Notice
4.1. Introduction
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Descriptif
Welcome to the fourth week of the MOOC Code-based Cryptography. Recall that we have mainlytwo ways of cryptanalyzing in the McEliece cryptosystem.We have Message Attacks, which address the problem ofdecoding a random linear code; these attacks has alreadybeen studied in the third week, by Nicolas Sendrier. Notice that efficientgeneric attack just makes the use of larger code in theMcEliece scheme necessary. And we also have Key Attacks. These attacks try toretrieve the code structure, rather than attempting to use anspecific decoding algorithm. These attacks will bestudied during this week. First, let us give asmall introduction. The principle of theMcEliece cryptosystem is as follows: consider a large familyof codes, with an efficient decoding algorithm, whichis indistinguishable from a random family of linear codesof the same length and dimension. Then, the public key is agenerator matrix of a code of the chosen family and thenumber of errors that we can correct. And the secret key is anefficient decoding algorithm specific for such code. The encryption algorithm:we take a plaintext and the public key, and we generatean error-vector of weight at most t, which is theerror-correcting capacity. We encode the messageusing the public key, then, the ciphertext is just theresulting codeword, and the error. How to decrypt? We justapply the secret key that is an efficient decoding algorithm,to retrieve the original message. McEliece proposed to usebinary Goppa code, but the parameters that heproposed are not enough nowadays. But there exist other familiessuitable for the McEliece scheme? On the following slides, we give asummary of these different proposals.
Intervention
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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
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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
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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
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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
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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,
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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
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4.2. Support Splitting Algorithm
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuThis session will be about the support splitting algorithm. For the q-ary case, there are three different notions of equivalence. The general one: two codes of length n are semi-linear equivalent
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4.3. Distinguisher for GRS codes
Marquez-CorbellaIreneSendrierNicolasFiniaszMatthieuIn this session we will see that generalized Reed-Solomon codes behave differently than random codes with respect to the star operation. Thus we can define a distinguisher for Generalized Reed
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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
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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,
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5.4. Parallel-CFS
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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
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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
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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
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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
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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
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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
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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
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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
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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
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