Mathematics One for Cyber Security

Practical mathematical techniques for the development and analysis of secure software.

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Abertay Attributes: Through engaging with this module, students will develop the Intellectual, Personal, Professional, Digital and Active Citizen Abertay Attributes.

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<ul><li>Intellectual: Students will be supported to develop skills in their chosen specialism. They will be supported to evaluate information critically and rigorously, and tackle uncertainty and information gaps with confidence and self-awareness. </li>

<li>Personal: Students will undertake activities as part of this module which will support them to be determined, ambitious, articulate, adaptable, self-reflective, resilient, practical, proactive, innovative, and enterprising. </li>

<li>Professional: Students will be supported to develop portfolios of professional development and awareness which will equip and motivate them to continue learning and professional development throughout their careers.</li>

<li>Digital: This module focuses on digital skill development as a tool for their analysis and practice. Students will be supported to develop digital fluency, knowledge, skills, and confidence to embrace digital solutions. This will prepare them for the world of work and allow them to understand the likely impact of digital technology in their chosen subject and across contexts. </li>

<li>Be active citizens: The module will encourage students to consider personality in context and support them to be inclusive, globally conscientious, and socially respectful, and self-reflective. We will maintain and continuously develop an awareness of their civic, ethical and environmental responsibilities.</li>

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By the end of this module the student should be able to:

1. Understand and apply the mathematical techniques that underpin secure software development and analysis.
2. Describe potential applications of formal methods within the software development process, and apply formal specification and analysis techniques to simple software systems.
3. Explain standard cryptographic primitives and protocols, and apply these in a critical, safe and cautious manner in real-world scenarios.

1 Discrete Mathematics

The theory that supports the two areas below: basic number theory; finite arithmetic; functions, sets, rings, groups; elliptic curves; propositional and predicate logic; proof techniques; additional statistics.

2 Introduction to Formal Methods

The idea of formal specification and analysis. Simple pre/post-conditions. Formal specification languages. Model-checkers. Protocol analysis and session types. Proof-carrying code. Limitations of formal modelling in practice.

3 Introduction to Cryptography

Structures of cryptographic systems. Cryptographic primitives: stream and block ciphers, PRFs, hash functions, MACs, KDFs, and real-world instantiations of these. Symmetric and public-key cryptography. Key exchange. Definitions and proofs of security. Real-world cryptographic protocols and attacks. Basic post-quantum cryptography.

4 Introduction Post-Quantum Cryptography

The impact of quantum computing on cybersecurity: quantum mechanics principles, quantum algorithms like Shor's and Grover's, and their implications for cryptographic practices. The vulnerability of existing cryptographic algorithms to quantum attacks: public-key systems like RSA and ECC. Post-quantum cryptography: quantum-resistant algorithms such as lattice-based, hash-based, code-based, and multivariate polynomial cryptography. Challenges and strategies for transitioning to quantum cryptographic standards.