We prove a version of the derandomized Direct Product lemma for deterministic space-bounded algorithms. Suppose a Boolean function g : {0, 1}n {0, 1} cannot be computed on more th...
We analyze the multivariate generalization of Howgrave-Graham’s algorithm for the approximate common divisor problem. In the m-variable case with modulus N and approximate common...
We prove the equivalence, up to a small polynomial approximation factor n/ log n, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and...
We propose a new homomorphic encryption scheme based on the hardness of decoding under independent random noise from certain affine families of codes. Unlike in previous latticeba...
We present an explicit construction of codes that can be list decoded from a fraction (1 - ) of errors in sub-exponential time and which have rate / logO(1) (1/). This comes close...