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Secure Remote Password (SRP) protocol is an augmented Password-based Authenticated Key Exchange (PAKE) protocol based on discrete logarithm problem (DLP) with various attractive security features. Compared with basic PAKE protocols, SRP does not require server to store user’s password and user does not send password to server to authenticate. These features are desirable for secure client-server applications. SRP has gained extensive real-world deployment, including Apple iCloud, 1Password etc. However, with the advent of quantum computer and Shor’s algorithm, classic DLP-based public key cryptography algorithms are no longer secure, including SRP. Motivated by importance of SRP and threat from quantum attacks, we propose a RLWE-based SRP protocol (RLWE-SRP) which inherit advantages from SRP and elegant design from RLWE key exchange. We also present parameter choice and efficient portable C++ implementation of RLWE-SRP. Implementation of our 209-bit secure RLWE-SRP is more than 3x faster than 112-bit secure original SRP protocol, 5.5x faster than 80-bit secure J-PAKE and 14x faster than two 184-bit secure RLWE-based PAKE protocols with more desired properties.

We study out-of-time ordered four-point functions in two dimensional conformal field theories by suitably analytically continuing the Euclidean correlator. For large central charge theories with a sparse spectrum, chaotic dynamics is revealed in an exponential decay; this is seen directly in the contribution of the vacuum block to the correlation function. However, contributions from individual non-vacuum blocks with large spin and small twist dominate over the vacuum block. We argue, based on holographic intuition, that suitable summations over such intermediate states in the block decomposition of the correlator should be sub-dominant, and attempt to use this criterion to constrain the OPE data with partial success. Along the way we also discuss the relation between the spinning Virasoro blocks and the on-shell worldline action of spinning particles in an asymptotically AdS spacetime.

Consider an unstable quantum system that has been found undecayed at an instant s and denote by R(t,s) the rate of its regeneration into an original (undecayed) state at a later instant t+s. It is proved that the reduced evolution is a semigroup, i.e., there is no regeneration at all, provided R(t,s)1/2 can be estimated by a sufficiently regular function that is nondecreasing in s and has zero derivative with respect to t at t=0 for every s. This generalizes the theorem of Misra and Sinha [Helv. Phys. Acta 45, 619 (1972)] in a different direction than in a recent paper by Nishioka [J. Math. Phys. 29, 1860 (1988)].

No abstract uploaded!

No abstract uploaded!

We present a quantum field theoretic description on the t−J model on a square lattice with dilute holes (i.e. near half-filling), based on the compact mutual Chern-Simons gauge theory. We show that, due to the presence of non-perturbative monopole plasma configuration from the antiferromagnetic background, holons (carrying electric charge) are linearly confined and strongly localized even without extrinsic disorder taken into account. Accordingly, the translation symmetry is spontaneously broken at ground state. Such an exotic localization is distinct from Anderson localization and essentially rooted in intrinsic Mott physics of the t−J model. Finally, a finite-temperature phase diagram is proposed. The metal-insulator transition observed in in-plane resistivity measurement is identified to a confinement-deconfinement transition from the perspective of gauge theory. The transition is characterized by the order parameter "Polyakov-line".

We present a closed form expression for the semiclassical OPE coefficients that are universal for all 2D CFTs with a “weak” light spectrum, by taking the semiclassical limit of the fusion kernel. We match this with a properly regularized and normalized bulk action evaluated on a geometry with three conical defects, analytically continued in the deficit angles beyond the range for which a metric with positive signature exists. The analytically continued geometry has a codimension-one coordinate singularity surrounding the heaviest conical defect. This singularity becomes a horizon after Wick rotating to Lorentzian signature, suggesting a connection between universality and the existence of a horizon.

We investigate a class of supersymmetric quantum mechanical theories (with two supercharges) having tensor-valued degrees of freedom which are dominated by melon diagrams in the large N limit. One motivation was to examine the interplay between supersymmetry and melonic dominance and potential implications for building toy models of holography. We find a definite tension between supersymmetry (with dynamical bosons) and melonic dominance in this class of systems. More specifically, our theories attain a low energy non-supersymmetric conformal fixed point. The origin of supersymmetry breaking lies in the need to regularize bosonic and fermionic degrees of freedom independently. We investigate various aspects of the low energy spectrum and also comment on related examples with different numbers of supercharges. Along the way we also derive some technical results for SL(2, ℝ) wavefunctions for fermionic excitations.

We study two dimensional N = (2, 2) Landau-Ginzburg models with tensor valued superfields with the aim of constructing large central charge superconformal field theories which are solvable using large N techniques. We demonstrate the viability of such constructions and motivate the study of anisotropic tensor models. Such theories are a novel deformation of tensor models where we break the continuous symmetries while preserving the large N solvability. Specifically, we examine theories with superpotentials involving tensor contractions chosen to pick out melonic diagrams. The anisotropy is introduced by further biasing individual terms by different coefficients, all of the same order, to retain large N scaling. We carry out a detailed analysis of the resulting low energy fixed point and comment on potential applications to holography. Along the way we also examine gauged versions of the models (with partial anisotropy) and find generically that such theories have a non-compact Higgs branch of vacua.