Notice
2.4. Notions of Security
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
In this session, we will study thenotion of security of public-key scheme. A public-key scheme isone-way if the probability of success of any adversaryrunning in polynomial time is negligible. That is,without the private key, it is computationally impossibleto recover the plaintext. For the McEliece, if weassume that the general decoding problem of a linear codeis on average a difficult problem and there exists noefficient distinguisher for Goppa codes, then the McEliecescheme has the One-Wayness property. However, McEliece isvulnerable to many attacks as we will see in the followingslides, and also in the next session. In this session, we will usethe notion of Oracle, along the following slides. An Oracle is simply a system thattakes queries and provides answers. The queries might beplaintext or ciphertext and the answers are thecorresponding ciphertext or plaintext. Non-malleabilityguarantees that it is infeasible to modify the ciphertext intoanother ciphertext of related messages. The following attack tellsus that the McEliece does not satisfy non-malleability.Suppose that the adversary intercepts a ciphertext.That is, the ciphertext is the sum of an encodedmessage and a random error. Then, the adversary canchoose a codeword and generate a new ciphertext withoutknowing the original plaintext. And there exists a relationbetween the first plaintext and the new plaintext.Now, suppose that the adversary has accessto a decryption Oracle.
Intervention
Dans la même collection
-
2.3. McEliece Assumptions
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we will talk about McEliece assumptions. The security of the McEliece scheme is based on two assumptions as we have already seen: the hardness of decoding a random linear code and
-
2.7. Reducing the Key Size - LDPC codes
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuLDPC codes have an interesting feature: they are free of algebraic structure. We will study in detail this proposal for the McEliece cryptosystem in this session. LDPC codes were originally
-
2.1. Formal Definition
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuWelcome to the second week of this MOOC entitled Code-Based Cryptography. This week, we will talk in detail about the McEliece cryptosystem. First, in this session, we will describe formally the
-
2.5. Critical Attacks - Semantic Secure Conversions
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we will study critical attacks against the public-key cryptosystem. The partial knowledge on the plaintext reduces drastically the computational cost of the attack to the McEliece
-
2.8. Reducing the Key Size - MDPC codes
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuThis is the last session where we will talk about reducing the key size. Here we will introduce the MDPC codes. In 2012, the MDPC codes were proposed for the McEliece schemes. An MDPC code is a
-
2.2. Security-Reduction Proof
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuWelcome to the second session. We will talk about the security-reduction proof. The security of a given cryptographic algorithm is reduced to the security of a known hard problem. To prove that a
-
2.6. Reducing the Key Size
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn the next three sessions, I will explain how to reduce the key size of code-based cryptosystem. Circulant matrices are the central point in many attempts to reduce the key size of code-based
-
2.9. Implementation
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuThis is the last session of the second week. The cryptography community has different options for using public key cryptosystems, among others, they have RSA or DSA. But … McEliece has the same
Avec les mêmes intervenants et intervenantes
-
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
-
5.6. An Efficient Provably Secure One-Way Function
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session, we are going to see how to build an efficient provably secure one-way function from coding theory. As you know, a one-way function is a function which is simple to evaluate and
-
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,
Sur le même thème
-
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
-
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
-
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.
-
Alexandre Booms : « Usage de matériel pédagogique adapté en géométrie : une transposition à interro…
« Usage de matériel pédagogique adapté en géométrie : une transposition à interroger ». Alexandre Booms, doctorant (Université de Reims Champagne-Ardenne - Cérep UR 4692)
-
Présentation de la rencontre. A l’heure du numérique « Quelles mesures pour la mesure ? ». Le relev…
BadieAlainTardyDominiqueMalmaryJean-JacquesZugmeyerStéphanieRencontre-Atelier de l'ANR Ornementation Architecturale des Gaules. À l’heure du numérique, « Quelles mesures pour la mesure ? ». Le relevé des blocs d’architecture décorés et l’apport des outils
-
Photogrammétrie : Performances et limitations
EgelsYvesRencontre-Atelier de l'ANR Ornementation Architecturale des Gaules. À l’heure du numérique, « Quelles mesures pour la mesure ? ». Le relevé des blocs d’architecture décorés et l’apport des outils
-
Relever et publier des blocs d’architecture : objectifs et méthodes
BadieAlainRencontre-Atelier de l'ANR Ornementation Architecturale des Gaules. À l’heure du numérique, « Quelles mesures pour la mesure ? ». Le relevé des blocs d’architecture décorés et l’apport des outils
-
D. Stern - Harmonic map methods in spectral geometry
SternDanielOver the last fifty years, the problem of finding sharp upper bounds for area-normalized Laplacian eigenvalues on closed surfaces has attracted the attention of many geometers, due in part to
-
R. Bamler - Compactness and partial regularity theory of Ricci flows in higher dimensions
BamlerRichard H.We present a new compactness theory of Ricci flows. This theory states that any sequence of Ricci flows that is pointed in an appropriate sense, subsequentially converges to a synthetic flow.
