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# Résultats de recherche

**9538**

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## 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 ... Voir la vidéole (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, ... Voir la vidéole (3m58s)

## 3.1. From Generic Decoding to Syndrome Decoding

... 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... Voir la vidéo

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 ... Voir la vidéole (3m12s)

## 3.3. Information Set Decoding: the Power of Linear Algebra

... the following*form*which is called systematic

*form*or standard

*form.*If the first n-k columns of matrix H*P are independent, then I am able to compute such a

*form.*If this is the case, the last k column of the matrix

*forms*an information set. If I... Voir la vidéo

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## 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 ... Voir la vidéole (3m8s)

## 3.5. Lee and Brickell Algorithm

... with all positions on the left, we will allow error patterns of the*form*given in the slide. So, in the left part we have w-p coordinate to 1 and on the right hand side we allow a small number p of positions to have a value 1. So, at each iteration,... Voir la vidéo

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 ... Voir la vidéole (7m28s)