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A key challenge in cryptography is to ensure that a protocol resists all computationally feasible attacks, even when an adversary decides to follow a completely arbitrary and unpredictable strategy. This often turns out to be notoriously difficult — for example, proofs of security must typically extract an adversary’s implicit input, but this is at odds with other goals like privacy, which require that inputs be hidden and difficult to extract. In this talk, I will describe my work that reimagines how we reason about adversaries, thereby making progress on foundational questions in classical and quantum protocol design. On the classical front, these insights have helped understand the mathematical assumptions required to immunize protocols against coordinated attacks on the internet, and verify computations while preserving privacy. On the quantum front, these methods help exploit the “destructive” nature of measurements and open up fundamentally new possibilities for cryptography. I will discuss examples that leverage quantum information to (1) weaken the assumptions needed for core tasks like secure computation on distributed data, and (2) allow outsourcing computations on sensitive data while also verifying that data was deleted after processing.