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<title><string language="fre"><![CDATA[2.5. Critical Attacks - Semantic Secure Conversions]]></string></title>
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<string language="fre"><![CDATA[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 need to observe
this equation where G_I denotes the restriction of the matrix G
to the rows indexed by I. We study another attack, which
is called the reaction attack. 
In this attack, the
adversary just needs to observe the
reaction of the
receiver. So, this attack can be classified as a CCA but
with a weaker assumption.
This attack rests upon
the following premise:
a decoder will not attempt
to correct a vector with t + 1 or more errors. The idea of
the attack is the following:
first of all, an adversary
flips one bit of the ciphertext. Then, the adversary
transmits the flipped ciphertext to the receiver and
observes his reaction. 
The receiver could have
two possible reactions.
First reaction: if the flipped bit is an error-free position, then
the ciphertext will have t + 1
errors, so it is
uncorrectable. The second reaction: if
i is an error position, then
the flipped ciphertext will
have t - 1 error, and the
receiver will be able to decrypt it. We repeat this process for
every position until we have retrieved the error pattern. Another possible attack is
the resend-message attack. 
Note that the encryption
of the same message twice 
produces two different
ciphertext. A message-resend condition can be easily
detected by observing the weight of the sum of the two ciphertexts.
Note that the sum of the
two ciphertexts is the sum of 
the two error
vectors, what we have here. But, if the underlying
plaintexts are different, then the expected weight of the sum is
about the dimension of the code. 
Let]]></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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<date><dateTime>2015-05-05</dateTime></date>
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