From Graphs to Keyed Quantum Hash Functions

We present two new constructions of quantum hash functions: the first based on expander graphs and the second based on extractor functions and estimate the amount of randomness that is needed to construct them. We also propose a keyed quantum hash function based on extractor function that can be used in quantum message authentication codes and assess its security in a limited attacker model

PPP-Completeness with Connections to Cryptography

Polynomial Pigeonhole Principle (PPP) is an important subclass of TFNP with profound connections to the complexity of the fundamental cryptographic primitives: collision-resistant hash functions and one-way permutations. In contrast to most of the other subclasses of TFNP, no complete problem is known for PPP. Our work identifies the first PPP-complete problem without any circuit or Turing Machine given explicitly in the input, and thus we answer a longstanding open question from [Papadimitriou1994]. Specifically, we show that constrained-SIS (cSIS), a generalized version of the well-known Short Integer Solution problem (SIS) from lattice-based cryptography, is PPP-complete. In order to give intuition behind our reduction for constrained-SIS, we identify another PPP-complete problem with a circuit in the input but closely related to lattice problems. We call this problem BLICHFELDT and it is the computational problem associated with Blichfeldt's fundamental theorem in the theory of lattices. Building on the inherent connection of PPP with collision-resistant hash functions, we use our completeness result to construct the first natural hash function family that captures the hardness of all collision-resistant hash functions in a worst-case sense, i.e. it is natural and universal in the worst-case. The close resemblance of our hash function family with SIS, leads us to the first candidate collision-resistant hash function that is both natural and universal in an average-case sense. Finally, our results enrich our understanding of the connections between PPP, lattice problems and other concrete cryptographic assumptions, such as the discrete logarithm problem over general groups

Trusty URIs: Verifiable, Immutable, and Permanent Digital Artifacts for Linked Data

To make digital resources on the web verifiable, immutable, and permanent, we propose a technique to include cryptographic hash values in URIs. We call them trusty URIs and we show how they can be used for approaches like nanopublications to make not only specific resources but their entire reference trees verifiable. Digital artifacts can be identified not only on the byte level but on more abstract levels such as RDF graphs, which means that resources keep their hash values even when presented in a different format. Our approach sticks to the core principles of the web, namely openness and decentralized architecture, is fully compatible with existing standards and protocols, and can therefore be used right away. Evaluation of our reference implementations shows that these desired properties are indeed accomplished by our approach, and that it remains practical even for very large files.Comment: Small error corrected in the text (table data was correct) on page 13: "All average values are below 0.8s (0.03s for batch mode). Using Java in batch mode even requires only 1ms per file.