Concurrent Knowledge-Extraction in the Public-Key Model

Knowledge extraction is a fundamental notion, modelling machine possession of values (witnesses) in a computational complexity sense. The notion provides an essential tool for cryptographic protocol design and analysis, enabling one to argue about the internal state of protocol players without ever looking at this supposedly secret state. However, when transactions are concurrent (e.g., over the Internet) with players possessing public-keys (as is common in cryptography), assuring that entities ``know'' what they claim to know, where adversaries may be well coordinated across different transactions, turns out to be much more subtle and in need of re-examination. Here, we investigate how to formally treat knowledge possession by parties (with registered public-keys) interacting over the Internet. Stated more technically, we look into the relative power of the notion of ``concurrent knowledge-extraction'' (CKE) in the concurrent zero-knowledge (CZK) bare public-key (BPK) model.Comment: 38 pages, 4 figure

Constant-Round Concurrent NMWI and its relation to NMZK

One of the central questions in Cryptography is to design round-efficient protocols that are secure under man-in-the-middle attacks. In this paper we introduce and study the notion of non-malleable witness indistinguishability (NMWI) and examine its relation with the classic notion of non-malleable zero knowledge (NMZK). Indeed, despite tremendous applicability of witness indistinguishability, while a lot of attention has been given to NMZK, very little attention has been given to witness indistinguishability in case of man-in-the-middle attacks. We initiate this study, with several (perhaps somewhat surprising) results: • We give the first definition of NMWI proof systems. Just like every NMZK proof is a zero-knowledge proof which aims to attain a very strong proof independence property, we require (and formalize) the notion that every NMWI proof is a witness indistinguishable proof system which enjoys a very strong witness independence property against any man-in-the-middle attack. • We show the existence of a constant-round NMWI argument system for NP in the standard model (i.e. without any trusted or any other setup assumptions)