Dive deep into the world of asymmetric cryptography in this 42-minute conference talk from Devoxx Greece 2024. Explore the inner workings of commonly used algorithms like RSA and ECDSA, understanding their foundations, limitations, and vulnerabilities. Learn why ECDSA has become more prevalent than RSA and discover the challenges these algorithms face in a post-quantum world. Gain insights into the mathematical principles behind asymmetric encryption, from its inception to modern-day applications. Suitable for developers with basic knowledge of asymmetric encryption concepts and elementary mathematical literacy, this talk provides a comprehensive look at the crucial role of asymmetric cryptography in everyday security infrastructure, including web traffic protection, git commit signing, and authentication processes.