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Explore how to construct quantum cryptographic systems from mathematical assumptions that don't require one-way functions in this conference talk by Dakshita Khurana from the University of Illinois Urbana-Champaign. Learn about recent breakthroughs showing that quantum cryptosystems can exist relative to certain oracles that break all classical cryptography, while discovering how to move beyond these relativized results. Understand the construction of quantum commitments and secure computation protocols based on concrete, well-studied mathematical assumptions from quantum advantage literature that are weaker than traditional cryptographic foundations. Examine the theoretical foundations for quantum cryptography that leverage computational complexity theory, specifically #P-hardness, to establish security guarantees without relying on classical cryptographic primitives like one-way functions.
