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We show that given oracle access to a subroutine which returns approximate closest vectors in a lattice, one may find in polynomial time approximate shortest vectors in a lattice. The level of approximation is maintained; that is, for any function f, the following holds: Suppose that the subroutine, on input of a lattice L and a target vector w (not necessarily in the lattice), outputs v L such that...
Abstract. One of the many contributions of the paper of Goldwasser, Micali and Rackoff is the introduction of the notion of knowledge complexity. Knowledge complexity zero (also known as zero-knowledge) has received most of the attention of the authors and all the attention of their followers. In this paper, we present several alternative definitions of knowledge complexity and investigate the relations...
We define a p-party ping-pong protocol and its security problem, along the lines of Dolev and Yao's definition for twoparty ping-pong protocol. In the case of two parties, it was assumed, with no loss of generality, that there exists a single saboteur in the net and the protocol was defined to be secure iff it was secure against the active interventions of one saboteur. We show that for more than...
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