Public-Key Cryptography: Standards and Applications

This lecture covers the principles and applications of public-key cryptography, focusing on widely-used standards such as RSA, DSA, and AES. It begins with an overview of public-key cryptography, explaining its significance in providing privacy and authenticity. The instructor discusses the advantages of different cryptographic standards, highlighting why alternatives to RSA, like DSA and symmetric-key algorithms, are necessary for efficiency. The lecture then delves into the Advanced Encryption Standard (AES), detailing its structure, key sizes, and operational principles. The instructor illustrates how AES is implemented in real-world applications, such as Apple's iMessage service, showcasing the integration of various cryptographic standards. The discussion also touches on error detection and correction codes, emphasizing their importance in secure communications. The lecture concludes with a summary of key concepts, reinforcing the relationship between cryptography and computational complexity, and the necessity of understanding number theory and algebra in this context.