Boolean functions with optimal stability of their cryptographic indicators under restriction of their inputs

Encrypting data is essential for ensuring the security of our electronic communications. The ciphers in current use are built from smaller components, one of them being a cryptographic Boolean function. Such functions must satisfy several properties in order to withstand cryptographic attacks: high non-linearity, high algebraic degree, low differential uniformity etc.

This project will look at how these properties can change if the inputs of the functions are maliciously manipulated. We aim to answer questions like: What are the optimal values that can be achieved for the stability of the indicators? How many optimal functions are there? How to construct such functions? How to test if proposed or existing functions (from currently existing ciphers) are optimal or close to optimal from this point is view? These results will feed into the design and analysis of future ciphers.

This work is related to an EPSRC project. Your main supervisor will be Dr Ana Salagean, who has a long track record of research in the area of mathematical aspects of cryptography. You will also work alongside a postdoctoral research associate, Dr Serge Feukoua. The work will involve close collaboration, with weekly meetings and opportunities to present the work in the Department and at international conferences and workshops. The PhD student will be free to develop their research in new directions, according to their own interests, as the work progresses. While the total working hours are expected to be similar to a full-time job, there is flexibility on when and where the work is done.

Loughborough University has an applied research culture. In REF 2021, 94% of the work submitted was judged to be top-rated as world-leading or internationally excellent. We are a community based on mutual support and collaboration. Through our Doctoral College there are continual opportunities for building important research skills and networks among your peers and research academics.

Supervisors

Name of primary supervisor: Dr Ana Salagean

Entry requirements for United Kingdom

Applicants should have, or expect to achieve, a degree in Computer Science or Mathematics, with at least a 2:1 Honours degree in the UK system, or an equivalently high result from non-UK universities. Experience in cryptography and/or a relevant Master’s degree will be an advantage.

English language requirements

Applicants must meet the minimum English language requirements. Further details are available on the International website.

Applicants must meet the minimum English language requirements. Further details are available on the International website (http://www.lboro.ac.uk/international/applicants/english/).

Find out more about research degree funding

How to apply

All applications should be made online. Under programme name, select Computer Science. Please quote the advertised reference number: SCI23-AS in your application.

To avoid delays in processing your application, please ensure that you submit the minimum supporting documents.

See studentship assessment criteria.

If you have any questions, please contact: [Email Address Removed]

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