Anyon trajectories and the systematics of the three-anyon spectrum

We develop the concept of trajectories in anyon spectra, i.e., the continuous dependence of energy levels on the kinetic angular momentum. It provides a more economical and unified description, since each trajectory contains an infinite number of points corresponding to the same statistics. For a system of non-interacting anyons in a harmonic potential, each trajectory consists of two infinite straight line segments, in general connected by a nonlinear piece. We give the systematics of the three-anyon trajectories. The trajectories in general cross each other at the bosonic/fermionic points. We use the (semi-empirical) rule that all such crossings are true crossings, i.e.\ the order of the trajectories with respect to energy is opposite to the left and to the right of a crossing.Comment: 15 pages LaTeX + 1 attached uuencoded gzipped file with 7 figure

Interpolation and Approximation of Polynomials in Finite Fields over a Short Interval from Noisy Values

Motivated by a recently introduced HIMMO key distribution scheme, we consider a modification of the noisy polynomial interpolation problem of recovering an unknown polynomial $f(X) \in Z[X]$ from approximate values of the residues of $f(t)$ modulo a prime $p$ at polynomially many points $t$ taken from a short interval

Improved key-reconciliation method

At PQ Crypto 2014, Peikert proposed efficient and practical lattice-based protocols for key transport, encryption and authenticated key exchange. One of the main technical innovations of this work is a reconciliation technique that allows two parties who approximately agree on a secret value to reach exact agreement, a setting common to essentially all lattice-based encryption schemes. Peikert\u27s reconciliation technique has been extended in the Frodo key exchange scheme, allowing for agreement on more than one bit. In both cases, only one reconciliation bit is required to reach exact agreement. As symmetric keys typically require many bits, say 128 or more, the parties compute multiple secret values, and reach exact agreement on each of those values individually. In this paper, we propose a reconciliation method that sends more than one reconciliation bit. In this way, the parties can agree on the same number of bits as with Peikert\u27s method with less stringent conditions on how approximate the approximate agreement must be. An instance of our method allows the two parties on a secret value that is one bit longer than with the previous methods, with virtually the same approximation requirements (i.e., with virtually the same security guarantees) as before. We numerically illustrate the advantages of our method with the impact to the instantiations of the Frodo scheme

spKEX: An optimized lattice-based key exchange

The advent of large-scale quantum computers has resulted in significant interest in quantum-safe cryptographic primitives. Lattice-based cryptography is one of the most attractive post-quantum cryptographic families due to its well-understood security, efficient operation and versatility. However, LWE-based schemes are still relatively bulky and slow. In this work, we present spKEX, a forward-secret, post-quantum, unauthenticated lattice-based key-exchange scheme that combines four techniques to optimize performance. spKEX relies on Learning with Rounding (LWR) to reduce bandwidth; it uses sparse and ternary secrets to speed up computations and reduce failure probability; it applies an improved key reconciliation scheme to reduce bandwidth and failure probability; and computes the public matrix A by means of a permutation to improve performance while allowing for a fresh A in each key exchange. For a quantum security level of 128 bits, our scheme requires 30% lesser bandwidth than the LWE-based key-exchange proposal Frodo [9] and allows for a fast implementation of the key exchange

Results on polynomial interpolation with mixed modular operations and unknown moduli

Motivated by a recently introduced HIMMO key predistribution scheme, we investigate the limits of various attacks on the polynomial interpolation problem with mixedmodular operations and hidden moduli. We firstly review the classical attack and consider itin a quantum-setting. Then, we introduce new techniques for finding out the secret moduli and consider quantum speed-ups

DTLS-HIMMO: Efficiently Securing a Post-Quantum World with a Fully-Collusion Resistant KPS

The future development of quantum-computers could turn many key agreement algorithms used in the Internet today fully insecure, endangering many applications such as online banking, e-commerce, e-health, etc. At the same time, the Internet is further evolving to enable the Internet of Things (IoT) in which billions of devices deployed in critical applications like healthcare, smart cities and smart energy are being connected to the Internet. The IoT not only requires strong and quantum-secure security, as current Internet applications, but also efficient operation. The recently introduced HIMMO scheme enables lightweight identity-based key sharing and verification of credentials in a non-interactive way. The collusion resistance properties of HIMMO enable direct secure communication between any pair of Internet-connected devices. The facts that attacking HIMMO requires lattice techniques and that it is extremely lightweight make HIMMO an ideal lightweight approach for key agreement and information verification in a post-quantum world. Building on the HIMMO scheme, this paper firstly shows how HIMMO can be efficiently implemented even in resource-constrained devices enabling combined key agreement and credential verification one order of magnitude more efficiently than using ECDH-ECDSA, while being quantum secure. We further explain how HIMMO helps to secure the Internet and IoT by introducing the DTLS- HIMMO operation mode. DTLS, the datagram version of TLS, is becoming the standard security protocol in the IoT, however, it is very frequently discussed that it does not offer the right performance for IoT scenarios. Our design, implementation, and evaluation show that DTLS-HIMMOoperation mode achieves the security properties of DTLS Certificate security suite while being quantum secure and exhibiting the overhead of symmetric-key primitives