Discrete phase-locked loop systems and spreadsheets

This paper demonstrates the use of a spreadsheet in exploring non-linear difference equations that describe digital control systems used in radio engineering, communication and computer architecture. These systems, being the focus of intensive studies of mathematicians and engineers over the last 40 years, may exhibit extremely complicated behaviour interpreted in contemporary terms as transition from global asymptotic stability to chaos through period-doubling bifurcations. The authors argue that embedding advanced mathematical ideas in the technological tool enables one to introduce fundamentals of discrete control systems in tertiary curricula without learners having to deal with complex machinery that rigorous mathematical methods of investigation require. In particular, in the appropriately designed spreadsheet environment, one can effectively visualize a qualitative difference in the behviour of systems with different types of non-linear characteristic.

Broadcast anti-jamming systems

In a traditional anti-jamming system a transmitter who wants to send a signal to a single receiver spreads the signal power over a wide frequency spectrum with the aim of stopping a jammer from blocking the transmission. In this paper, we consider the case that there are multiple receivers and the transmitter wants to broadcast a message to all receivers such that colluding groups of receivers cannot jam the reception of any other receiver. We propose efficient coding methods that achieve this goal and link this problem to well-known problems in combinatorics. We also link a generalisation of this problem to the Key Distribution Pattern problem studied in combinatorial cryptography.

Modular green roof systems in mid-rise multifamily residential units

This paper presents the results of a full-scale research project undertaken to assess scour losses/gains for modular tray green roof specimens placed on a mock-up building, and identify important factors to consider for wind design criteria. Visual assessment of the experimental results showed that usage of vegetation, parapet height, wind direction, and test duration were the predominant factors affecting scour resistance of the growth media in tested specimens. Statistical analysis results indicated that the differences in soil losses measured among Phase 2’s test trials were more significant than those in Phase 1. This was attributed to the lack of parapet, cornering wind conditions, and longer test duration found in Phase 2. Findings presented in this paper constitute a benchmark for future research to improve the knowledge gap that exists in green roof wind design.

Formal analysis of card-based payment systems in mobile devices

To provide card holder authentication while they are conducting an electronic transaction using mobile devices, VISA and MasterCard independently proposed two electronic payment protocols: Visa 3D Secure and MasterCard Secure Code. The protocols use pre-registered passwords to provide card holder authentication and Secure Socket Layer/ Transport Layer Security (SSL/TLS) for data confidentiality over wired networks and Wireless Transport Layer Security (WTLS) between a wireless device and a Wireless Application Protocol (WAP) gateway. The paper presents our analysis of security properties in the proposed protocols using formal method tools: Casper and FDR2. We also highlight issues concerning payment security in the proposed protocols.

Cryptanalysis of block ciphers with overdefined systems of equations

Several recently proposed ciphers, for example Rijndael and Serpent, are built with layers of small S-boxes interconnected by linear key-dependent layers. Their security relies on the fact, that the classical methods of cryptanalysis (e.g. linear or differential attacks) are based on probabilistic characteristics, which makes their security grow exponentially with the number of rounds N r r. In this paper we study the security of such ciphers under an additional hypothesis: the S-box can be described by an overdefined system of algebraic equations (true with probability 1). We show that this is true for both Serpent (due to a small size of S-boxes) and Rijndael (due to unexpected algebraic properties). We study general methods known for solving overdefined systems of equations, such as XL from Eurocrypt’00, and show their inefficiency. Then we introduce a new method called XSL that uses the sparsity of the equations and their specific structure. The XSL attack uses only relations true with probability 1, and thus the security does not have to grow exponentially in the number of rounds. XSL has a parameter P, and from our estimations is seems that P should be a constant or grow very slowly with the number of rounds. The XSL attack would then be polynomial (or subexponential) in N r> , with a huge constant that is double-exponential in the size of the S-box. The exact complexity of such attacks is not known due to the redundant equations. Though the presented version of the XSL attack always gives always more than the exhaustive search for Rijndael, it seems to (marginally) break 256-bit Serpent. We suggest a new criterion for design of S-boxes in block ciphers: they should not be describable by a system of polynomial equations that is too small or too overdefined.

Democratic systems

Digital signature is a breakthrough of modern cryptographic systems. A (t, n) threshold digital signature allows every set of cardinality t or more (out-of n) co-signers to authenticate a message. In almost all existing threshold digital signatures the threshold parameter t is fixed. There are applications, however, in which the threshold parameter needs to be changed from time to time. This paper considers such a scenario, in order to discuss relevant problems, and proposes a model that solves the related problems.