We prove that any oblivious algorithm using space S to find the median of a list of n integers from {1, . . . , 2n} requires time Ω(n log logS n). This bound also applies to the problem of determining whether the median is odd or even. It is nearly optimal since Chan, following Munro and Raman, has shown that there is a (randomized) selection algorithm using only s registers, each of which can ...

We construct an e cient interactive protocol for realizing veri able partial escrow of the factors of an integer n with time-delayed and threshold key recovery features. The computational cost of the new scheme amounts to 10k log2 P multiplications of numbers of size of P , where P is a protocol parameter which permits n of size up to (log2 P ) 4 to be dealt with and k is a security parameter w...

In this paper, we present two new adaptively secure identity-based encryption (IBE) schemes from lattices. The size of the public parameters, ciphertexts, and private keys are Õ(nκ), Õ(n), and Õ(n) respectively. Here, n is the security parameter, κ is the length of the identity, and d ∈ N is a flexible constant that can be set arbitrary (but will affect the reduction cost). Ignoring the poly-lo...

The GGH Graded Encoding Scheme [10], based on ideal lattices, is the first plausible approximation to a cryptographic multilinear map. Unfortunately, using the security analysis in [10], the scheme requires very large parameters to provide security for its underlying “encoding re-randomization” process. Our main contributions are to formalize, simplify and improve the efficiency and the securit...

In this paper, we study the problem of computing the multiparty equality (MEQ) function: n ≥ 2 nodes, each of which is given an input value from {1, · · · ,K}, determine if their inputs are all identical, under the point-to-point communication model. The MEQ function equals to 1 if and only if all n inputs are identical, and 0 otherwise. The communication complexity of the MEQ problem is define...

We consider the problem of finding a Steiner minimum tree in a hypercube. Specifically, given n terminal vertices in an m dimensional cube and a parameter q, we compute the Steiner minimum tree in time O(72 + 8nm), under the assumption that the length of the minimum Steiner tree is at most m+ q. This problem has extensive applications in taxonomy and biology. The Steiner tree problem in hypercu...