We develop new tools to study the relative complexities of secure
multi-party computation tasks (functionalities) in the Universal
Composition framework. When one task can be securely realized using
another task as a black-box, we interpret this as a
qualitative, complexity-theoretic reduction between the two tasks.
Virtually all previous characterizations of ... more >>>

We give a randomized polynomial-time identity test for
noncommutative circuits of polynomial degree based on the isolation
lemma. Using this result, we show that derandomizing the isolation
lemma implies noncommutative circuit size lower bounds. More
precisely, we consider two restricted versions of the isolation
lemma and show that derandomizing each ... more >>>

Functions in arithmetic NC1 are known to have equivalent constant
width polynomial degree circuits, but the converse containment is
unknown. In a partial answer to this question, we show that syntactic
multilinear circuits of constant width and polynomial degree can be
depth-reduced, though the resulting circuits need not be ... more >>>