Lower Bounds for Zero Knowledge on the Internet

Concurrent Zero - Knowledge in Poly - logarithmic

A proof is concurrent zero-knowledge if it remains zero-knowledge when run in an asynchronous environment, such as the Internet. It is known that zero-knowledge is not necessarily preserved in such an environment; Kilian, Petrank and Rackoff have shown that any 4 rounds zero-knowledge interactive proof (for a non-trivial language) is not concurrent zero-knowledge. On the other hand, Richardson ...

The Round-Complexity of Black-Box Zero-Knowledge: A Combinatorial Characterization

The round-complexity of black-box zero-knowledge has for years been a topic of much interest. Results in this area generally focus on either proving lower bounds in various settings (e.g., Canetti, Kilian, Petrank, and Rosen [3] prove concurrent zero-knowledge (cZK) requires Ω(log n/ log log n) rounds and Barak and Lindell [2] show no constant-round single-session protocol can be zero-knowledge...

Lower bounds of Copson type for the transpose of matrices on weighted sequence spaces

Lower Bounds for Non-Black-Box Zero Knowledge

We show new lower bounds and impossibility results for general (possibly non-black-box ) zero-knowledge proofs and arguments. Our main results are that, under reasonable complexity assumptions: 1. There does not exist a two-round zero-knowledge proof system with perfect completeness for an NP-complete language. The previous impossibility result for two-round zero knowledge, by Goldreich and Ore...

The Knowledge Tightness of Parallel Zero-Knowledge

We investigate the concrete security of black-box zeroknowledge protocols when composed in parallel. As our main result, we give essentially tight upper and lower bounds (up to logarithmic factors in the security parameter) on the following measure of security (closely related to knowledge tightness): the number of queries made by black-box simulators when zero-knowledge protocols are composed ...