quantum cryptography and for initiating the Post-Quantum Cryptography workshop series in the  ...  Acknowledgements We thank Phong Nguyen and Markus Rückert for helpful discussions on the practical security of lattice-based cryptography.  ... 
doi:10.1007/978-1-4419-5906-5_386 fatcat:ucdkilta7zc3voq7nqctmjkcr4
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