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a/report/formal.tex +++ b/report/formal.tex @@ -127,7 +127,7 @@ $$ \phi(n) := |\{a\in\mathbb{N}: 1\leq a\leq n \gcd(a,n) = 1\}|. $$ Let us characterize $\phi(n)$. -\begin{lem} +\begin{lem}\label{lem:eulerfermat} Let $k,m,n\in\mathbb{N}$, $p,p_1,p_2$ be prime. \begin{itemize} \item $\phi(p) = p-1$; @@ -191,7 +191,27 @@ TODO: Baby Step Giant Step Algorithm \subsection{The RSA cryptosystem} -TODO +At the RSA cryptosystem, named after its authors Rivest, Shamir and Adleman, the two +protagonists \textbf{A}lice and \textbf{B}ob want to exchange secret messages. To that +end, Alice generates two primes $p$ and $q$ which are approximately of the same size. +Then, Alice calculates the product $n=pq$ and $\phi(n) = (p-1)(q-1)$, and proceeds by +choosing $1