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@@ -25,14 +25,14 @@ protocol, \openssl implemented it with the following signature:
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The computation proceeds under the well-known Euclidean algorithm, specifically
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the binary variant developed by Josef Stein in 1961 \cite{AOCPv2}. This variant
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-exploits some interesting properties of $gcd(u, v)$
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+exploits some interesting properties of $gcd(a, b)$
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\begin{itemize}
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\setlength{\itemsep}{1pt}
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\setlength{\parskip}{0pt}
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\setlength{\parsep}{0pt}
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- \item if $u,\ v$ are even, then $gcd(u, v) = 2gcd(u/2, v/2)$
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- \item if $u$ is even and $v$ is odd, then $gcd(u, v) = gcd(u/2, v)$
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- \item $gcd(u, v) = gcd(u-v, v)$, as in the standard Euclid's algorithm
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+ \item if $a,\ b$ are even, then $gcd(a, b) = 2gcd(a/2, b/2)$
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+ \item if $a$ is even and $b$ is odd, then $gcd(a, b) = gcd(a/2, b)$
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+ \item $gcd(a, b) = gcd(a-b, b)$, as in the standard Euclid's algorithm
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\item the sum of two odd numbers is always even
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\end{itemize}
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@@ -256,7 +256,7 @@ explainations, the reference is still \cite{Dijkstra:adop}.
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\end{algorithm}
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A fair approxidmation of the magnitude of the Dijkstra algorithm can be studied
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-by looking at the pseudocode in ~\ref{alg:sqrt:dijkstra_naif}.Exactely as with
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+by looking at the pseudocode in ~\ref{alg:sqrt:dijkstra_naif}. Exactely as with
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the dicotomic search case, we split the interval $[a, b]$ in half on each step,
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and choose wether to take the leftmost or the rightmost part. This results in
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$log(n+1)$ steps. During each iteration, instead, as we have seen in
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