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Near-collisions finding problem for decoding and recognition of error correcting codes ; Recherche de presque-collisions pour le décodage et la reconnaissance de codes correcteurs

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Title: Near-collisions finding problem for decoding and recognition of error correcting codes ; Recherche de presque-collisions pour le décodage et la reconnaissance de codes correcteurs
Authors: Carrier, Kevin
Contributors: Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ), Centre Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Sorbonne Université, Jean-Pierre Tillich, Nicolas Sendrier
Source: https://theses.hal.science/tel-03370678 ; Cryptographie et sécurité [cs.CR]. Sorbonne Université, 2020. Français. ⟨NNT : 2020SORUS281⟩.
Publisher Information: CCSD
Publication Year: 2020
Subject Terms: Search for the nearest neighbour, Polar codes, LDPC codes, Generic decoding, Post-quantum cryptography, Code recognition, Reconnaissance de codes, Cryptographie post-quantique, Décodage générique, Codes LDPC, Codes polaires, Recherche du plus proche voisin, [INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR], [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI], [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT]
Description: Error correcting codes are tools whose initial function is to correct errors caused by imperfect communication channels. In a non-cooperative context, there is the problem of identifying unknown codes based solely on knowledge of noisy codewords. This problem can be difficult for certain code families, in particular LDPC codes which are very common in modern telecommunication systems. In this thesis, we propose new techniques to more easily recognize these codes. At the end of the 1970s, McEliece had the idea of redirecting the original function of codes to use in ciphers; thus initiating a family of cryptographic solutions which is an alternative to those based on number theory problems. One of the advantages of code-based cryptography is that it seems to withstand the quantum computing paradigm; notably thanks to the robustness of the generic decoding problem. The latter has been thoroughly studied for more than 60 years. The latest improvements all rely on using algorithms for finding pairs of points that are close to each other in a list. This is the so called near-collisions search problem. In this thesis, we improve the generic decoding by asking in particular for a new way to find close pairs. To do this, we use list decoding of Arikan's polar codes to build new fuzzy hashing functions. In this manuscript, we also deal with the search for pairs of far points. Our solution can be used to improve decoding over long distances. This new type of decoding finds very recent applications in certain signature models. ; Les codes correcteurs d'erreurs sont des outils ayant pour fonction originale de corriger les erreurs produites par des canaux de communication imparfaits. Dans un contexte non coopératif, se pose le problème de reconnaître des codes inconnus à partir de la seule connaissance de mots de code bruités. Ce problème peut s'avérer difficile pour certaines familles de codes, notamment pour les codes LDPC qui sont très présents dans nos systèmes de télécommunication modernes. Dans cette thèse, nous ...
Document Type: doctoral or postdoctoral thesis
Language: French
Relation: NNT: 2020SORUS281
Availability: https://theses.hal.science/tel-03370678
https://theses.hal.science/tel-03370678v4/document
https://theses.hal.science/tel-03370678v4/file/CARRIER_Kevin_2020.pdf
Rights: info:eu-repo/semantics/OpenAccess
Accession Number: edsbas.2126FCFE
Database: BASE
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  Data: Near-collisions finding problem for decoding and recognition of error correcting codes ; Recherche de presque-collisions pour le décodage et la reconnaissance de codes correcteurs
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  Data: Cryptologie symétrique, cryptologie fondée sur les codes et information quantique (COSMIQ)<br />Centre Inria de Paris<br />Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)<br />Sorbonne Université<br />Jean-Pierre Tillich<br />Nicolas Sendrier
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  Data: <i>https://theses.hal.science/tel-03370678 ; Cryptographie et sécurité [cs.CR]. Sorbonne Université, 2020. Français. ⟨NNT : 2020SORUS281⟩</i>.
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  Data: <searchLink fieldCode="DE" term="%22Search+for+the+nearest+neighbour%22">Search for the nearest neighbour</searchLink><br /><searchLink fieldCode="DE" term="%22Polar+codes%22">Polar codes</searchLink><br /><searchLink fieldCode="DE" term="%22LDPC+codes%22">LDPC codes</searchLink><br /><searchLink fieldCode="DE" term="%22Generic+decoding%22">Generic decoding</searchLink><br /><searchLink fieldCode="DE" term="%22Post-quantum+cryptography%22">Post-quantum cryptography</searchLink><br /><searchLink fieldCode="DE" term="%22Code+recognition%22">Code recognition</searchLink><br /><searchLink fieldCode="DE" term="%22Reconnaissance+de+codes%22">Reconnaissance de codes</searchLink><br /><searchLink fieldCode="DE" term="%22Cryptographie+post-quantique%22">Cryptographie post-quantique</searchLink><br /><searchLink fieldCode="DE" term="%22Décodage+générique%22">Décodage générique</searchLink><br /><searchLink fieldCode="DE" term="%22Codes+LDPC%22">Codes LDPC</searchLink><br /><searchLink fieldCode="DE" term="%22Codes+polaires%22">Codes polaires</searchLink><br /><searchLink fieldCode="DE" term="%22Recherche+du+plus+proche+voisin%22">Recherche du plus proche voisin</searchLink><br /><searchLink fieldCode="DE" term="%22[INFO%2EINFO-CR]Computer+Science+[cs]%2FCryptography+and+Security+[cs%2ECR]%22">[INFO.INFO-CR]Computer Science [cs]/Cryptography and Security [cs.CR]</searchLink><br /><searchLink fieldCode="DE" term="%22[INFO%2EINFO-NI]Computer+Science+[cs]%2FNetworking+and+Internet+Architecture+[cs%2ENI]%22">[INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI]</searchLink><br /><searchLink fieldCode="DE" term="%22[INFO%2EINFO-IT]Computer+Science+[cs]%2FInformation+Theory+[cs%2EIT]%22">[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT]</searchLink>
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  Data: Error correcting codes are tools whose initial function is to correct errors caused by imperfect communication channels. In a non-cooperative context, there is the problem of identifying unknown codes based solely on knowledge of noisy codewords. This problem can be difficult for certain code families, in particular LDPC codes which are very common in modern telecommunication systems. In this thesis, we propose new techniques to more easily recognize these codes. At the end of the 1970s, McEliece had the idea of redirecting the original function of codes to use in ciphers; thus initiating a family of cryptographic solutions which is an alternative to those based on number theory problems. One of the advantages of code-based cryptography is that it seems to withstand the quantum computing paradigm; notably thanks to the robustness of the generic decoding problem. The latter has been thoroughly studied for more than 60 years. The latest improvements all rely on using algorithms for finding pairs of points that are close to each other in a list. This is the so called near-collisions search problem. In this thesis, we improve the generic decoding by asking in particular for a new way to find close pairs. To do this, we use list decoding of Arikan's polar codes to build new fuzzy hashing functions. In this manuscript, we also deal with the search for pairs of far points. Our solution can be used to improve decoding over long distances. This new type of decoding finds very recent applications in certain signature models. ; Les codes correcteurs d'erreurs sont des outils ayant pour fonction originale de corriger les erreurs produites par des canaux de communication imparfaits. Dans un contexte non coopératif, se pose le problème de reconnaître des codes inconnus à partir de la seule connaissance de mots de code bruités. Ce problème peut s'avérer difficile pour certaines familles de codes, notamment pour les codes LDPC qui sont très présents dans nos systèmes de télécommunication modernes. Dans cette thèse, nous ...
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      – Text: French
    Subjects:
      – SubjectFull: Search for the nearest neighbour
        Type: general
      – SubjectFull: Polar codes
        Type: general
      – SubjectFull: LDPC codes
        Type: general
      – SubjectFull: Generic decoding
        Type: general
      – SubjectFull: Post-quantum cryptography
        Type: general
      – SubjectFull: Code recognition
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      – SubjectFull: Reconnaissance de codes
        Type: general
      – SubjectFull: Cryptographie post-quantique
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      – SubjectFull: Décodage générique
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      – SubjectFull: Codes LDPC
        Type: general
      – SubjectFull: Codes polaires
        Type: general
      – SubjectFull: Recherche du plus proche voisin
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      – SubjectFull: [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT]
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