Quantum Physics and Computers

Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit quantum features could factor large composite integers. This task is believed to be out of reach of classical computers as soon as the number of digits in the number to factor exceeds a certain limit. The additional power of quantum computers comes from the possibility of employing a superposition of states, of following many distinct computation paths and of producing a final output that depends on the interference of all of them. This ``quantum parallelism'' outstrips by far any parallelism that can be thought of in classical computation and is responsible for the ``exponential'' speed-up of computation. This is a non-technical (or at least not too technical) introduction to the field of quantum computation. It does not cover very recent topics, such as error-correction.Comment: 27 pages, LaTeX, 8 PostScript figures embedded. A bug in one of the postscript files has been fixed. Reprints available from the author. The files are also available from http://eve.physics.ox.ac.uk/Articles/QC.Articles.htm

A measurement study of peer-to-peer bootstrapping and implementations of delay-based cryptography

This thesis researches two distinct areas of study in both peer-to-peer networking formodern cryptocurrencies and implementations of delay-based cryptography.The first part of the thesis researches elements of peer-to-peer network mechanisms,with a specific focus on the dependencies on centralised infrastructure required for theinitial participation in such networks.Cryptocurrencies rely on decentralised peer-to-peer networks, yet the method bywhich new peers initially join these networks, known as bootstrapping, presents a significantchallenge. Our original research consists of a measurement study of 74 cryptocurrencies.Our study reveals a prevalent reliance on centralised infrastructure which leadsto censorship-prone bootstrapping techniques leaving networks vulnerable to censorshipand manipulation.In response, we explore alternative bootstrapping methods seeking solutions lesssusceptible to censorship. However, our research demonstrates operational challengesand limitations which hinder their effectiveness, highlighting the complexity of achievingcensorship-resistance in practice.Furthermore, our global measurement study uncovers the details of cryptocurrencypeer-to-peer networks, revealing instances outages and intentional protocol manipulationimpacting bootstrapping operations. Through a volunteer network of probes deployedacross 42 countries, we analyse network topology, exposing centralisation tendencies andunintentional peer exposure.Our research also highlights the pervasive inheritance of legacy bootstrapping methods,perpetuating security vulnerabilities and censorship risks within cryptocurrencysystems. These findings illuminate broader concerns surrounding decentralisation andcensorship-resistance in distributed systems.In conclusion, our study offers valuable insights into cryptocurrency bootstrappingtechniques and their susceptibility to censorship, paving the way for future research andinterventions to enhance the resilience and autonomy of peer-to-peer networks.In the second part of the thesis, attention shifts towards delay-based cryptography,where the focus lies on the creation and practical implementations of timed-release encryptionschemes. Drawing from the historical delay-based cryptographic protocols, thisthesis presents two original research contributions.The first is the creation of a new timed-release encryption scheme with a propertytermed implicit authentication. The second contribution is the development of a practicalconstruction called TIDE (TIme Delayed Encryption) tailored for use in sealed-bidauctions.Timed-Release Encryption with Implicit Authentication (TRE-IA) is a cryptographicprimitive which presents a new property named implicit authentication (IA). This propertyensures that only authorised parties, such as whistleblowers, can generate meaningfulciphertexts. By incorporating IA techniques into the encryption process, TRE-IAaugments a new feature in standard timed-release encryption schemes by ensuring thatonly the party with the encryption key can create meaningful ciphertexts. This propertyensures the authenticity of the party behind the sensitive data disclosure. Specifically, IAenables the encryption process to authenticate the identity of the whistleblower throughthe ciphertext. This property prevents malicious parties from generating ciphertextsthat do not originate from legitimate sources. This ensures the integrity and authenticityof the encrypted data, safeguarding against potential leaks of information not vettedby the party performing the encryption.TIDE introduces a new method for timed-release encryption in the context of sealedbidauctions by creatively using classic number-theoretic techniques. By integratingRSA-OEAP public-key encryption and the Rivest Shamir Wagner time-lock assumptionwith classic number theory principles, TIDE offers a solution that is both conceptuallystraightforward and efficient to implement.Our contributions in TIDE address the complexities and performance challengesinherent in current instantiations of timed-release encryption schemes. Our researchoutput creates a practical timed-release encryption implementation on consumer-gradehardware which can facilitate real-world applications such as sealed-bid auctions withclear steps for implementation.Finally, our thesis concludes with a review of the prospects of delay-based cryptographywhere we consider potential applications such as leveraging TIDE for a publicrandomness beacon.<br/

A novel augmented graph approach for estimation in localisation and mapping

This thesis proposes the use of the augmented system form - a generalisation of the information form representing both observations and states. In conjunction with this, this thesis proposes a novel graph representation for the estimation problem together with a graph based linear direct solving algorithm. The augmented system form is a mathematical description of the estimation problem showing the states and observations. The augmented system form allows a more general range of factorisation orders among the observations and states, which is essential for constraints and is beneficial for sparsity and numerical reasons. The proposed graph structure is a novel sparse data structure providing more symmetric access and faster traversal and modification operations than the compressed-sparse-column (CSC) sparse matrix format. The graph structure was developed as a fundamental underlying structure for the formulation of sparse estimation problems. This graph-theoretic representation replaces conventional sparse matrix representations for the estimation states, observations and their interconnections. This thesis contributes a new implementation of the indefinite LDL factorisation algorithm based entirely in the graph structure. This direct solving algorithm was developed in order to exploit the above new approaches of this thesis. The factorisation operations consist of accessing adjacencies and modifying the graph edges. The developed solving algorithm demonstrates the significant differences in the form and approach of the graph-embedded algorithm compared to a conventional matrix implementation. The contributions proposed in this thesis improve estimation methods by providing novel mathematical data structures used to represent states, observations and the sparse links between them. These offer improved flexibility and capabilities which are exploited in the solving algorithm. The contributions constitute a new framework for the development of future online and incremental solving, data association and analysis algorithms for online, large scale localisation and mapping

Studies of Quantum Chromodynamics at the LHC

A successful description of hadron-hadron collision data demands a profound understanding of quantum chromodynamics. Inevitably, the complexity of strong-interaction phenomena requires the use of a large variety of theoretical techniques -- from perturbative cross-section calculations up to the modelling of exclusive hadronic final states. Together with the unprecedented precision of the data provided by the experiments in the first running period of the LHC, a solid foundation of hadron-hadron collision physics at the TeV scale could be established that allowed the discovery of the Higgs boson and that is vital for estimating the background in searches for new phenomena. This chapter on studies of quantum chromodynamics at the LHC is part of a recent book on the results of LHC Run 1 and presents the advances in theoretical methods side-by-side with related key measurements in an integrated approach.Comment: 49 pages, 24 figures, To appear in "The Large Hadron Collider -- Harvest of Run 1", Thomas Sch\"orner-Sadenius (ed.), Springer, 2015 (532 pages, 253 figures; ISBN 978-3-319-15001-7, for more details, see http://www.springer.com/de/book/9783319150000

Solving the "Isomorphism of Polynomials with Two Secrets" Problem for all Pairs of Quadratic Forms

We study the Isomorphism of Polynomial (IP2S) problem with m=2 homogeneous quadratic polynomials of n variables over a finite field of odd characteristic: given two quadratic polynomials (a, b) on n variables, we find two bijective linear maps (s,t) such that b=t . a . s. We give an algorithm computing s and t in time complexity O~(n^4) for all instances, and O~(n^3) in a dominant set of instances. The IP2S problem was introduced in cryptography by Patarin back in 1996. The special case of this problem when t is the identity is called the isomorphism with one secret (IP1S) problem. Generic algebraic equation solvers (for example using Gr\"obner bases) solve quite well random instances of the IP1S problem. For the particular cyclic instances of IP1S, a cubic-time algorithm was later given and explained in terms of pencils of quadratic forms over all finite fields; in particular, the cyclic IP1S problem in odd characteristic reduces to the computation of the square root of a matrix. We give here an algorithm solving all cases of the IP1S problem in odd characteristic using two new tools, the Kronecker form for a singular quadratic pencil, and the reduction of bilinear forms over a non-commutative algebra. Finally, we show that the second secret in the IP2S problem may be recovered in cubic time

Q-Map: Quantum Circuit Implementation of Boolean Functions

Quantum computing has gained attention in recent years due to the significant progress in quantum computing technology. Today many companies like IBM, Google and Microsoft have developed quantum computers and simulators for research and commercial use. The development of quantum techniques and algorithms is essential to exploit the full power of quantum computers. In this paper we propose a simple visual technique (we call Q-Map) for quantum realisation of classical Boolean logic circuits. The proposed method utilises concepts from Boolean algebra to produce a quantum circuit with minimal number of quantum gates.Comment: 17 page

Les Houches 2013: Physics at TeV Colliders: Standard Model Working Group Report

This Report summarizes the proceedings of the 2013 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt primarily with (1) the techniques for calculating standard model multi-leg NLO and NNLO QCD and NLO EW cross sections and (2) the comparison of those cross sections with LHC data from Run 1, and projections for future measurements in Run 2.Comment: Proceedings of the Standard Model Working Group of the 2013 Les Houches Workshop, Physics at TeV Colliders, Les houches 3-21 June 2013. 200 page