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These programs have been sponsored in part by the Quantum Pod.
In the wake of the National Quantum Initiative, the Simons Institute’s Research Pod in Quantum Computing brings together researchers from computer...
Meta-complexity refers to the study of the computational complexity of computing natural complexity measures, such as time-bounded Kolmogorov complexity and the minimal circuit size. Despite decades of interest, important basic questions about these problems remain unresolved.
In this talk I will present few open questions in the field, and their implications on cryptography.
Classical results starting with [Lipton92] showed that it is possible to construct better error-correcting codes when assuming that the adversary is computationally bounded. Specifically, it is possible to construct codes with better rates than what is possible information-theoretically (when the adversary is computationally unbounded). In this talk, I will present new results in this area, together with connections to multi-input correlation intractable hash functions.
I will also briefly mention some results in complexity and derandomization. Specifically, I will discuss recent progress on constructing seedless extractors for samplable distributions and their relationship to new notions of hardness in complexity theory.
Our society increasingly relies on computations over the Internet. Typically, these follow a centralised paradigm, where clients delegate the computation to a trusted authority, giving it access to the inputs. This inevitably raises security concerns: what happens if the authority’s server were to be taken over by an attacker?
Secure multiparty computation (MPC) studies protocols that avoid this type of single points of failure, ensuring the privacy of the inputs and the correctness of the outputs even if a subset of participants were to be corrupted.
In my research, I investigate the cost of these solutions: given any notion of complexity, what is the maximum ratio between the cost of the insecure protocol and that of the secure solution?
In this talk, I describe how I have tackled this question by studying simpler primitives: distributed samplers, homomorphic secret-sharing, trapdoor hashing and laconic function evaluation. I give a brief discussion of these problems and an overview of open questions I would like to explore.