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Canal-u.fr
2.1. Formal Definition
Description
:
Welcome 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 McEliece and the Niederreiter systems, which are the principal public-key schemes, based on error-correct ...
Date
:
05-05-2015
Description complète
2.1. Formal Definition
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2.2. Security-Reduction Proof
Description
:
Welcome 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 cryptosystem is secure, we select a problem which we know is hard to solve, and we reduce the problem to ...
Date
:
05-05-2015
Description complète
2.2. Security-Reduction Proof
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Canal-u.fr
2.3. McEliece Assumptions
Description
:
In 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 the problem of distinguishing a code with a prescribed structure from a random one. In this sequence, w ...
Date
:
05-05-2015
Description complète
2.3. McEliece Assumptions
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2.4. Notions of Security
Description
:
In this session, we will study the notion of security of public-key scheme. A public-key scheme is one-way if the probability of success of any adversary running in polynomial time is negligible. That is, without the private key, it is computationally impossible to recover the plaintext. For the McE ...
Date
:
05-05-2015
Description complète
2.4. Notions of Security
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Canal-u.fr
2.5. Critical Attacks - Semantic Secure Conversions
Description
:
In 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 cryptosystem. For example, suppose that the adversary knows r bits of the plaintext. Then the difficult ...
Date
:
05-05-2015
Description complète
2.5. Critical Attacks - Semantic Secure Conversions
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2.6. Reducing the Key Size
Description
:
In 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 cryptosystems since they provide efficient representation. A circulant matrix is a square matrix, its rows ...
Date
:
05-05-2015
Description complète
2.6. Reducing the Key Size
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2.7. Reducing the Key Size - LDPC codes
Description
:
LDPC 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 introduced by Gallager, in his doctoral thesis, in 1963. One of the characteristic of LDPC codes is the existe ...
Date
:
05-05-2015
Description complète
2.7. Reducing the Key Size - LDPC codes
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Canal-u.fr
2.8. Reducing the Key Size - MDPC codes
Description
:
This 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 code that admits a binary moderate density-parity check matrix. Typically, the Hamming weight of each row ...
Date
:
05-05-2015
Description complète
2.8. Reducing the Key Size - MDPC codes
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Canal-u.fr
2.9. Implementation
Description
:
This 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 level of performance of the current protocol? eBATS is a competition to identify the most efficient public ...
Date
:
05-05-2015
Description complète
2.9. Implementation
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