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Circuit complexity is the study of resource-bounded circuits and the functions computed by such circuits.
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Non-uniform hierarchy theorem for approximating functions
It is easy to show (by probabilistic argument) that there exist functions that require circuits of size $O(2^n/n)$. This, in turn, can be used to prove a non-deterministic hierarchy theorem showing (r …
6
votes
Threshold Fully Homomorphic Cryptosystems
A new paper by Steven Myers, Mona Sergi, and Abhi Shelat on eprint, "Threshold Fully Homomorphic Encryption and Secure Computation", claims a threshold fully homomorphic encryption scheme.
From their …
11
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Variants of direct product theorems
A direct product theorem, informally, says that computing $k$ instances of a function $f$ is harder than computing $f$ once.
Typical direct product theorems (e.g., Yao's XOR Lemma) look at average-ca …