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<title><string language="fre"><![CDATA[5.2. The Courtois-Finiasz-Sendrier (CFS) Construction]]></string></title>
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<string language="fre"><![CDATA[In this session, I am
going to present the Courtois-Finiasz-Sendrier
Construction of a code-based digital signature. In the previous session,
we have seen that it is impossible to hash a
document into decodable syndromes. But it is possible to hash
onto the space of all syndromes. The document is not always decodable. And we are going to see two
techniques to work around this problem. The first technique is to
add a counter to the document. This way, we hash both the
counter and the document and obtain a hash which is tied to
both the document and the counter. We increment the counter until
a decodable syndrome is found. The signature is the
decoding of the syndrome but also contains the counter which is
required for the verification. The second method is to
perform complete decoding. Complete decoding is the
idea of being able to decode any syndrome in the space. And
for this, we need to modify the decoding algorithm.
The idea is to add some exhaustive search to
the decoding algorithm. For example, if we want to
decode one more error in the decoding capacity of the
code, we simply do an exhaustive search on one position. Add this error
to the syndrome and try to decode it. We can do the same with two
errors or up to ? errors by doing a search on ? positions. This way, we can reach the
covering radius, which is the number of errors we need to
correct to decode any element in the syndrome space. Both techniques are expensive. Decodable syndromes must
have high enough density in the space of all syndromes. The
covering radius and decoding capacity must be
close to one another. If they are too distant,
it will be too expensive to perform complete decoding. What are the requirements for
code-based digital signatures? As for a public-key
encryption, we need to be able to keep the decoding algorithm secret. So, we need codes where it is
possible to hide the structure efficiently. Binary Goppa codes are
one of very few candidates. And so, we will use this
in the construction, exactly like in the original McEliece scheme. Then, to have some
efficient signature schemes, we need the highest possible
density of decodable syndromes.]]></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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<entity><![CDATA[BEGIN:VCARD
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REV:2021-09-16 17:26:56
FN:Irene MARQUEZ-CORBELLA
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<date><dateTime>2015-05-05</dateTime></date>
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<entity><![CDATA[BEGIN:VCARD
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REV:2021-09-16 17:26:56
FN:Matthieu FINIASZ
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URL;TYPE=work:https://www.canal-u.tv/auteurs/finiasz_matthieu
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<date><dateTime>2015-05-05</dateTime></date>
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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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<string language="fre"><![CDATA[5: Other cryptographic constructions relying on coding theory]]></string>
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