<?xml version="1.0" encoding="UTF-8"?><lom xmlns="http://ltsc.ieee.org/xsd/LOM" xmlns:lomfr="http://www.lom-fr.fr/xsd/LOMFR" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://ltsc.ieee.org/xsd/LOM http://www.lom-fr.fr/xsd/lomfrv1.0/std/lomfr.xsd">
<general>
<identifier>
<catalog>Canal-U_Ocms</catalog>
<entry>32989</entry>
</identifier>
<title><string language="fre"><![CDATA[5.6. An Efficient Provably Secure One-Way Function]]></string></title>
<language>ENG</language>
<description>
<string language="fre"><![CDATA[In this session, we are
going to see how to build an efficient provably secure
one-way function from coding theory. As you know, a one-way
function is a function which is simple to evaluate and
which should be as fast as possible and hard to invert,
ideally with good security arguments. There are many
applications of one-way functions, especially in symmetric
cryptography. For example, for compression functions to
build hash functions, expansion functions to build pseudorandom
number generators but many more. Unfortunately, one-way
functions are hard to build. We know some very fast
functions which have very few security arguments and we
have some very strong security arguments for
functions which are very slow. What we will try to do is to
get a fast and secure function. Niederreiter Encryption is a
good candidate for one-way function. Any public key encryption
scheme is a one-way function with a trapdoor, which
is the decryption key. It has very strong security
arguments usually a proof of security. But public key
encryption is usually very slow, especially if you take
construction from numbers theory, you require an expentiation
which is expensive to compute. Niederreiter Encryption is much
faster than other public key schemes. It simply converts the
input into a low weight word. There are many different
techniques to do this and then compute its syndrome which
is only a few XORs, especially if the weight is very small.  The trapdoor can be easily
removed by simply using a random binary matrix which
is enough when we don't need to invert this one-way function. And with a few tweaks, it
can be made even faster than the usual Niederreiter Encryption. Here, we will give an overview of
the one-way function we are building. The parameters are matrix H
of size r*n and the constant weight encoding function ?
which takes l bits and output a word of weight w and length n. The one-way function simply
takes an input x and computes ?(x) and multiplies it by
H to obtain a value, a syndrome y. Security of
this function: inverting the function requires to
solve an instance of syndrome decoding; and efficiency:
if ? is fast and w is small, then the function
can be very efficient.]]></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>
<lomfr:documentType>
<lomfr:source>LOMFRv1.0</lomfr:source>
<lomfr:value>image en mouvement</lomfr:value>
</lomfr:documentType>
</general><lifeCycle>
<contribute>
<role>
<source>LOMv1.0</source>
<value>author</value>
</role>
<entity><![CDATA[BEGIN:VCARD
VERSION:3.0
CLASS:PUBLIC
REV:2021-07-06 18:03:09
FN:Irene MARQUEZ-CORBELLA
N:MARQUEZ-CORBELLA;Irene;;;
URL;TYPE=work:https://www.canal-u.tv/auteurs/marquez_corbella_irene
ROLE:author
TZ:+0200
END:VCARD
]]></entity>
<date><dateTime>2015-05-05</dateTime></date>
</contribute>
<contribute>
<role>
<source>LOMv1.0</source>
<value>author</value>
</role>
<entity><![CDATA[BEGIN:VCARD
VERSION:3.0
CLASS:PUBLIC
REV:2021-07-06 18:03:09
FN:Nicolas SENDRIER
N:SENDRIER;Nicolas;;;
URL;TYPE=work:https://www.canal-u.tv/auteurs/sendrier_nicolas
ROLE:author
TZ:+0200
END:VCARD
]]></entity>
<date><dateTime>2015-05-05</dateTime></date>
</contribute>
<contribute>
<role>
<source>LOMv1.0</source>
<value>author</value>
</role>
<entity><![CDATA[BEGIN:VCARD
VERSION:3.0
CLASS:PUBLIC
REV:2021-07-06 18:03:09
FN:Matthieu FINIASZ
N:FINIASZ;Matthieu;;;
URL;TYPE=work:https://www.canal-u.tv/auteurs/finiasz_matthieu
ROLE:author
TZ:+0200
END:VCARD
]]></entity>
<date><dateTime>2015-05-05</dateTime></date>
</contribute>
</lifeCycle>
<metaMetadata>
<metadataSchema>LOMv1.0</metadataSchema>
<metadataSchema>LOMFRv1.0</metadataSchema>
</metaMetadata>
<technical>
<format>video/mp4</format>
<location><![CDATA[https://www.canal-u.tv/video/inria/5_6_an_efficient_provably_secure_one_way_function.32989]]></location>
<location><![CDATA[https://streaming-canal-u.fmsh.fr/vod/media/canalu/videos/fuscia/5.6.an.efficient.provably.secure.one.way.function_32989/c015im.w5.s6.mov]]></location>
<size>141914104</size>
<duration><duration>PT0H5M21S</duration></duration>
</technical>
<educational>
<learningResourceType>
<source>LOMv1.0</source>
<value>lecture</value>
</learningResourceType>
<context>
<source>LOMv1.0</source>
<value>master</value>
</context>
<context>
<source>LOMv1.0</source>
<value>doctorat</value>
</context>
</educational>
<rights>
<cost>
<source>LOMv1.0</source>
<value>no</value>
</cost>
<copyrightAndOtherRestrictions>
<source>LOMv1.0</source>
<value>no</value>
</copyrightAndOtherRestrictions>
<description>
<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>
</description>
</rights>
<relation>
<kind>
<source>LOMv1.0</source>
<value>ispartof</value>
</kind>
<resource>
<identifier>
<catalog>URI</catalog>
<entry>https://www.canal-u.tv/producteurs/inria/cours_en_ligne/code_based_cryptography/5_other_cryptographic_constructions_relying_on_coding_theory</entry>
</identifier>
<description>
<string language="fre"><![CDATA[5: Other cryptographic constructions relying on coding theory]]></string>
</description>
</resource>
</relation>
<classification>
<purpose>
<source>LOMv1.0</source>
<value>discipline</value>
</purpose>
<taxonPath>
<source>
<string language="fre"><![CDATA[Universités Numériques Thématiques 2009 http://www.universites-numeriques.fr]]></string>
</source>
<taxon>
<id/>
<entry>
<string language="fre"/>
</entry>
</taxon>
</taxonPath>
</classification>
<classification>
<purpose>
<source>LOMv1.0</source>
<value>discipline</value>
</purpose>
<taxonPath>
<source>
<string language="fre">CDD 22e éd.</string>
<string language="eng">DDC 22nd ed.</string>
</source>
<taxon>
<id>518</id>
<entry>
<string language="fre"><![CDATA[Analyse numérique]]></string>
</entry>
</taxon>
</taxonPath>
<taxonPath>
<source>
<string language="fre">CDD 22e éd.</string>
<string language="eng">DDC 22nd ed.</string>
</source>
<taxon>
<id>003.54</id>
<entry>
<string language="fre"><![CDATA[Théorie de l'information]]></string>
</entry>
</taxon>
</taxonPath>
<taxonPath>
<source>
<string language="fre">CDD 22e éd.</string>
<string language="eng">DDC 22nd ed.</string>
</source>
<taxon>
<id>005.7</id>
<entry>
<string language="fre"><![CDATA[données dans les systèmes informatiques]]></string>
</entry>
</taxon>
</taxonPath>
<taxonPath>
<source>
<string language="fre">CDD 22e éd.</string>
<string language="eng">DDC 22nd ed.</string>
</source>
<taxon>
<id>652.8</id>
<entry>
<string language="fre"><![CDATA[cryptographie]]></string>
</entry>
</taxon>
</taxonPath>
<taxonPath>
<source>
<string language="fre">CDD 22e éd.</string>
<string language="eng">DDC 22nd ed.</string>
</source>
<taxon>
<id>510</id>
<entry>
<string language="fre"><![CDATA[Mathématiques]]></string>
</entry>
</taxon>
</taxonPath>
</classification> </lom>