uofsc-fall-2022-math-587-001 Goto Github PK

homework0

Getting used to editing tex and go files in GitPod.

homework1

Substitution ciphers

homework10

The index calculus for the DLP, quadratic reciprocity, and Tonelli-Shanks.

homework11

Basics on elliptic curves and their discrete log problem

homework12

Elliptic curve cryptography

homework2

Mathematical preliminaries: division, the Euclidean algorithm, and modular arithmetic

homework3

Prime factorization and primitive powers mod p

homework4

Introduction to the discrete logarithm problem and a comparison of symmetric vs asymmetric ciphers

homework5

Diffie-Hellman key exchange and ElGamal cryptosystem. Plus Shanks' algorithm for solving the discrete logarithm problem.

homework6

The Chinese remainder theorem and its application in the Pohlig-Hellman algorithm for solving the discrete logarithm problem.

homework7

Roots mod pq, RSA, and Miller-Rabin witnesses for compositeness

homework8

A bit about distribution of primes and Pollard's p-1 test

homework9

B-smooth numbers, the quadratic sieve, and the number field sieve

jekyll

quizzes

uofsc-fall-2022-math-587-001.github.io

Course webpage for Fall 2022 Introduction to Cryptography at the University of South Carolina.