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<title><string language="fre"><![CDATA[2.2. Security-Reduction Proof]]></string></title>
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<string language="fre"><![CDATA[Welcome to the second session. We will talk about the
security-reduction proof. The security of a given cryptographic algorithm is reduced to the security
of a known hard problem. To prove that a
cryptosystem is secure, we select a problem which we know is
hard to solve, and we reduce the problem to the
security of the cryptosystem. Since the problem is hard to solve,
the cryptosystem is hard to break. A security reduction is a
proof that an adversary able to attack the scheme is able
to solve some presumably hard computational problem,
with a similar effort. For the given parameters n,
k, let G be the public-key
space, K be the apparent
public-key space. In the
original McEliece scheme G
is the set of all generator matrices of a family of binary Goppa
codes of length n and dimension k. K is the set of binary
matrices of a size (k x n). A distinguisher is a mapping
that takes as input a binary matrix of size (k x n), and
returns true if the matrix
is distinguishable. We define the following
sample space, the set of all matrices of size
(k x n) uniformly distributed,
and we define the event: the
set of binary matrices such that the distinguisher
returns true, that is the matrices which are distinguishable.
The advantage of a
distinguisher for the subset D, measures how such a
distinguisher could be used as a characterization for G;
formally, the probability that the event will occur,
minus the probability that the  
event happens
restricted to the subset G.
In other words, it is the
probability that the distinguisher detects a matrix from G, from a
randomly picked up binary matrix. We will denote the running time of
a distinguisher by this formula.
An algorithm is a (T, ?)-distinguisher 
for G against K, if
it runs in time at most T, and the
advantage for G is greater than ?. So, for given
parameters n, k and t, we define
this, the message space,
this, the apparent public key space, and W the error vector space.]]></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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