We revisit 't Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-reflection-positive or non-compact theories; on the other hand, without insisting on reflection-positivity, the exotic anomalies present a caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1)×SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The isotopy anomaly can be canceled by an extrinsic curvature improvement term, but at the cost of creating a periodicity anomaly. We survey the holomorphic bc ghost system which realizes all the exotic consistent anomalies, and end with comments on a subtlety regarding the anomalies of finite subgroups of U(1).

In addition to the conventional renormalized-coupling-constant picture, point interactions in two and three dimensions are shown to model within a suitable energy range scattering on localized potentials, both attractive and repulsive.

Secure group communication systems have become increasingly important for many emerging network applications. An efficient and robust group key management approach is indispensable to a secure group communication system. Motivated by the theory of hyper-sphere, this paper presents a new group key management approach with a group controller (GC). In our new design, a hyper-sphere is constructed for a group and each member in the group corresponds to a point on the hyper-sphere, which is called the member's private point. The GC computes the central point of the hyper-sphere, intuitively, whose “distance” from each member's private point is identical. The central point is published such that each member can compute a common group key, using a function by taking each member's private point and the central point of the hyper-sphere as the input. This approach is provably secure under the pseudo-random function (PRF) assumption. Compared with other similar schemes, by both theoretical analysis and experiments, our scheme (1) has significantly reduced memory and computation load for each group member; (2) can efficiently deal with massive membership change with only two re-keying messages, i.e., the central point of the hyper-sphere and a random number; and (3) is efficient and very scalable for large-size groups.

We consider a Schrdinger particle on a graph consisting of <i>N</i> links joined at a single point. Each link supports a real locally integrable potential <i>V</i> _<i>j</i>; the self-adjointness is ensured by the type boundary condition at the vertex. If all the links are semi-infinite and ideally coupled, the potential decays as <i>x</i> ¹ along each of them, is nonrepulsive in the mean and weak enough, the corresponding Schrdinger operator has a single negative eigenvalue; we find its asymptotic behavior. We also derive a bound on the number of bound states and explain how the coupling constant may be interpreted in terms of a family of squeezed potentials.

In this paper, we attempt to reconstruct one of the last and incomplete projects of Volodya Geyler. We study the motion of a quantum particle in the plane to which a halfline lead is attached, assuming that the particle has spin and the plane component of the Hamiltonian contains a spin-orbit interaction, of Rashba or Dresselhaus type. We construct a class of admissible Hamiltonians and derive an explicit expression for the Green function, which is applied to scattering in a system of this kind.

The subject of the paper is Schrdinger operators on tree graphs which are radial, having the branching number bn at all the vertices at the distance tn from the root. We consider a family of coupling conditions at the vertices characterized by (bn1)2+4 real parameters. We prove that if the graph is sparse so that there is a subsequence of {tn+1tn} growing to infinity, in the absence of the potential the absolutely continuous spectrum is empty for a large subset of these vertex couplings, but on the the other hand, there are cases when the spectrum of such a Schrdinger operator can be purely absolutely continuous.

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We establish that boundary degrees of freedom associated with a generic codimension one null surface in D-dimensional pure Einstein gravity naturally admit a thermodynamical description. We expect the null surface thermodynamics to universally follow as a result of the diffeomorphism invariance of the theory, not relying on other special features of the null surface or the gravity theory. Using standard surface charge analysis and covariant phase-space method, we formulate laws of null surface thermodynamics which are local equations over an arbitrary null surface paralleling local versions of the zeroth- and first laws and the Gibbs-Duhem equation. This thermodynamical system is generally an open system and can be closed only when there is no flux of gravitons through the null surface. Our analysis extends the usual black hole thermodynamics to a universal feature of any area element on a generic null surface. We discuss the relevance of our study for the membrane paradigm and black hole microstates.

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We review some recent developments in Chern-Simons theory on a hyperbolic 3-manifold M with complex gauge group G. We focus on the case G=SL(N,C) and with M a knot complement. The main result presented in this note is the cluster partition function, a computational tool that uses cluster algebra techniques to evaluate the Chern-Simons path integral. We also review various applications and open questions regarding the cluster partition function and some of its relation with string theory.

We study the behavior of a quantum particle confined to a hard-wall strip of a constant width in which there is a finite number<i>N</i>of point perturbations. Constructing the resolvent of the corresponding Hamiltonian by means of Krein's formula, we analyze its spectral and scattering properties. The bound state problem is analogous to that of point interactions in the plane: since a two-dimensional point interaction is never repulsive, there are<i>m</i>discrete eigenvalues, 1<i>m</i><i>N</i>, the lowest of which is nondegenerate. On the other hand, due to the presence of the boundary the point interactions give rise to infinite series of resonances; if the coupling is weak they approach the thresholds of higher transverse modes. We derive also spectral and scattering properties for point perturbations in several related models: a cylindrical surface, both of a finite and of an infinite height, threaded by a magnetic flux, and a straight strip which

We propose a new basic trapdoor ℓIC (ℓ-Invertible Cycles) of the mixed field type for Multivariate Quadratic public key cryptosystems. This is the first new basic trapdoor since the invention of Unbalanced Oil and Vinegar in 1997. ℓIC can be considered an extended form of the well-known Matsumoto-Imai Scheme A (also MIA or C^∗), and share some features of stagewise triangular systems. However ℓIC has very distinctive properties of its own. In practice, ℓIC is much faster than MIA, and can even match the speed of single-field MQ schemes.

The SFLASH signature scheme stood for a decade as the most successful cryptosystem based on multivariate polynomials, before an efficient attack was finally found in 2007. In this paper, we review its recent cryptanalysis and we notice that its weaknesses can all be linked to the fact that the cryptosystem is built on the structure of a large field. As the attack demonstrates, this richer structure can be accessed by an attacker by using the specific symmetry of the core function being used. Then, we investigate the effect of restricting this large field to a purely linear subset and we find that the symmetries exploited by the attack are no longer present. At a purely defensive level, this defines a countermeasure which can be used at a moderate overhead. On the theoretical side, this informs us of limitations of the recent attack and raises interesting remarks about the design itself of multivariate schemes.

We propose a new efficient hardware implementation of Rainbow signature scheme. We enhance the implementation in three directions. First, we develop a new parallel hardware design for the Gauss-Jordan elimination, and solve a 12 ×12 system of linear equations with only 12 clock cycles. Second, a novel multiplier is designed to speed up multiplication of three elements over a finite field. Third, we design a novel partial multiplicative inverter to speed up the multiplicative inversion of finite field elements. Through further other minor optimizations of the parallelization process and by integrating the major optimizations above, we build a new hardware implementation, which takes only 198 clock cycles to generate a Rainbow signature, a new record in generating digital signatures and four times faster than the 804-clock-cycle Balasubramanian-Bogdanov-Carter-Ding-Rupp design with similar parameters.

In CT-RSA 2019, Bauer et al. have analyzed the case when the public key is reused for the NewHope key encapsulation mechanism (KEM), a second-round candidate in the NIST Post-quantum Standard process. They proposed an elegant method to recover coefficients ranging from −6 to 4 in the secret key. We repeat their experiments but there are two fundamental problems. First, even for coefficients in [−6, 4] we cannot recover at least 262 of them in each secret key with 1024 coefficients. Second, for the coefficient outside [−6, 4], they suggested an exhaustive search. But for each secret key on average there are 10 coefficients that need to be exhaustively searched, and each of them has 6 possibilities. This makes Bauer et al.’s method highly inefficient. We propose an improved method, which with 99.22% probability recovers all the coefficients ranging from −6 to 4 in the secret key. Then, inspired by Ding et al.’s key mismatch attack, we propose an efficient strategy which with a probability of 96.88% succeeds in recovering all the coefficients in the secret key. Experiments show that our proposed method is very efficient, which completes the attack in about 137.56 ms using the NewHope parameters.

In this paper, we present a new algorithm, such that, for the learning with errors (LWE) problems, if the errors are bounded -- the errors do not span the whole prime finite field F_q but a fixed known subset of size D (D<q), which we call the learning with bounded errors (LWBE) problems, we can solve it with complexity O(n^D).

The most general admissible boundary conditions are derived for an idealized AharonovBohm flux intersecting the plane at the origin on the background of a homogeneous magnetic field. A standard technique based on self-adjoint extensions yields a four-parameter family of boundary conditions; the other two parameters of the model are the AharonovBohm flux and the homogeneous magnetic field. The generalized boundary conditions may be regarded as a combination of the AharonovBohm effect with a point interaction. Spectral properties of the derived Hamtonians are studied in detail.

The initial decay rate of a mixed state is discussed; is shown to be zero for finite energy states. In the previous paper [1] we investigated a general scheme for description of unstable systems. One of our results concerned the initial decay rate. Generalizing the earlier results of Horwitz and Marchand (see [2] and other references contained in [1]) we proved there, that the initial decay rate of any pure state of the unstable system equals to zero, if this state is so called finite energy state. Here we shall be interested in the same problem, assuming now the state of the decaying system to be in general mixed. Such assumption seems to be reasonable: firstly, from the point of view of an experiment it is too restrictive to treat only pure states of unstable systems. In particular, mixed states are generally considered in the recent studies about the influence of measuring devices on the time evolution of the unstable system [3

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In this paper, we present a new algorithm, such that, for the small integer solution (SIS) problem, if the solution is bounded ( by an integer \beta in l_\infty norm, which we call a bounded SIS (BSIS) problem, {\it and if the difference between the row dimension n and the column dimension m of the corresponding matrix is relatively small with respect the row dimension m}, we can solve it easily with a complexity of polynomial in m.

As a discrete-time quantum walk model on the one-dimensional integer lattice Z, the quantum walk recently constructed byWang and Ye [CaishiWang and Xiaojuan Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Information Processing 15 (2016), 1897–1908] exhibits quite different features. In this paper, we extend this walk to a higher dimensional case. More precisely, for a general positive integer d ≥ 2, by using quantum Bernoulli noises we introduce a model of discrete-time quantum walk on the d-dimensional integer lattice Z^d, which we call the d-dimensional QBN walk. The d-dimensional QBN walk shares the same coin space with the quantum walk constructed by Wang and Ye, although it is a higher dimensional extension of the latter. Moreover we prove that, for a range of choices of its initial state, the d-dimensional QBN walk has a limit probability distribution of d-dimensional standard Gauss type, which is in sharp contrast with the case of the usual higher dimensional quantum walks. Some other results are also obtained.

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 study 2d and 3d gravity theories on spacetimes with causal (timelike or null) codimension one boundaries while allowing for variations in the position of the boundary. We construct the corresponding solution phase space and specify boundary degrees freedom by analysing boundary (surface) charges labelling them. We discuss Y and W freedoms and change of slicing in the solution space. For D dimensional case we find D + 1 surface charges, which are generic functions over the causal boundary. We show that there exist solution space slicings in which the charges are integrable. For the 3d case there exists an integrable slicing where charge algebra takes the form of Heisenberg ⊕ A3 where A3 is two copies of Virasoro at Brown-Henneaux central charge for AdS3 gravity and BMS3 for the 3d flat space gravity.

Recently, the Little Dragon Two and Poly-Dragon multivariate based public-key cryptosystems were proposed as efficient and secure schemes. In particular, the inventors of the two schemes claim that Little Dragon Two and Poly-Dragon resist algebraic cryptanalysis. In this paper, we show that MXL2, an algebraic attack method based on the XL algorithm and Ding’s concept of Mutants, is able to break Little Dragon Two with keys of length up to 229 bits and Poly-Dragon with keys of length up to 299. This contradicts the security claim for the proposed schemes and demonstrates the strength of MXL2 and the Mutant concept. This strength is further supported by experiments that show that in attacks on both schemes the MXL2 algorithm outperforms the Magma’s implementation of F4.

In 2017, Ward Beullens et al. submitted Lifted Unbalanced Oil and Vinegar (LUOV) [4], a signature scheme based on the famous multivariate public key cryptosystem (MPKC) called Unbalanced Oil and Vinegar (UOV), to NIST for the competition for post-quantum public key scheme standardization. The defining feature of LUOV is that, though the public key P works in the extension field of degree r of F_2, the coefficients of P come from F_2. This is done to significantly reduce the size of P. The LUOV scheme is now in the second round of the NIST PQC standardization process. In this paper we introduce a new attack on LUOV. It exploits the “lifted” structure of LUOV to reduce direct attacks on it to those over a subfield. We show that this reduces the complexity below the targeted security for the NIST post-quantum standardization competition.