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<title><string language="fre"><![CDATA[2.1. Formal Definition]]></string></title>
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<string language="fre"><![CDATA[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-correcting code. Let K be a security
parameter. An encryption scheme
is defined by the
following spaces: the space of all possible messages, the
space of all ciphertexts, the
space of the public-keys, and
the space of the secret-keys.Then, we need to define
the following algorithms.
A key generation
algorithm, which is a randomized algorithm that outputs a
public-key and a secret-key;
this algorithm should run
in expected polynomial time.
An encryption algorithm,
which is also a randomized algorithm that takes a
message and the public-key and outputs a ciphertext;
this algorithm runs also in
expected polynomial time.
And a decryption algorithm,
which is an algorithm that
takes a ciphertext and a
secret-key, and outputs the
original plaintext or
declares a failure; this algorithm
runs in polynomial time.
It is required that the
decryption of the ciphertext is
again the plaintext, and we
demand that the fasten attack on the system requires at
least 2^k bit operations.
In 1978, McEliece
introduced the first public-key
cryptosystem, as we have already
seen, based on error-correcting codes.
The security of this scheme
is based on two intractable
problems: the hardness of
decoding, and the problem of
distinguishing a code
with a prescribed structure.
This property makes
this scheme an interesting candidate for
post-quantum cryptography. Another advantage consists of its fast
encryption and decryption algorithms. But the main drawback is
the large size of the keys. We will use as public-key,
a large generator matrix.]]></string></description>
<keyword><string language="fre"><![CDATA[algèbre linéaire]]></string></keyword><keyword><string language="fre"><![CDATA[chiffrement à clé publique]]></string></keyword><keyword><string language="fre"><![CDATA[cryptage des données]]></string></keyword><keyword><string language="fre"><![CDATA[cryptographie]]></string></keyword><keyword><string language="fre"><![CDATA[McEliece]]></string></keyword><keyword><string language="fre"><![CDATA[LDPC]]></string></keyword><keyword><string language="fre"><![CDATA[MDPC]]></string></keyword>
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