Group theory in cryptography

This paper is a guide for the pure mathematician who would like to know more about cryptography based on group theory. The paper gives a brief overview of the subject, and provides pointers to good textbooks, key research papers and recent survey papers in the area.Comment: 25 pages References updated, and a few extra references added. Minor typographical changes. To appear in Proceedings of Groups St Andrews 2009 in Bath, U

Internet security for mobile computing

Mobile devices are now the most dominant computer platform. Every time a mobile web application accesses the internet, the end user’s data is susceptible to malicious attacks. For instance, when paying a bill at a store with NFC mobile payment, navigating through a city operating GPS on a smartphone, or dictating the temperature at a household with a home automation device. These activities seem routine, yet, when vulnerabilities are present they can leave holes for hackers to access bank accounts, pinpoint a user’s recent location, or tell when someone is not at home. The awareness of the end user cannot be trusted. Device vendors and developers must provide safeguards. An ongoing issue is that the present security standards are outdated and were never envisioned with mobile devices in mind. It can be suggested that security is only idling the progress of mobile computing. Still, many application developers and IT professionals do not adopt security standards fast enough to keep up-to-date with known vulnerabilities. The main goals of the next generation of security standards, TLS, will provide developers with greater security efficiency and improved mobile throughput. These proposed capabilities of the TLS protocol will streamline mobile computing into the forefront of security practices. The analysis of this report demonstrates concepts on the direction mobile security, usability, and performance from a development standpoint.Electrical and Computer Engineerin

Isogeny-based post-quantum key exchange protocols

The goal of this project is to understand and analyze the supersingular isogeny Diffie Hellman (SIDH), a post-quantum key exchange protocol which security lies on the isogeny-finding problem between supersingular elliptic curves. In order to do so, we first introduce the reader to cryptography focusing on key agreement protocols and motivate the rise of post-quantum cryptography as a necessity with the existence of the model of quantum computation. We review some of the known attacks on the SIDH and finally study some algorithmic aspects to understand how the protocol can be implemented

A New Cryptosystem Based On Hidden Order Groups

Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having oracle access to a `Diffie-Hellman Problem' solver with fixed generator $g$, it is possible to compute $g^{1/x} \in G_1$ in polynomial time (see theorem 3.2). On the other hand, it is not known if such a reduction exists when $\phi(n)$ is unknown (see conjuncture 3.1). We exploit this ``gap'' to construct a cryptosystem based on hidden order groups and present a practical implementation of a novel cryptographic primitive called an \emph{Oracle Strong Associative One-Way Function} (O-SAOWF). O-SAOWFs have applications in multiparty protocols. We demonstrate this by presenting a key agreement protocol for dynamic ad-hoc groups.Comment: removed examples for multiparty key agreement and join protocols, since they are redundan