Explore the cutting-edge world of Elliptic Curve Cryptography (ECC) in this informative 28-minute talk by Nick Gonella, an officer of White Hat Cal Poly. Delve into the machinery behind this revolutionary encryption method that's transforming the cryptography landscape. Discover why encryption is necessary, learn about modern encryption techniques, and understand the concept of asymmetric encryption. Examine the principles of trapdoor functions and their role in cryptography, with a focus on RSA and its limitations. Uncover the advantages of ECC, including its unique properties and implementation as a new trapdoor function. Gain insights into key generation processes and the improved Diffie-Hellman protocol. Analyze common ECC implementations, potential downsides, and the NIST incident. Conclude by weighing the significant benefits of this innovative cryptographic approach.