Lossy trapdoor functions (LTDF) and all-but-one trapdoor functions (ABO-TDF) are fundamental cryptographic primitives. And given the recent advances in quantum computing, it would be much desirable to develop new and improved lattice-based LTDF and ABO-TDF. In this work, we provide more compact constructions of LTDF and ABO-TDF based on the learning with errors (LWE) problem. In addition, our L...

We argue that all locality-preserving mappings between fermionic observables and Pauli matrices on a two-dimensional lattice can be generated from the exact bosonization in Ref. [1], whose gauge constraints project onto subspace of toric code with emergent fermions. Starting applying Clifford finite-depth generalized local unitary (gLU) transformation, we achieve possible fermion-to-qubit (up t...

Let Γ < SLn(Z) be a subgroup of finite index, where n≥5. Suppose Γ acts continuously on a manifold M , where π1(M) = Z n, preserving a measure that is positive on open sets. Further assume that the induced Γ action on H(M) is non-trivial. We show there exists a finite index subgroup Γ′ < Γ and a Γ′ equivariant continuous map ψ :M→Tn that induces an isomorphism on fundamental group. We prove mor...

Suppose that (A0, A1) and (B0, B1) are Banach couples, and that T is a linear operator which maps A0 compactly into B0 and A1 boundedly (or even compactly) into B1. Does this imply that T : [A0, A1]θ → [B0, B1]θ compactly? (Here, as usual, [A0, A1]θ denotes the complex interpolation space of Alberto Calderón.) This question has been open for 44 years. Affirmative answers are known for it in man...

We construct an identity-based encryption (IBE) scheme from the standard Learning with Errors (LWE) assumption, which both has a compact public-key (with size similar to known lattice-based PKE schemes) and also achieves adaptive security in the standard model. This improves over previous IBE schemes from lattices, which either have a public key that grows at least linearly with the length of t...

We explore the compact U(1) lattice gauge theory with staggered fermions and gauge field action − ∑ P [β cos(ΘP ) + γ cos(2ΘP )], both for dynamical fermions and in the quenched approximation. (ΘP denotes the plaquette angle.) In simulations with dynamical fermions at various γ ≤ −0.2 on 64 lattices we find the energy gap at the phase transition of a size comparable to the pure gauge theory for...

Since the seminal work of Ajtai [1], lattice-based cryptography has attracted many researchers. As fruitful results, there are one-way and collision-resistant hash functions (e.g., [1, 6]) and public-key cryptosystems, which are secure based on the worst-case hardness of lattice problems. However, the primitives have drawbacks; The size of a public key and that of an index of hash functions is ...

Simulations in compact U(1) lattice gauge theory in 4D show now beyond any reasonable doubts that the phase transition separating the Coulomb from the confined phase is of first order, albeit a very weak one. This settles the issue from the numerical side. On the analytical side, it was suggested some time ago, based on the qualitative analogy between the phase diagram of such a model and the o...

We compute Neuberger’s overlap operator by the Lanczos algorithm applied to the Wilson-Dirac operator. Locality of the operator for quenched QCD data and its eigenvalue spectrum in an instanton background are studied. 1. Although brute force calculations of the quenched lattice QCD with Wilson fermions have been able to approach the chiral limit [1], there are increased efforts to make the chir...

We propose, demonstrate and investigate highly compact circulators with ultra-low insertion loss in square-lattice- square-rod-photonic-crystal waveguides. Only a single magneto- optical square rod is required to be inserted into the cross center of waveguides, making the structure very compact and ultra efficient. The square rods around the center defect rod are replaced by several right-angle...