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Explore the mathematical foundations and practical applications of asymmetric encryption in this comprehensive conference talk from NDC Oslo 2025. Delve into the algebraic underpinnings of widely-used algorithms like RSA and ECDSA, understanding not just their names but how they actually function at a fundamental level. Examine the evolution from RSA to ECDSA, discovering why this transition occurred and what advantages ECDSA offers over its predecessor. Investigate the drawbacks, limitations, and vulnerabilities inherent in current asymmetric encryption methods that developers and consumers rely on daily for secure web traffic, git commit signing, and authentication flows. Learn about the post-quantum cryptography landscape and why even ECDSA falls short in preparing for quantum computing threats. Gain insights into the future direction of asymmetric encryption and what new approaches are being developed to address emerging security challenges in our increasingly connected world.
