Maiorana-McFarland Functions with High Second-Order Nonlinearity

The second-order nonlinearity, and the best quadratic approximations, of Boolean functions are studied in this paper. We prove that cubic functions within the Maiorana-McFarland class achieve very high second order nonlinearity, which is close to an upper bound that was recently proved by Carlet et al., and much higher than the second order nonlinearity obtained by other known constructions. The structure of the cubic Boolean functions considered allows the efficient computation of (a subset of) their best quadratic approximations

Supervised learning with quantum enhanced feature spaces

Machine learning and quantum computing are two technologies each with the potential for altering how computation is performed to address previously untenable problems. Kernel methods for machine learning are ubiquitous for pattern recognition, with support vector machines (SVMs) being the most well-known method for classification problems. However, there are limitations to the successful solution to such problems when the feature space becomes large, and the kernel functions become computationally expensive to estimate. A core element to computational speed-ups afforded by quantum algorithms is the exploitation of an exponentially large quantum state space through controllable entanglement and interference. Here, we propose and experimentally implement two novel methods on a superconducting processor. Both methods represent the feature space of a classification problem by a quantum state, taking advantage of the large dimensionality of quantum Hilbert space to obtain an enhanced solution. One method, the quantum variational classifier builds on [1,2] and operates through using a variational quantum circuit to classify a training set in direct analogy to conventional SVMs. In the second, a quantum kernel estimator, we estimate the kernel function and optimize the classifier directly. The two methods present a new class of tools for exploring the applications of noisy intermediate scale quantum computers [3] to machine learning.Comment: Fixed typos, added figures and discussion about quantum error mitigatio

Heuristic search of (semi-)bent functions based on cellular automata

An interesting thread in the research of Boolean functions for cryptography and coding theory is the study of secondary constructions: given a known function with a good cryptographic profile, the aim is to extend it to a (usually larger) function possessing analogous properties. In this work, we continue the investigation of a secondary construction based on cellular automata (CA), focusing on the classes of bent and semi-bent functions. We prove that our construction preserves the algebraic degree of the local rule, and we narrow our attention to the subclass of quadratic functions, performing several experiments based on exhaustive combinatorial search and heuristic optimization through Evolutionary Strategies (ES). Finally, we classify the obtained results up to permutation equivalence, remarking that the number of equivalence classes that our CA-XOR construction can successfully extend grows very quickly with respect to the CA diameter

Ongoing Research Areas in Symmetric Cryptography

This report is a deliverable for the ECRYPT European network of excellence in cryptology. It gives a brief summary of some of the research trends in symmetric cryptography at the time of writing. The following aspects of symmetric cryptography are investigated in this report: • the status of work with regards to different types of symmetric algorithms, including block ciphers, stream ciphers, hash functions and MAC algorithms (Section 1); • the recently proposed algebraic attacks on symmetric primitives (Section 2); • the design criteria for symmetric ciphers (Section 3); • the provable properties of symmetric primitives (Section 4); • the major industrial needs in the area of symmetric cryptography (Section 5)

D.STVL.9 - Ongoing Research Areas in Symmetric Cryptography

This report gives a brief summary of some of the research trends in symmetric cryptography at the time of writing (2008). The following aspects of symmetric cryptography are investigated in this report: • the status of work with regards to different types of symmetric algorithms, including block ciphers, stream ciphers, hash functions and MAC algorithms (Section 1); • the algebraic attacks on symmetric primitives (Section 2); • the design criteria for symmetric ciphers (Section 3); • the provable properties of symmetric primitives (Section 4); • the major industrial needs in the area of symmetric cryptography (Section 5)

Journal of Telecommunications and Information Technology, 2006, nr 3

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Design and Analysis of Honeycomb Structures with Advanced Cell Walls

Honeycomb structures are widely used in engineering applications. This work consists of three parts, in which three modified honeycombs are designed and analyzed. The objectives are to obtain honeycomb structures with improved specific stiffness and specific buckling resistance while considering the manufacturing feasibility. The objective of the first part is to develop analytical models for general case honeycombs with non-linear cell walls. Using spline curve functions, the model can describe a wide range of 2-D periodic structures with nonlinear cell walls. The derived analytical model is verified by comparing model predictions with other existing models, finite element analysis (FEA) and experimental results. Parametric studies are conducted by analytical calculation and finite element modeling to investigate the influences of the spline waviness on the homogenized properties. It is found that, comparing to straight cell walls, spline cell walls have increased out-of-plane buckling resistance per unit weight, and the extent of such improvement depends on the distribution of the spline’s curvature. The second part of this research proposes a honeycomb with laminated composite cell walls, which offer a wide selection of constituent materials and improved specific stiffness. Analytical homogenization is established and verified by FEA comparing the mechanical responses of a full-detailed honeycomb and a solid cuboid assigned with the calculated homogenization properties. The results show that the analytical model is accurate at a small computational cost. Parametric studies reveal nonlinear relationships between the ply thickness and the effective properties, based on which suggestions are made for property optimizations. The third part studies honeycomb structures with perforated cell walls. The homogenized properties of this new honeycomb are analytically modeled and investigated by finite element modeling. It is found that comparing to conventional honeycombs, honeycombs with perforated cell walls demonstrate enhanced in-plane stiffness, out-of-plane bending rigidity, out-of-plane compressive buckling stress, approximately the same out-of-plane shear buckling strength, and reduced out-of-plane stiffness. For the future design, empirical formulas, based on finite element results and expressed as functions of the perforation size, are derived for the mechanical properties and verified by mechanical tests conducted on a series of 3D printed perforated honeycomb specimens

Applications of the Quantum Kernel Method on a Superconducting Quantum Processor

The widespread benefits of classical machine learning along with promised speedups by quantum algorithms over their best performing classical counterparts have motivated development of quantum machine learning algorithms that combine these two approaches. Quantum Kernel Methods (QKMs) [22, 49] describe one such combination, which seeks to leverage the high dimensional Hilbert space over quantum states to perform classification on encoded classical data. In this work I present an analysis of QKM algorithms used to encode and classify real data using a quantum processor, aided by a suite of custom noise models and hardware optimizations. I introduce and validate techniques for error mitigation and readout error correction designed specifically for this algorithm/hardware combination. Though I do not achieve high accuracy with one type of QKM-based classifier, I provide evidence for possible fundamental limitations to the QKM as well as hardware limitations that are unaccounted for by a reasonable Markovian noise model