Generic Security Proof of Quantum Key Exchange using Squeezed States

Recently, a Quantum Key Exchange protocol that uses squeezed states was presented by Gottesman and Preskill. In this paper we give a generic security proof for this protocol. The method used for this generic security proof is based on recent work by Christiandl, Renner and Ekert.Comment: 5 pages, 7 figures, accepted at IEEE ISIT 200

Explicit Optimal Binary Pebbling for One-Way Hash Chain Reversal

We present explicit optimal binary pebbling algorithms for reversing one-way hash chains. For a hash chain of length $2^k$, the number of hashes performed in each output round does not exceed $\lceil k/2 \rceil$, whereas the number of hash values stored (pebbles) throughout is at most $k$. This is optimal for binary pebbling algorithms characterized by the property that the midpoint of the hash chain is computed just once and stored until it is output, and that this property applies recursively to both halves of the hash chain. We introduce a framework for rigorous comparison of explicit binary pebbling algorithms, including simple speed-1 binary pebbling, Jakobsson\u27s speed-2 binary pebbling, and our optimal binary pebbling algorithm. Explicit schedules describe for each pebble exactly how many hashes need to be performed in each round. The optimal schedule turns out to be essentially unique and exhibits a nice recursive structure, which allows for fully optimized implementations that can readily be deployed. In particular, we develop the first in-place implementations with minimal storage overhead (essentially, storing only hash values), and fast implementations with minimal computational overhead. Moreover, we show that our approach is not limited to hash chains of length $n=2^k$, but accommodates hash chains of arbitrary length $n\geq1$, without incurring any overhead. Finally, we show how to run a cascade of pebbling algorithms along with a bootstrapping technique, facilitating sequential reversal of an unlimited number of hash chains growing in length up to a given bound

Proofs of partial knowledge and simplified design of witness hiding protocols

Suppose we are given a proof of knowledge P in which a prover demonstrates that he knows a solution to a given problem instance. Suppose also that we have a secret sharing scheme S on n participants. Then under certain assumptions on P and S , we show how to transform P into a witness indistinguishable protocol, in which the prover demonstrates knowledge of the solution to some subset of n problem instances out of a collection of subsets defined by S . For example, using a threshold scheme, the prover can show that he knows at least d out of n solutions without revealing which d instances are involved. If the instances are independently generated, we get a witness hiding protocol, even if P did not have this property. Our results can be used to efficiently implement general forms of group oriented identification and signatures. Our transformation produces a protocol with the same number of rounds as P and communication complexity n times that of P . Our results use no unproven complexity assumptions