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Nombre de programmes trouvés : 17838
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le (3m15s)

2.3. McEliece Assumptions

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, we will study in detail these two assumptions. The first assumption claims that decoding a random linear code is difficult.  First, notice that the general decoding problem is basically a re-writing of the Syndrome Decoding problem. And both are equivalent ...
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le (5m32s)

2.4. Notions of Security

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 McEliece, if we assume that the general decoding problem of a linear code is on average a difficult problem and there exists no efficient distinguisher for Goppa codes, then the McEliece scheme has the One-Wayness property. However, McEliece is vulnerable to many ...
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le (5m5s)

2.5. Critical Attacks - Semantic Secure Conversions

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 difficulty of recovering the remaining k - r bits in the complete McEliece with parameters [n, k] is equivalent to that of recovering the full plaintext in the McEliece with parameters [n, k - r]. This is given by this formula. You just ...
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le (3m45s)

2.6. Reducing the Key Size

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 are obtained by cyclically shifting the first row. An alternative representation of an n-tuple of elements is using polynomial. Thus, this matrix can be described by a polynomial. And the i-th row of a circulant matrix can be expressed by this formula. ...
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le (4m41s)

2.7. Reducing the Key Size - LDPC codes

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 existence of several iterative decoding algorithms which achieve excellent performances. Tanner, later, in the 1981, introduced a graphical representation to these codes as bipartite graph. However, they remained almost forgotten by the coding theory community until 1996 when MacKay and Neal re-discovered ...
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le (4m55s)

2.8. Reducing the Key Size - MDPC codes

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 is of the order the square of the length. In this sequence, I will describe this scheme of quasi-cyclic MDPC McEliece for a binary code of rate one half. So, we use circulant matrices of blocks of size p ...
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le (3m59s)

2.9. Implementation

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 key cryptosystem. They mesure among other criteria: the key size, the time of the key generation algorithm, the encryption algorithm, and the decryption algorithm. The eBATS benchmarking includes seven public key encryption schemes. A McEliece implementation, from Biswas and Sendrier, ...
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le (3m58s)

3.1. From Generic Decoding to Syndrome Decoding

Welcome 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 part of generic decoding and the last four will be devoted to more advanced matters. The first session is about generic decoding; a   presentation of what a message attack and what generic decoding is about. A cryptogram in the McEliece encryption scheme has the following form. A cryptogram is composed by multiplying a message by a public ...
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le (5m17s)

3.2. Combinatorial Solutions: Exhaustive Search and Birthday Decoding

In 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 and check whether the corresponding column plus the syndrome is equal to zero modulo 2. In detail here is how we will do. We have w loops enumerating the indices from j1 to jw, and in the innermost loop, we add the w columns plus the syndrome and either we test the value of the syndrome or ...
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le (3m12s)

3.3. Information Set Decoding: the Power of Linear Algebra

In 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 linear code, we may also use Linear Algebra. In particular, we are able to transform the Computational Syndrome Decoding problem by multiplying the matrix by a permutation P on the right and a nonsingular matrix U on the left. This will transform the problem of syndrome decoding into an equivalent one. It is very easy to prove that the ...
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