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<title><string language="fre"><![CDATA[3.1. From Generic Decoding to Syndrome Decoding]]></string></title>
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<string language="fre"><![CDATA[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 key and
adding a random error. The adversary knows the
cryptogram and the public key and wish to recover the message
or, equivalently, the error. Without any additional
information on the public key, solving that problem is
called generic decoding. Generic decoding, in
contrast with the usual situation where the code is known in
advance, takes as argument a q-ary linear code. It can be either a
generator matrix, or a parity check matrix.
In the first case, we speak
of generic decoding; it takes as argument a vector,
presumably noisy, and a generator matrix and will return a message. The desirable feature of
a generic decoder is to succeed in removing an
error "e" as long as this error is small enough. By
small, I mean small hamming weight. A generic syndrome
decoder will take as argument a syndrome and a parity check matrix. It will succeed if it
manages to correct an error whenever the weight of
the error is small enough. Those two kind of decoders
are equivalent and so, in the sequel of this course, we would
only consider syndrome decoding. Syndrome decoding is
an NP complete problem. It takes as argument a
matrix, parity check matrix H, a syndrome s and an integer
w, and try to return an error pattern that will
correspond to this syndrome. In fact, we are trying to
find w column in the matrix H such that their sum is
equal to the target syndrome s. In other terms, we are
looking for w indices, j1 to jw such that the
corresponding column has a sum equal to s. The syndrome
decoding problem may have one or several solutions. We will denote CSD(H,s,w)
the set of all solutions to the above problem. Where a CSD stands
for computational syndrome decoding.]]></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[algorithmes]]></string></keyword>
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<date><dateTime>2015-05-05</dateTime></date>
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