Department of Applied Mathematics Academic Program Review, Self Study / June 2010

The Department of Applied Mathematics has a multi-faceted mission to provide an exceptional mathematical education focused on the unique needs of NPS students, to conduct relevant research, and to provide service to the broader community. A strong and vibrant Department of Applied Mathematics is essential to the university's goal of becoming a premiere research university. Because research in mathematics often impacts science and engineering in surprising ways, the department encourages mathematical explorations in a broad range of areas in applied mathematics with specific thrust areas that support the mission of the school

Compilation of thesis abstracts, September 2009

NPS Class of September 2009This quarter’s Compilation of Abstracts summarizes cutting-edge, security-related research conducted by NPS students and presented as theses, dissertations, and capstone reports. Each expands knowledge in its field.http://archive.org/details/compilationofsis109452751

Cube-Type Algebraic Attacks on Wireless Encryption Protocols

Short-range (Bluetooth) and to some extent medium-range (WiFi) wireless networks are ubiquitous, being used in such places as the homes, hospitals, assembly lines, aircraft, and even wearable computers. Several types of attack have been successful at defeating the cryptosystems used by IEEE 802.11 and 802.16 technologies, leading on to ask the questions: how much trust should we place in the woreless encryption protocols? In 2008 Dinur and Shamir proposed a type of algebraic attack call the cube attack (1) in which the active assault on a crytosystem requires the attacker to extract useful information from the bit stream. By skilfully choosing some publicly settable bits, the attacker may be able to replace the degree of the polynomial that represent the encryption function by a system of linear equations

Cube-type algebraic attacks on wireless encryption protocols

In this study, we investigated an algebraic-type attack, known as the cube attack, against wireless networks. We implemented the cube attack in a wireless system, namely Bluetooth. We formally modeled the encryption function of E0 Bluetooth key generator and automated the process of the cube attack on E0 of the factorization process (preprocessing phase). In this phase, an attacker finds as many maxterms (a term of the encryption function such that its co-factor is a linear nonconstant polynomial) as possible. In the actual attacking phase, the attacker solves the system of linear equations through a chosen plaintext attack and reveals useful information about the cryptosystem. The number of operations needed in the computational process is 221.1 and is considerably less than that of similar algebraic types of attacks, but it is limited to the output of the LFSRs at any clock cycle. The results of our analysis indicate that if an attacker is an unauthorized participant of the security protocol, then by manipulating some of the output bits of the LFSRs of two arbitrary clock cycles and intercepting the output bits of the entire machine the attacker then succeeds in finding the output bits of the LFSRs at any clock tick.http://archive.org/details/cubetypelgebraic109454637Outstanding ThesisHellenic Navy authorApproved for public release; distribution is unlimited