In recent years, quantum computers are being developed, built, and tested in organizations ranging from universities and national laboratories to private start-ups and big companies. In addition to the promise of computational speedups, quantum technologies are also useful for secure communication and computation. A multitude of applications, apart from quantum key distribution, include certifiable randomness generation, secure multi-party computation, computing on encrypted data, and verification of quantum devices.

In this talk, I will discuss recent progress, limitations, and challenges of these above-mentioned settings when performed over classical networks and local quantum devices.  This field of hybrid quantum/classical cryptography — cryptography with quantum devices and classical channels —  is an emerging area with a lot of exciting results and lies at the intersection of post-quantum and quantum cryptography.  In particular, I will give an overview of some of my past and ongoing works, at a very high level and assuming minimum quantum background, with a particular focus on the delegation of quantum computation and the role of computational assumptions in this area of hybrid cryptography. At the heart of these works are techniques from quantum algorithms, information theory, interactive proof systems, and modern cryptography.

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