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<title><string language="fre"><![CDATA[5.7. The Fast Syndrome-Based (FSB) Hash Function]]></string></title>
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<string language="fre"><![CDATA[In the last session of this
week, we will have a look at the FSB Hash Function which
is built using the one-way function we saw in
the previous session. What are the requirements for
a cryptographic hash function? So, it is a function which
takes an input of arbitrary size and outputs a fixed size. From a security point of
view, it should be hard to solve any of the three following
problems: first, find an input with a given hash which is
what we call preimage attacks; find an input with the same
hash as a given input which is what we call second
preimage attack; or find two inputs with the same hash which
is what we call collision attack. In addition, hash function have
some implementation constraints. It should be fast in
both software and hardware implementations, it should
be fast for both small inputs and large inputs and it
should have a compact description. Building a function of
arbitrary length is something which is not that obvious.
Usually, you simply iterate a function with a fixed input
size on blocks of the input. There are several
constructions to achieve this, the oldest one is the
Merkle-Damgård Construction. This function iterates a
compression function f which takes at each round a
part of the message m0, m1 or something like this and
starts with an IV or the chaining value which is the output of
the previous compression function. It is easy to understand and
it has a simple security proof. So, it is something that is used
pretty commonly in cryptography. Another construction
which is commonly used in cryptography is the
Davies-Meyer Construction. For the compression function, this
construction uses a block cipher E. The message is used as the
key of the block cipher and the input is the chaining value. An interesting element of
this construction is that it reuses the same
hardware as the block cipher. So, if you have an
implementation which already includes a block cipher, you don't
need any more implementations. A much more recent
construction is the Sponge construction. This construction uses a function
with the same input and output size. The message is XORed to a part
of an internal state fed to the function which is
some kind of permutation, then, another part of the
message is exhorted and so on. This is the absorb phase. Once you have finished
absorbing all the message in the padding, you have a squeeze
out phase where you take out - bits of the message from the internal
state, iterating the function f again. The interesting aspect of this
construction is its versatility. It can be used as both the
hash function where the input is larger than the output
or a pseudo-random generator where the input is small
and the output is large.]]></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[code correcteur]]></string></keyword><keyword><string language="fre"><![CDATA[algorithmes]]></string></keyword><keyword><string language="fre"><![CDATA[CFS]]></string></keyword><keyword><string language="fre"><![CDATA[Courtois-Finiasz-Sendrier]]></string></keyword>
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<string language="fre"><![CDATA[Droits réservés à l'éditeur et aux auteurs. 
Ces ressources de cours sont, sauf mention contraire, diffusées sous Licence Creative Commons. L’utilisateur doit mentionner le nom de l’auteur, il peut exploiter l’œuvre sauf dans un contexte commercial et il ne peut apporter de modifications à l’œuvre originale.]]></string>
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