#### Introduction to Cryptography

*CryptUTy Cryptography Circle, University of Tehran*

*Bahar Bagheri, Zahra Honjani, Mohammad Mahdi Kooranifar, Negarin Mohammadi, Zahra Salari, Alireza Tavakoli*

cryptuty@gmail.com

Humans have been writing secret messages ever since they have been around. But the need for more complex difficult-to-break ciphers grows with the rise of remote communications, more devious adversaries, and advanced technologies. We are going to investigate how these ciphers were designed, broken, and later improved throughout history. With these historical lessons in mind, we are going to formulate the requirements of a secure system.

Thereafter we shall introduce some basic mathematical concepts underlying nowadays cryptography, modular arithmetics and Euclidean algorithm for finding modular inverses. As an example of their usage, we try to help two people deal their hands in order to play cards over a phone call. Eventually feeling ready enough, we would demonstrate RSA cryptosystem.

*Date: October 22, 2020*