Academic literature on the topic 'Cryptographie à base de codes correcteurs'
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Dissertations / Theses on the topic "Cryptographie à base de codes correcteurs":
Peirani, Béatrice. "Cryptographie à base de codes correcteurs d'erreurs et générateurs aléatoires." Aix-Marseille 1, 1994. http://www.theses.fr/1994AIX11046.
Aragon, Nicolas. "Cryptographie à base de codes correcteurs d’erreurs en métrique rang et application." Thesis, Limoges, 2020. http://www.theses.fr/2020LIMO0061.
Code-based cryptography is one of the fields allowing to build post-quantum cryptosystems, i.e secure against a quantum computer. Contrary to factorization and discrete logarithm, which are the two most used problems in cryptography right now, no algorithm is known to solve the decoding problem for random codes in polynomial time using a quantum computer. In this thesis, we focus on rank-based cryptography, in which we study codes based on the rank metric instead of the Hamming metric. This metric has the advantage of allowing to build cryptosystems with lower key sizes, but is less mature than the Hamming metric. Firstly, we present two new decoding algorithms in the rank metric : the first one is a combinatorial algorithm solving the decoding problem for random codes, hence allowing to better estimate the complexity of the attacks. The second one is an improvement of the decoding algorithm for Low Rank Parity Check (LRPC). We then present two code-based cryptosystems : a rank-based signature scheme which is an adaptation of the Schnorr-Lyubashevsky approach in the Euclidean metric, and an improvement of the Hamming Quasi-Cyclic (HQC) encryption scheme, for which we propose a new analysis of the decryption failure rate and the use of another family of error correcting codes. We then study two adaptations of the Schnorr-Lyubashevsky approach : one in the Hamming metric and the other one in the rank metric, for which we propose cryptanalysis allowing to recover secret keys using information leakage from the signatures. Finally we present the choices used to implement rank-based cryptosystems in the Rank-Based Cryptography (RBC) library
Urvoy, De Portzamparc Frédéric. "Sécurités algébrique et physique en cryptographie fondée sur les codes correcteurs d'erreurs." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066106/document.
Code-based cryptography, introduced by Robert McEliece in 1978, is a potential candidate to replace the asymetric primitives which are threatened by quantum computers. More generral, it has been considered secure for more than thirty years, and allow very vast encryption primitives. Its major drawback lies in the size of the public keys. For this reason, several variants of the original McEliece scheme with keys easier to store were proposed in the last years.In this thesis, we are interested in variants using alternant codes with symmetries and wild Goppa codes. We study their resistance to algebraic attacks, and reveal sometimes fatal weaknesses. In each case, we show the existence of hidden algebraic structures allowing to describe the secret key with non-linear systems of multivariate equations containing fewer variables then in the previous modellings. Their resolutions with Gröbner bases allow to find the secret keys for numerous instances out of reach until now and proposed for cryptographic purposes. For the alternant codes with symmetries, we show a more fondamental vulnerability of the key size reduction process. Prior to an industrial deployment, it is necessary to evaluate the resistance to physical attacks, which target device executing a primitive. To this purpose, we describe a decryption algorithm of McEliece more resistant than the state-of-the-art.Code-based cryptography, introduced by Robert McEliece in 1978, is a potential candidate to replace the asymetric primitives which are threatened by quantum computers. More generral, it has been considered secure for more than thirty years, and allow very vast encryption primitives. Its major drawback lies in the size of the public keys. For this reason, several variants of the original McEliece scheme with keys easier to store were proposed in the last years.In this thesis, we are interested in variants using alternant codes with symmetries and wild Goppa codes. We study their resistance to algebraic attacks, and reveal sometimes fatal weaknesses. In each case, we show the existence of hidden algebraic structures allowing to describe the secret key with non-linear systems of multivariate equations containing fewer variables then in the previous modellings. Their resolutions with Gröbner bases allow to find the secret keys for numerous instances out of reach until now and proposed for cryptographic purposes. For the alternant codes with symmetries, we show a more fondamental vulnerability of the key size reduction process. Prior to an industrial deployment, it is necessary to evaluate the resistance to physical attacks, which target device executing a primitive. To this purpose, we describe a decryption algorithm of McEliece more resistant than the state-of-the-art
Urvoy, De Portzamparc Frédéric. "Sécurités algébrique et physique en cryptographie fondée sur les codes correcteurs d'erreurs." Electronic Thesis or Diss., Paris 6, 2015. http://www.theses.fr/2015PA066106.
Code-based cryptography, introduced by Robert McEliece in 1978, is a potential candidate to replace the asymetric primitives which are threatened by quantum computers. More generral, it has been considered secure for more than thirty years, and allow very vast encryption primitives. Its major drawback lies in the size of the public keys. For this reason, several variants of the original McEliece scheme with keys easier to store were proposed in the last years.In this thesis, we are interested in variants using alternant codes with symmetries and wild Goppa codes. We study their resistance to algebraic attacks, and reveal sometimes fatal weaknesses. In each case, we show the existence of hidden algebraic structures allowing to describe the secret key with non-linear systems of multivariate equations containing fewer variables then in the previous modellings. Their resolutions with Gröbner bases allow to find the secret keys for numerous instances out of reach until now and proposed for cryptographic purposes. For the alternant codes with symmetries, we show a more fondamental vulnerability of the key size reduction process. Prior to an industrial deployment, it is necessary to evaluate the resistance to physical attacks, which target device executing a primitive. To this purpose, we describe a decryption algorithm of McEliece more resistant than the state-of-the-art.Code-based cryptography, introduced by Robert McEliece in 1978, is a potential candidate to replace the asymetric primitives which are threatened by quantum computers. More generral, it has been considered secure for more than thirty years, and allow very vast encryption primitives. Its major drawback lies in the size of the public keys. For this reason, several variants of the original McEliece scheme with keys easier to store were proposed in the last years.In this thesis, we are interested in variants using alternant codes with symmetries and wild Goppa codes. We study their resistance to algebraic attacks, and reveal sometimes fatal weaknesses. In each case, we show the existence of hidden algebraic structures allowing to describe the secret key with non-linear systems of multivariate equations containing fewer variables then in the previous modellings. Their resolutions with Gröbner bases allow to find the secret keys for numerous instances out of reach until now and proposed for cryptographic purposes. For the alternant codes with symmetries, we show a more fondamental vulnerability of the key size reduction process. Prior to an industrial deployment, it is necessary to evaluate the resistance to physical attacks, which target device executing a primitive. To this purpose, we describe a decryption algorithm of McEliece more resistant than the state-of-the-art
Turrel, Bardet Magali. "Etude des systèmes algébriques surdéterminés : applications aux codes correcteurs et à la cryptographie." Paris 6, 2004. https://tel.archives-ouvertes.fr/tel-00449609.
Bardet, Magali. "Étude des systèmes algébriques surdéterminés. Applications aux codes correcteurs et à la cryptographie." Phd thesis, Université Pierre et Marie Curie - Paris VI, 2004. http://tel.archives-ouvertes.fr/tel-00449609.
Lequesne, Matthieu. "Analysis of code-based post-quantum cryptosystems." Electronic Thesis or Diss., Sorbonne université, 2021. http://www.theses.fr/2021SORUS046.
Today, most public-key cryptosystems used to ensure the privacy and authenticity of communications rely on the hardness of number theoretic problems. For instance, the security of the RSA algorithm is based on the fact that factoring a product of large prime numbers is computationally hard. However, in 1994, Shor proposed an algorithm to efficiently solve this problem using a quantum computer. Large-scale quantum computers do not exists yet, but this could change within the next decades. Therefore, we need new public-key cryptosystems that resist quantum attacks. This is known as post-quantum cryptography. In 2017, the American National Institute of Standards and Technologies (NIST) invited researchers to submit proposals for the standardisation of post-quantum cryptographic algorithms. One promising solution is to design cryptosystems based of the hardness of decoding error-correcting codes. A significant proportion of cryptosystems submitted to the NIST use this approach. In this thesis, we propose an analysis of different code-based post-quantum cryptosystems. First, we study the case of QC-MDPC codes and show that one can recover the private key by observing the syndrome weight or the number of iterations of the decoding algorithm. Then, we propose key-recovery attacks exploiting the structure of three cryptosystems: Edon-K, RLCE and XGRS. Finally, we study the hardness of the general decoding problem for ternary codes, in the large weight setting, which is used in the Wave signature scheme
Augot, Daniel. "Décodage des codes algébriques et cryptographie." Habilitation à diriger des recherches, Université Pierre et Marie Curie - Paris VI, 2007. http://tel.archives-ouvertes.fr/tel-00159149.
les codes cycliques binaires et les codes de Reed-Solomon sur un
alphabet $q$-aire (ainsi que les codes géométriques). En ce qui
concerne les codes cycliques, ceux-ci n'ont pas d'algorithme générique
de décodage, mis à part les codes BCH ou assimilés (bornes de
Hartman-Tzeng, de Roos). Au premier rang des codes intéressants pour
lesquels on ne connaît pas d'algorithme de décodage {\em générique}
figurent les {\em codes à résidus quadratiques}, qui ont de bons
paramètres. J'étudie une mise en équation du problème du décodage par
syndrôme de ces codes, que l'on peut résoudre avec des outils de base
de Gröbner. On obtient ainsi des algorithmes de décodage de complexité
raisonnable pour ces codes. Ces travaux ont fait l'objet d'une partie
de la thèse de Magali Bardet.
En ce qui concerne les codes de Reed-Solomon, ceux-ci peuvent être vus
comme des {\em codes d'évaluation}, et le problème de décodage associé
revient à approcher une fonction par des polynômes de base degré. De
grands progrès ont été réalisés par Guruswami et Sudan, qui ont trouvé
un algorithme qui décode bien au delà des rayons classiques de
décodage, en relaxant l'hypothèse que la solution doit être unique. Je
propose d'améliorer certaines étapes de cet algorithme, en le rendant
plus rapide et déterministe (notamment en évitant une factorisation de
polynôme sur un corps fini), dans le cas des codes Reed-Solomon, et
dans le cas des codes géométriques. Ces travaux ont été effectués en
encadrant Lancelot Pecquet.
Du point de vue théorique, j'ai étudié des généralisations
multivariées, qui correspondent à certains codes: les codes produits
de Reed-Solomon, et les codes de Reed-Muller. On obtient ainsi un bon
rayon de décodage, dans le cas des codes de petit taux. Dans le cas de
codes de Reed-Muller sur l'alphabet binaire, Cédric Tavernier, dans sa
thèse sous ma direction, a produit et implanté un algorithme efficace,
plus que ceux basés sur l'algorithme de Guruswami-Sudan.
J'ai étudié les aspects négatifs du problème de décodage par syndrôme
des codes linéaires, et du décodage des codes de Reed-Solomon, quand
le nombre d'erreurs est élevé, en but d'application en cryptographie.
Dans le premier cas, j'ai construit une fonction de hachage
cryptographique à réduction de sécurité, c'est-à-dire que trouver une
faiblesse dans le fonction de hachage revient à résoudre un problème
réputé difficile de codage. J'ai aussi construit une nouvelle
primitive de chiffrement à clé publique, reposant sur la difficulté de
décoder les codes de Reed-Solomon.
Dans un domaine plus appliqué, j'ai proposé avec Raghav Bhaskar un
nouvel algorithme d'échange de clé multi-utilisateurs, fondé sur le
problème du logarithme discret. Raghav Bhaskar a fourni une preuve de
sécurité de ce protocole, pendant sa thèse sous ma direction. Nous
avons aussi étudié comment adapter ce protocole aux pertes de
messages, car notre protocole est un des seuls qui est robuste à ces
pertes.
Cheriere, Agathe. "Side-channel resistance of cryptographic primitives based on error-correcting codes." Electronic Thesis or Diss., Université de Rennes (2023-....), 2023. http://www.theses.fr/2023URENS092.
For about three decades, we have been aware of attacks targeting implementations of cryptosystems, exploiting physical information such as execution time. Naturally, questions arise about the threats these attacks pose to the upcoming industry deployments of post-quantum schemes. In this thesis, we focus on the resistance of error-correcting code-based cryptographic algorithms against side-channel attacks. We specifically studied two schemes, ROLLO and BIKE, which were candidates for the second round of post-quantum standardization organized by NIST. Through our research, we demonstrate that their constant-time implementation is notably vulnerable to attacks using power consumption analysis. To demonstrate these vulnerabilities, we employ techniques such as machine learning and linear algebra. Furthermore, for both scheme, the attack requires a single trace of power consumption to recover the private key. Following the identification of these vulnerabilities, we propose countermeasure strategies to prevent these attacks while maintaining constant-time operation. For about three decades, we have been aware of attacks targeting implementations of cryptosystems, exploiting physical information such as execution time. Naturally, questions arise about the threats these attacks pose to the upcoming industry deployments of post-quantum schemes. In this thesis, we focus on the resistance of error-correcting code-based cryptographic algorithms against side-channel attacks. We specifically studied two schemes, ROLLO and BIKE, which were candidates for the second round of post-quantum standardization organized by NIST. Through our research, we demonstrate that their constant-time implementation is notably vulnerable to attacks using power consumption analysis. To demonstrate these vulnerabilities, we employ techniques such as machine learning and linear algebra. Furthermore, for both scheme, the attack requires a single trace of power consumption to recover the private key. Following the identification of these vulnerabilities, we propose countermeasure strategies to prevent these attacks while maintaining constant-time operation
Cayrel, Pierre-Louis. "Construction et optimisation de cryptosystèmes basés sur les codes correcteurs d'erreurs." Limoges, 2008. https://aurore.unilim.fr/theses/nxfile/default/46aac3f7-1539-4684-bef6-9b1ae632c183/blobholder:0/2008LIMO4026.pdf.
In this thesis, we are interested in the study of encryption systems as well as signature schemes whose security relies on difficult problems of error-correcting codes. These research activities have been motivated, a part of a theoretical point of view by creating : new signature schemes with special properties and a way of reducing the size of the key of the McEliece scheme, and on the other hand, a practical point of view to use structural properties to obtain effective implementations of a signature scheme which is based on error-correcting codes. As its title indicates, this thesis deals with the construction and optimization of cryptosystems based on error-correcting codes and more particularly five new protocols. It presents a secure version of the Stern scheme in a low-resources environment, a new construction of the Kabatianski, Krouk and Smeets scheme, a signature scheme based on the identity proved secure in the random oracle model, a threshold ring signature scheme and a reduction of the size of the key of the McEliece scheme using quasi-cyclic alternant codes. In the annex, this work deals with algebraic attacks against linear feedback shift register with memory. It also presents a brief study of cyclic codes on rings of matrices