Limits of Extractability Assumptions with Distributional Auxiliary Input

Extractability, or “knowledge,” assumptions have recently gained popularity in the crypto- graphic community, leading to the study of primitives such as extractable one-way functions, extractable hash functions, succinct non-interactive arguments of knowledge (SNARKs), and (public-coin) differing-inputs obfuscation ((PC-)diO), and spurring the development of a wide spectrum of new applications relying on these primitives. For most of these applications, it is required that the extractability assumption holds even in the presence of attackers receiving some auxiliary information that is sampled from some fixed efficiently computable distribution Z. We show that, assuming the existence of public-coin collision-resistant hash functions, there exists an efficient distributions Z such that either - PC-diO for Turing machines does not exist, or - extractable one-way functions w.r.t. auxiliary input Z do not exist. A corollary of this result shows that additionally assuming existence of fully homomorphic encryption with decryption in NC1, there exists an efficient distribution Z such that either - SNARKs for NP w.r.t. auxiliary input Z do not exist, or - PC-diO for NC1 circuits does not exist. To achieve our results, we develop a “succinct punctured program” technique, mirroring the powerful punctured program technique of Sahai and Waters (STOC’14), and present several other applications of this new technique. In particular, we construct succinct perfect zero knowledge SNARGs and give a universal instantiation of random oracles in full-domain hash applications, based on PC-diO. As a final contribution, we demonstrate that even in the absence of auxiliary input, care must be taken when making use of extractability as- sumptions. We show that (standard) diO w.r.t. any distribution D over programs and bounded-length auxiliary input is directly implied by any obfuscator that satisfies the weaker indistinguishability obfuscation (iO) security notion and diO for a slightly modified distribution D′ of programs (of slightly greater size) and no auxiliary input. As a consequence, we directly obtain negative results for (standard) diO in the absence of auxiliary input

Predictable arguments of knowledge

We initiate a formal investigation on the power of predictability for argument of knowledge systems for NP. Specifically, we consider private-coin argument systems where the answer of the prover can be predicted, given the private randomness of the verifier; we call such protocols Predictable Arguments of Knowledge (PAoK). Our study encompasses a full characterization of PAoK, showing that such arguments can be made extremely laconic, with the prover sending a single bit, and assumed to have only one round (i.e., two messages) of communication without loss of generality. We additionally explore PAoK satisfying additional properties (including zero-knowledge and the possibility of re-using the same challenge across multiple executions with the prover), present several constructions of PAoK relying on different cryptographic tools, and discuss applications to cryptography

Charges in gravitational fields: from Fermi, via Hanni-Ruffini-Wheeler, to the "electric Meissner effect"

Recent developments in obtaining a detailed model for gamma ray bursts have shown the need for a deeper understanding of phenomena described by solutions of the Einstein-Maxwell equations, reviving interest in the behavior of charges close to a black hole. In particular a drastic difference has been found between the lines of force of a charged test particle in the fields of Schwarzschild and Reissner-Nordstrom black holes. This difference characterizes a general relativistic effect for the electric field of a charged test particle around a (charged) Reissner-Nordstrom black hole similar to the "Meissner effect" for a magnetic field around a superconductor. These new results are related to earlier work by Fermi and Hanni-Ruffini-Wheeler.Comment: 25 pages, 17 figures, to appear on the Proceedings of "Analysis, manifolds and geometric structures in physics", International Conference in Honour of Y. Choquet-Bruhat, Isola d'Elba June 24th-26th, 200

Trade-off Between Work and Correlations in Quantum Thermodynamics

Quantum thermodynamics and quantum information are two frameworks for employing quantum mechanical systems for practical tasks, exploiting genuine quantum features to obtain advantages with respect to classical implementations. While appearing disconnected at first, the main resources of these frameworks, work and correlations, have a complicated yet interesting relationship that we examine here. We review the role of correlations in quantum thermodynamics, with a particular focus on the conversion of work into correlations. We provide new insights into the fundamental work cost of correlations and the existence of optimally correlating unitaries, and discuss relevant open problems.Comment: 11 pages, 1 figure

On the History of Number Line

The notion of number line was formed in XX c. We consider the generation of this conception in works by M. Stiefel (1544), Galilei (1633), Euler (1748), Lambert (1766), Bolzano (1830-1834), Meray (1869-1872), Cantor (1872), Dedekind (1872), Heine (1872) and Weierstrass (1861-1885).Comment: 9 page