Classical Cryptography and Applications: From Digital Signatures to Cryptocurrencies

With the formation of human societies, the need for secure communication and the secret and secure transmission of messages marked the beginning of cryptography as a field of knowledge. Today, in addition to secure communications, cryptography is used in secret sharing, digital signatures and certificates, blockchain, and many everyday services. In this course, the history and types of classical cryptography and the required mathematical concepts will be introduced. Various cryptographic algorithms, including RSA, ElGamal, and elliptic curve-based cryptography, will also be examined, followed by an introduction to different hash functions and their applications. Alongside cryptographic algorithms, their applications in various digital signature protocols will be explored. The architecture of Bitcoin and its connection to cryptographic algorithms will also be introduced. Throughout the workshop, applications of cryptography in services such as social networks, bank accounts, cryptocurrencies, and smart contracts will be discussed. Finally, a brief overview of the challenges facing classical cryptography in the era of quantum technologies will be provided.