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Nombre de programmes trouvés : 9538
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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 (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 (5m30s)

3.4. Complexity Analysis

In 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 similar to the Prange algorithm that we have just seen. All variants of Information Set Decoding repeat a large number of independent iterations which all have a constant cost K and a success probability P. This means that this iteration has to be repeated an expected number of times N where N = 1/P. And the total workfactor ...
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le (6m37s)

3.6. Stern/Dumer Algorithm

In 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.  So, instead of a full Gaussian elimination, we will simply have a partial Gaussian elimination as presented here. And if we look at the lower part, what is called step 1, in red here in this slide, it is, in fact, a smaller CSD problem with a smaller matrix H', with a smaller target syndrome s' and with ...
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le (7m28s)

3.7. May, Meurer, and Thomae Algorithm

So, 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 by Howgrave-Graham and Joux in 2010 in which we will relax the way we construct the two lists in Birthday Decoding. So, if you remember, we could relax the size of the matrices H1 and H2 slightly to gain a polynomial factor on Birthday Decoding. But, we may push the idea further and increase the size of H1 and ...
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