Notice
3.5. Lee and Brickell Algorithm
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
In this fifth session,we will study a variant of information set decodingproposed by Lee and Brickell. So, the main ideaconsists in relaxing the Prange algorithm to amortize thecost of the Gaussian elimination. So, instead of error patterns with allpositions on the left, we will allow error patterns ofthe form given in the slide. So, in the left part wehave w-p coordinate to 1 and on the right hand sidewe allow a small number p of positions to have a value 1. So, at each iteration, wewill simply enumerate all the possible k to p valuesfor the right hand side. Note that the Prangealgorithm corresponds to weight p = 0. The computational syndromedecoding and the solution we are going to propose to ithas an additional parameter p which is an integer between 0 and w. As before, we repeat thefollowing: we pick a permutation matrix P, we computethe systematic form of that matrix using aGaussian elimination, and next, we enumerate thisset and we check every element in that setuntil we find one element of weight w-p. If thishappens, then we have a solution to our problem, we return it. The cost of the iterationin that case will increase because in addition to theGaussian elimination we now have an enumeration costwhich is equal to (k,p). Now, the complexity analysis. The probability to obtainan error pattern of that form in a specific iteration is equal to P∞ as given in the slide. It follows that theexpected number of iteration N∞ is the inverse of the probability. And as I said before, theiteration cost is the sum of those two terms. Thetotal cost of the Lee and Brickell algorithm is thefollowing: the product of N∞ * K, and in fact, it appears that we never gain more than apolynomial factor compare with Prange algorithm, and I give herethe idea of how to prove this fact. And the last thing to do inthis formula is to minimize it over all possiblevalues of p and, except for very strangeparameters that's either w or W, the minimum value of thatformula is obtained for p=2.
Intervention
Dans la même collection
-
3.6. Stern/Dumer Algorithm
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we will present the Stern algorithm for decoding. In fact, the idea is to combine two algorithms that we have seen before, the Lee and Brickell algorithm and the Birthday Decoding.
-
3.9. Generalized Birthday Algorithm for Decoding
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuThe session nine is devoted to the application of the Generalized Birthday Algorithm to decoding. The Generalized Birthday Algorithm was presented by David Wagner in 2002, in a more general
-
3.3. Information Set Decoding: the Power of Linear Algebra
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this third session, we will present the most important concept of the week: Information Set Decoding. The problem of decoding is not only a combinatorial problem. Because we are dealing with
-
3.7. May, Meurer, and Thomae Algorithm
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuSo, with the session 7 we are entering the most advanced part of that course. The idea of what I called the Improved Birthday Decoding is to use the so-called "representation technique" introduced
-
3.1. From Generic Decoding to Syndrome Decoding
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuWelcome to the third week of the MOOC on code-based cryptography. This week, we will learn about message attacks. Among the ten sessions of this week, the first six will present the most essential
-
3.10. Decoding One Out of Many
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuThe final session of this week is devoted to Decoding One Out of Many. Decoding One Out of Many is interested in solving the following variant of Syndrome Decoding. In this variant, the only
-
3.4. Complexity Analysis
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, I will present the main technique to make the analysis of the various algorithms presented in this course. So, Information Set Decoding refers to a family of algorithms which is
-
3.8. Becker, Joux, May, and Meurer Algorithm
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuNow in session 8, we will present yet another evolution of information set decoding. Before presenting this improvement, we will first improve the Birthday Decoding algorithm what I call a Further
-
3.2. Combinatorial Solutions: Exhaustive Search and Birthday Decoding
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, I will detail two combinatorial solutions to the decoding problem. The first one is the Exhaustive Search. To find our w columns, we will simply enumerate all the tuples j1 to jw
Avec les mêmes intervenants et intervenantes
-
5.1. Code-Based Digital Signatures
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuWelcome to the last week of this MOOC on code-based cryptography. This week, we will be discussing other cryptographic constructions relying on coding theory. We have seen how to do public key
-
4.5. Error-Correcting Pairs
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuWe present in this session a general decoding method for linear codes. And we will see it in an example. Let C be a generalized Reed-Solomon code of dimension k associated to the pair (c, d). Then,
-
5.4. Parallel-CFS
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, I will present a variant of the CFS signature scheme called parallel-CFS. We start from a simple question: what happens if you try to use two different hash functions and compute
-
4.8. Attack against Algebraic Geometry codes
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we will present an attack against Algebraic Geometry codes (AG codes). Algebraic Geometry codes is determined by a triple. First of all, an algebraic curve of genus g, then a n
-
5.7. The Fast Syndrome-Based (FSB) Hash Function
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn the last session of this week, we will have a look at the FSB Hash Function which is built using the one-way function we saw in the previous session. What are the requirements for a
-
5.2. The Courtois-Finiasz-Sendrier (CFS) Construction
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, I am going to present the Courtois-Finiasz-Sendrier Construction of a code-based digital signature. In the previous session, we have seen that it is impossible to hash a document
-
4.6. Attack against GRS codes
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session we will discuss the proposal of using generalized Reed-Solomon codes for the McEliece cryptosystem. As we have already said, generalized Reed-Solomon codes were proposed in 1986 by
-
5.5. Stern’s Zero-Knowledge Identification Scheme
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we are going to have a look at Stern’s Zero-Knowledge Identification Scheme. So, what is a Zero-Knowledge Identification Scheme? An identification scheme allows a prover to prove
-
4.9. Goppa codes still resist
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuAll the results that we have seen this week doesn't mean that code based cryptography is broken. So in this session we will see that Goppa code still resists to all these attacks. So recall that
-
4.4. Attack against subcodes of GRS codes
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we will talk about using subcodes of a Generalized Reed–Solomon code for the McEliece Cryptosystem. Recall that to avoid the attack of Sidelnikov and Shestakov, Berger and
-
5.3. Attacks against the CFS Scheme
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we will have a look at the attacks against the CFS signature scheme. As for public-key encryption, there are two kinds of attacks against signature schemes. First kind of attack is
-
4.7. Attack against Reed-Muller codes
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we will introduce an attack against binary Reed-Muller codes. Reed-Muller codes were introduced by Muller in 1954 and, later, Reed provided the first efficient decoding algorithm
Sur le même thème
-
Des systèmes de numération pour le calcul modulaire
BajardJean-ClaudeLe calcul modulaire est utilisé dans de nombreuses applications des mathématiques, telles que la cryptographie. La réduction modulaire dans un contexte très général est coûteuse, car elle n
-
Projection methods for community detection in complex networks
LitvakNellyCommunity detection is one of most prominent tasks in the analysis of complex networks such as social networks, biological networks, and the world wide web. A community is loosely defined as a group
-
Lara Croft. doing fieldwork under surveillance
Dall'AgnolaJasminLara Croft. Doing Fieldwork Under Surveillance Intervention de Jasmin Dall'Agnola (The George Washington University), dans le cadre du Colloque coorganisé par Anders Albrechtslund, professeur en
-
Containing predictive tokens in the EU
CzarnockiJanContaining Predictive Tokens in the EU – Mapping the Laws Against Digital Surveillance, intervention de Jan Czarnocki (KU Leuven), dans le cadre du Colloque coorganisé par Anders Albrechtslund,
-
Inauguration de l'exposition - Vanessa Vitse : Nombres de Sophie Germain et codes secrets
VitseVanessaExposé de Vanessa Vitse (Institut Fourier) : Nombres de Sophie Germain et codes secrets
-
"Le mathématicien Petre (Pierre) Sergescu, historien des sciences, personnalité du XXe siècle"
HerléaAlexandreAlexandre HERLEA est membre de la section « Sciences, histoire des sciences et des techniques et archéologie industrielle » du CTHS. Professeur émérite des universités, membre effectif de l'Académie
-
Ivan Murit - Processus de création d'images
MuritIvanJe vais présenter une manière décalée d'aborder les outils d'impression. Pour cela nous ne partirons pas de l'envie d'imprimer une image préexistante, mais d'avant cela : comment se crée une forme
-
Retour d'expérience sur l'utilisation croisée de plusieurs archives de fouilles
TufféryChristopheDans le cadre d'une thèse de doctorat engagée depuis 2019, une étude historiographique et épistémologique des effets des dispositifs numériques sur l'archéologie et sur les archéologues au cours des
-
Information Structures for Privacy and Fairness
PalamidessiCatusciaInformation Structures for Privacy and Fairness
-
Le Creativ’Lab, au cœur de la robotique et de l’intelligence artificielle (ASR N°18 - LORIA)
HénaffPatrickLefebvreSylvainLe LORIA, laboratoire phare de la Grande Région dans le domaine de l’informatique, propose de rendre la recherche plus ouverte, plus collaborative, plus ambitieuse… en un mot, plus créative, à travers
-
AI and Human Decision-Making: An Interdisciplinary Perspective
CastellucciaClaudeThis seminar will talk about some of the privacy risks of these systems and will describe some recent attacks. It will also discuss why they sometimes fail to deliver. Finally, we will also show that
-
Webinaire sur la rédaction des PGD
LouvetViolaineRédaction des Plans de Gestion de Données (PGD) sous l’angle des besoins de la communauté mathématique.
