Notes from MATH 470 — Communications and Cryptography at Texas A&M. Based off of lectures by Dr. Josiah Park, and An Introduction to Mathematical Cryptography by J. Hoffstein, J. Pipher, and J.H. Silverman.


  • $\mathbb{Z}_n$ and $\mathbb{Z}/n\mathbb{Z}$ are used interchangably; as are $\left(\mathbb{Z}_n\right)^\times$ and $\left(\mathbb{Z}/n\mathbb{Z}\right)^\times$.
  • $\mathbb{N}$ is the set of natural numbers without 0.
  • $\mathbb{P}$ is the set of all prime integers.
  • $a \equiv_n b \iff a \equiv b \pmod{n}$.
  • $[a\dots b], (a\dots b), (a\dots b], [a\dots b)$ uses the regular interval notation of (in|ex)clusivity, except over the integers rather than reals.
  • DLP is the discrete logarithm problem, over any of $\left(\mathbb{Z}_n\right)^\times$, $\mathbb{F}_p$, or $E(\mathbb{F}_p)$.
  • CRT is the Chinese Remainder Theorem.


[$\dag$] — topic not covered in class; any information on these pages are from my own self study and could be incorrect

[$\text{\P}$] — this page is listed as a "blog" page, navigation through breadcrumbs may not work as expected