We introduce and study the \epsilon-rank of a real matrix A, defi ned, for any  \epsilon > 0 as the minimum rank over matrices that approximate every entry of A to within an additive \epsilon. This parameter is connected to other notions of approximate rank and is motivated by ... more >>>

An error-correcting code $C \subseteq \F^n$ is called $(q,\epsilon)$-strong locally testable code (LTC) if there exists a randomized algorithm (tester) that makes at most $q$ queries to the input word. This algorithm accepts all codewords with probability 1 and rejects all non-codewords $x\notin C$ with probability at least $\epsilon \cdot ... more >>>

The question whether Identity-Based Encryption (IBE) can be based on the Decisional Diffie-Hellman (DDH) assumption is one of the most prominent questions in Cryptography related to DDH. We study limitations on the use of the DDH assumption in cryptographic constructions, and show that it is impossible to construct a secure ... more >>>