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Explore the intersection of cryptographic group actions and quantum computing in this 53-minute conference talk from the Gemini Center on Quantum Technology's monthly track meeting. Learn how the Group Action formalism extends discrete-logarithm based hardness assumptions to achieve post-quantum security, particularly through isogeny-based cryptography implementations like CSIDH and PEGASIS. Discover how useful results from Diffie-Hellman assumptions can be adapted to post-quantum settings and examine the challenges of defining quantum variants of generic models. Understand the progression from classical Generic Group Model (GGM) and Algebraic Group Model (AGM) to their group action counterparts - the Generic Group Action Model (GGAM) and Algebraic Group Action Model (AGAM). Investigate the complexities involved in creating quantum versions of these models, similar to the transition from classical to quantum random oracle models (QROM) for hash functions. Gain insights into ongoing research challenges and potential solutions for establishing sound definitions of quantum generic models for group actions, based on collaborative work addressing fundamental questions in post-quantum cryptography.
