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fix spelling
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Andre Henriques 2023-11-07 22:08:31 +00:00
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@ -147,14 +147,14 @@
\subsection*{4.3} \subsection*{4.3}
Our random value is $R = u-bit long digit$ which means that it has $2^u$ possible values. Our random value is $R = u-bit long digit$ which means that it has $2^u$ possible values.
And since we know that $q$ balls into $p$ holes a colision is bound to happend at the probability of $\frac{q^2}{2p}$ we can calculate: And since we know that $q$ balls into $p$ holes a colision is bound to happend at the probability of $\frac{q^2}{2p}$ we can calculate:
$$\frac{q^2}{2(2^u)}\gt\frac{1}{2}\iff q\gt 2^{\frac{u}{2}}$$ $$\frac{q^2}{2(2^u)}>\frac{1}{2}\iff q> 2^{\frac{u}{2}}$$
\subsection*{4.4} \subsection*{4.4}
The size of TripleDES is 64 bit long which makes $u=64/2=32$ making the q The size of TripleDES is 64 bit long which makes $u=64/2=32$ making the q
$q\gt 2^\frac{32}{2}\iff q \gt 65536$ $q> 2^\frac{32}{2}\iff q > 65536$
\subsection*{4.5} \subsection*{4.5}
The size of AES is 128 bit long which makes $u=128/2=64$ making the q The size of AES is 128 bit long which makes $u=128/2=64$ making the q
$q\gt 2^\frac{64}{2}\iff q \gt 4294967296$ $q>t 2^\frac{64}{2}\iff q > 4294967296$
\subsection*{4.6} \subsection*{4.6}
Since in in both 4.4 and 4.5 the value of $q$ is not large enough the scheme is not CPA secure Since in in both 4.4 and 4.5 the value of $q$ is not large enough the scheme is not CPA secure