For Boolean functions that are $\epsilon$-far from the set of linear functions, we study the lower bound on the rejection probability (denoted $\textsc{rej}(\epsilon)$) of the linearity test suggested by Blum, Luby and Rubinfeld. The interest in this problem is partly due to its relation to PCP constructions and hardness of ... more >>>

We describe a public-key cryptosystem with worst-case/average case
equivalence. The cryptosystem has an amortized plaintext to
ciphertext expansion of $O(n)$, relies on the hardness of the
$\tilde O(n^2)$-unique shortest vector problem for lattices, and
requires a public key of size at most $O(n^4)$ bits. The new
cryptosystem generalizes a conceptually ... more >>>

We study the notion of "instance compressibility" of NP problems [Harnik-Naor06], closely related to the notion of kernelization in parameterized complexity theory [Downey-Fellows99, Flum-Grohe06, Niedermeier06]. A language $L$ in NP is instance compressible if there
is a polynomial-time computable function $f$ and a set $A$ such that
for each instance ... more >>>