Diophantine equations as a context for technology-enhanced training in conjecturing and proving

Solving indeterminate algebraic equations in integers is a classic topic in the mathematics curricula across grades. At the undergraduate level, the study of solutions of non-linear equations of this kind can be motivated by the use of technology. This article shows how the unity of geometric contextualization and spreadsheet-based amplification of this topic can provide a discovery experience for prospective secondary teachers and information technology students. Such experience can be extended to include a transition from a computationally driven conjecturing to a formal proof based on a number of simple yet useful techniques.

Security analysis of the non-aggressive challenge response of the DNP3 Protocol using a CPN Model

Distributed Network Protocol Version 3 (DNP3) is the de-facto communication protocol for power grids. Standard-based interoperability among devices has made the protocol useful to other infrastructures such as water, sewage, oil and gas. DNP3 is designed to facilitate interaction between master stations and outstations. In this paper, we apply a formal modelling methodology called Coloured Petri Nets (CPN) to create an executable model representation of DNP3 protocol. The model facilitates the analysis of the protocol to ensure that the protocol will behave as expected. Also, we illustrate how to verify and validate the behaviour of the protocol, using the CPN model and the corresponding state space tool to determine if there are insecure states. With this approach, we were able to identify a Denial of Service (DoS) attack against the DNP3 protocol.

Basic finance made accessible in Excel 2007 : "the big 5, plus 2"

The basic principles and equations are developed for elementary finance, based on the concept of compound interest. The five quantities of interest in such problems are present value, future value, amount of periodic payment, number of periods and the rate of interest per period. We consider three distinct means of computing each of these five quantities in Excel 2007: (i) use of algebraic equations, (ii) by recursive schedule and the Goal Seek facility, and (iii) use of Excel's intrinsic financial functions. The paper is intended to be used as the basis for a lesson plan and contains many examples and solved problems. Comment is made regarding the relative difficulty of each approach, and a prominent theme is the systematic use of more than one method to increase student understanding and build confidence in the answer obtained. Full instructions to build each type of model are given and a complete set of examples and solutions may be downloaded (Examples.xlsx and Solutions.xlsx).

Root caries patterns and risk factors of middle-aged and elderly people in China

The objectives of this study were to describe root caries patterns of Chinese adults and to analyze the effect of selected demographic and socioeconomic factors on these patterns. A total sample of 1080 residents aged 35-44-years-old and 1080 residents aged 65-74-years-old from three urban and three rural survey sites in Hubei Province participated in both an oral health interview and a clinical oral health examination. Root surface caries prevalence rates were 13.1% in the middle-aged group and 43.9% in the elderly group. The mean number of teeth affected by caries in the middle-aged group was reported at 0.21 and 1.0 in the elderly group. Mean Root Caries Index (RCI) scores of the middle-aged were reported at 6.29 and elderly subjects were reported at 11.95. Elderly people living in rural areas reported a higher RCI score (13.24) than those living in urban areas (10.70). A significantly higher frequency of root surface caries was observed in elderly participants (P < 0.001, OR = 3.80) and ethnic minorities (P < 0.001, OR = 1.93). In addition, smokers, nontea drinkers, and those with an annual household income of 10,000 yuan or less tended to have higher caries prevalence. RCI figures for the different tooth types ranged from 1% to 16%, indicating a wide variation in attack rates. In conclusion, our study suggests that root surface caries occurrence is high among the Chinese adult population, especially older adults. With an increasing number of retained teeth in both middle-aged and elderly people, root caries is a growing disease in the People's Republic of China which deserves more attention in future research.

Images inside a reflecting spherical surface with possible application in astronomy

This report studies an algebraic equation whose solution gives the image system of a source of light as seen by an observer inside a reflecting spherical surface. The equation is looked at numerically using GeoGebra. Under the hypothesis that our galaxy is enveloped by a reflecting interface this becomes a possible model for many mysterious extra galactic observations.

Characterisations of extended resiliency and extended immunity of S-boxes

New criteria of extended resiliency and extended immunity of vectorial Boolean functions, such as S-boxes for stream or block ciphers, were recently introduced. They are related to a divide-and-conquer approach to algebraic attacks by conditional or unconditional equations. Classical resiliency turns out to be a special case of extended resiliency and as such requires more conditions to be satisfied. In particular, the algebraic degrees of classically resilient S-boxes are restricted to lower values. In this paper, extended immunity and extended resiliency of S-boxes are studied and many characterisations and properties of such S-boxes are established. The new criteria are shown to be necessary and sufficient for resistance against the divide-and-conquer algebraic attacks by conditional or unconditional equations.

Cheating prevention in linear secret sharing

Cheating detection in linear secret sharing is considered. The model of cheating extends the Tompa-Woll attack and includes cheating during multiple (unsuccessful) recovery of the secret. It is shown that shares in most linear schemes can be split into subshares. Subshares can be used by participants to trade perfectness of the scheme with cheating prevention. Evaluation of cheating prevention is given in the context of different strategies applied by cheaters.

Finding good differential patterns for attacks on SHA-1

In this paper we analyse properties of the message expansion algorithm of SHA-1 and describe a method of finding differential patterns that may be used to attack reduced versions of SHA-1. We show that the problem of finding optimal differential patterns for SHA-1 is equivalent to the problem of finding minimal weight codeword in a large linear code. Finally, we present a number of patterns of different lengths suitable for finding collisions and near-collisions and discuss some bounds on minimal weights of them.

Cryptanalysis of FORK-256

In this paper we present a cryptanalysis of a new 256-bit hash function, FORK-256, proposed by Hong et al. at FSE 2006. This cryptanalysis is based on some unexpected differentials existing for the step transformation. We show their possible uses in different attack scenarios by giving a 1-bit (resp. 2-bit) near collision attack against the full compression function of FORK-256 running with complexity of 2^125 (resp. 2^120) and with negligible memory, and by exhibiting a 22-bit near pseudo-collision. We also show that we can find collisions for the full compression function with a small amount of memory with complexity not exceeding 2^126.6 hash evaluations. We further show how to reduce this complexity to 2^109.6 hash computations by using 273 memory words. Finally, we show that this attack can be extended with no additional cost to find collisions for the full hash function, i.e. with the predefined IV.

Social engineering in social networking sites : how good becomes evil

Social Engineering (ES) is now considered the great security threat to people and organizations. Ever since the existence of human beings, fraudulent and deceptive people have used social engineering tricks and tactics to trick victims into obeying them. There are a number of social engineering techniques that are used in information technology to compromise security defences and attack people or organizations such as phishing, identity theft, spamming, impersonation, and spaying. Recently, researchers have suggested that social networking sites (SNSs) are the most common source and best breeding grounds for exploiting the vulnerabilities of people and launching a variety of social engineering based attacks. However, the literature shows a lack of information about what types of social engineering threats exist on SNSs. This study is part of a project that attempts to predict a persons’ vulnerability to SE based on demographic factors. In this paper, we demonstrate the different types of social engineering based attacks that exist on SNSs, the purposes of these attacks, reasons why people fell (or did not fall) for these attacks, based on users’ opinions. A qualitative questionnaire-based survey was conducted to collect and analyse people’s experiences with social engineering tricks, deceptions, or attacks on SNSs.

Cryptology and network security

This book constitutes the refereed proceedings of the 11th International Conference on Cryptology and Network Security, CANS 2012, held in Darmstadt, Germany, in December 2012. The 22 revised full papers, presented were carefully reviewed and selected from 99 submissions. The papers are organized in topical sections on cryptanalysis; network security; cryptographic protocols; encryption; and s-box theory.

Reduction of amplitude equations by the renormalization group approach

This article elucidates and analyzes the fundamental underlying structure of the renormalization group (RG) approach as it applies to the solution of any differential equation involving multiple scales. The amplitude equation derived through the elimination of secular terms arising from a naive perturbation expansion of the solution to these equations by the RG approach is reduced to an algebraic equation which is expressed in terms of the Thiele semi-invariants or cumulants of the eliminant sequence { Zi } i=1 . Its use is illustrated through the solution of both linear and nonlinear perturbation problems and certain results from the literature are recovered as special cases. The fundamental structure that emerges from the application of the RG approach is not the amplitude equation but the aforementioned algebraic equation. © 2008 The American Physical Society.

Parallel authentication and public-key encryption

A parallel authentication and public-key encryption is introduced and exemplified on joint encryption and signing which compares favorably with sequential Encrypt-then-Sign (ɛtS) or Sign-then-Encrypt (Stɛ) schemes as far as both efficiency and security are concerned. A security model for signcryption, and thus joint encryption and signing, has been recently defined which considers possible attacks and security goals. Such a scheme is considered secure if the encryption part guarantees indistinguishability and the signature part prevents existential forgeries, for outsider but also insider adversaries. We propose two schemes of parallel signcryption, which are efficient alternative to Commit-then-Sign-and- Encrypt (Ct&G3&S). They are both provably secure in the random oracle model. The first one, called generic parallel encrypt and sign, is secure if the encryption scheme is semantically secure against chosen-ciphertext attacks and the signature scheme prevents existential forgeries against random-message attacks. The second scheme, called optimal parallel encrypt. and sign, applies random oracles similar to the OAEP technique in order to achieve security using encryption and signature components with very weak security requirements — encryption is expected to be one-way under chosen-plaintext attacks while signature needs to be secure against universal forgeries under random-plaintext attack, that is actually the case for both the plain-RSA encryption and signature under the usual RSA assumption. Both proposals are generic in the sense that any suitable encryption and signature schemes (i.e. which simply achieve required security) can be used. Furthermore they allow both parallel encryption and signing, as well as parallel decryption and verification. Properties of parallel encrypt and sign schemes are considered and a new security standard for parallel signcryption is proposed.

Hybrid graphite film–carbon nanotube platform for enzyme immobilization and protection

A novel platform consisting of a multilayered substrate, activated graphite-like carbon film, and dense forest of long, vertically-aligned multiwall carbon nanotubes grown by the chemical vapor deposition is designed, fabricated, and tested for covalent immobilization of enzymatic biocatalysts with the aim of protecting them from shear forces and microbial attacks present in bioreactors. The covalent bonding ensures enzyme retention in a flow, while the dense nanotube forest may serve as a protection of the enzymes from microbial attack without impeding the flow of reactants and products. This platform was demonstrated for the two reference enzymes, horseradish peroxidase and catalase, which were immobilized without degrading their biological activity. This combination of an activated carbon layer for an efficient immobilization of biocatalysts with a protective layer of inert carbon nanotubes could dramatically improve the efficiency and longevity of enzymatic bio-catalysis employed in a large variety of advanced biotechnological processes.

Malleability attacks on multi-party key agreement protocols

Multi-party key agreement protocols indirectly assume that each principal equally contributes to the final form of the key. In this paper we consider three malleability attacks on multi-party key agreement protocols. The first attack, called strong key control allows a dishonest principal (or a group of principals) to fix the key to a pre-set value. The second attack is weak key control in which the key is still random, but the set from which the key is drawn is much smaller than expected. The third attack is named selective key control in which a dishonest principal (or a group of dishonest principals) is able to remove a contribution of honest principals to the group key. The paper discusses the above three attacks on several key agreement protocols, including DH (Diffie-Hellman), BD (Burmester-Desmedt) and JV (Just-Vaudenay). We show that dishonest principals in all three protocols can weakly control the key, and the only protocol which does not allow for strong key control is the DH protocol. The BD and JV protocols permit to modify the group key by any pair of neighboring principals. This modification remains undetected by honest principals.