From 71bf935debd3a13265fcbc3eb6a3ecc4bf1186aa Mon Sep 17 00:00:00 2001 From: Holden Rohrer Date: Mon, 11 Nov 2019 23:33:03 -0500 Subject: defined totient --- final/rsa-method.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'final/rsa-method.tex') diff --git a/final/rsa-method.tex b/final/rsa-method.tex index bf75cd0..af2c15a 100644 --- a/final/rsa-method.tex +++ b/final/rsa-method.tex @@ -6,7 +6,7 @@ The encryption process begins with the selection of two large primes, $p$ and $q \pre{2.} Break the converted message into blocks of size less than $n$. \pre{3.} For each block B, an encrypted block C is created such that $$C \equiv B^e\thinspace(mod\thinspace n)$$. \noindent To decrypt that message: -\pre{1.} Calculate an integer $d$ such that $de \equiv 1 \mod{\phi(n)}$ using the Euclidean algorithm. +\pre{1.} Calculate an integer $d$ such that $de \equiv 1 \mod{\phi(n)}$ using the Euclidean algorithm. Note that $\phi(n)$ is the totient function, or the number of non-coprime integers with $n$ less than $n$. \pre{2.} Convert back using $B \equiv C^d \mod{n}$. The decryption process described above makes use of Euler’s theorem. -- cgit From ae29e0a69c85d1efc2a13779ad959287acb40af0 Mon Sep 17 00:00:00 2001 From: Holden Rohrer Date: Mon, 11 Nov 2019 23:36:41 -0500 Subject: added citation --- final/rsa-method.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'final/rsa-method.tex') diff --git a/final/rsa-method.tex b/final/rsa-method.tex index af2c15a..69bf4b1 100644 --- a/final/rsa-method.tex +++ b/final/rsa-method.tex @@ -1,4 +1,4 @@ -The encryption process begins with the selection of two large primes, $p$ and $q$, their product $n=pq$, and a fourth number $e$ relatively prime to $\phi(n)$. $n$ is public, whereas $p$ and $q$ are secret. +The encryption process begins with the selection of two large primes, $p$ and $q$, their product $n=pq$, and a fourth number $e$ relatively prime to $\phi(n)$. $n$ is public, whereas $p$ and $q$ are secret.\footnote{$^3$}{\link{https://primes.utm.edu/glossary/page.php?sort=RSA}} \def\mod#1{\thinspace(mod\thinspace #1)} \noindent Encryption is accomplished through the following three steps: -- cgit