In my recent lectures (10 and 11) on Applied Cryptography, I delved into Public Key Cryptography (PKC) with a particular emphasis on the RSA cryptosystem. Initiating with an examination of fundamental number theory, I introduced essential components such as the Extended Euclidean Algorithm, Euler’s Totient Function, and Fermat’s Little Theorem. Utilizing the whiteboard, I also explained through simple examples the Miller-Rabin primality test and the Square and Multiply algorithm.

Building upon this foundation, I then delved into the RSA cryptosystem and why and how it works. In a practical application, I leveraged the Python’s PyCryptodome library to demonstrate RSA encryption, incorporating also the Optimal Asymmetric Encryption Padding (OAEP) for secure session key exchange with AES. Close to the end of lecture, I also harnessed the power of SageMath to delve into mathematical attacks on RSA. 

In my upcoming lecture, I will introduce also Elliptic Curve Cryptography (ECC). ECC is an alternative to the RSA. It is based on a different trapdoor one-way function than RSA, and is used for digital signatures in cryptocurrencies, as well as one-way encryption of emails, data and software. While the RSA key generation involves the selection of two large prime numbers, ECC key generation essentially involves choosing a random elliptic curve over a finite field. 

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