Skip to main content
\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)
Mathematics LibreTexts

Yet Another Introductory Number Theory Textbook - Cryptology Emphasis (Poritz)

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    \(\newcommand{\NN}{\mathbb N}\)
    \(\newcommand{\RR}{\mathbb R}\)
    \(\newcommand{\QQ}{\mathbb Q}\)
    \(\newcommand{\ZZ}{\mathbb Z}\)
    \(\newcommand{\Cc}{\mathcal C}\)
    \(\newcommand{\Dd}{\mathcal D}\)
    \(\newcommand{\Ee}{\mathcal E}\)
    \(\newcommand{\Ff}{\mathcal F}\)
    \(\newcommand{\Kk}{\mathcal K}\)
    \(\newcommand{\Mm}{\mathcal M}\)
    \(\newcommand{\Pp}{\mathcal P}\)

    This introductory number theory textbook has a particular emphasis on connections to cryptology. The cryptologic material arising naturally out of the ambient number theory. The main cryptologic applications — being the RSA cryptosystem, Diffie-Hellman key exchange, and the ElGamal cryptosystem — come out so naturally from considerations of Euler's Theorem, primitive roots, and indices that it renders quite ironic G.H. Hardy's assertion of the purity and eternal inapplicability of number theory.

    Thumbnail: A scytale is a tool used to perform a transposition cipher, consisting of a cylinder with a strip of parchment wound around it on which is written a message. The ancient Greeks, and the Spartans in particular, are said to have used this cipher to communicate during military campaigns. (CC BY-SA 3.0; Luringen via Wikipedia)

    Yet Another Introductory Number Theory Textbook - Cryptology Emphasis (Poritz) is shared under a CC BY-SA license and was authored, remixed, and/or curated by Jonathan A. Poritz.