Explore post-quantum isogeny cryptography in this 52-minute conference talk from the 36C3 event. Dive into the world of elliptic curves and isogenies, understanding their potential for building strong cryptosystems in a post-quantum era. Learn about various post-quantum cryptography approaches, including lattice-based, code-based, and multivariate polynomial systems. Gain insights into how elliptic curve isogenies work and their applications in secure key exchange and signature algorithms. Follow along as the speaker breaks down complex concepts like supersingular curves, point addition law, and revolution graphs for a broad audience. Discover the implications of quantum supremacy on classical cryptography and the importance of developing secure post-quantum alternatives. Engage with topics such as generic algorithms, homomorphic encryption, and twin elliptic curves. Conclude with a summary, Q&A session, and references to further resources on this cutting-edge cryptographic field.