PhD on Symmetric Cryptography over Prime Fields and Integer Rings

Symmetric-key cryptography is of vital importance in the field of cybersecurity and data protection, offering tools for data encryption and authentication. While public-key cryptography is crucial for exchanging the key or signing data, symmetric cryptography guarantees better performance and faster speed for encrypting data.

Without doubt, AES (Advanced Encryption Standard) and Keccak/SHA-3 (Secure Hash Algorithm 3) are the two most used and famous symmetric cryptography algorithms. Winners of the standardization processes sponsored by the U.S. National Institute of Standards and Technology (NIST), they are currently adopted by the U.S. and the European governments. As the majority of the symmetric primitives, they are designed to naturally operate over bits, in order to maximize their performances in Software and Hardware implementations.

At the current state of the art, this design approach is showing all its limits when those symmetric primitives are used in new emerging contexts, such as rising applications of practical importance including Format Preserving Encryption (FPE), Multi-Party Computation (MPC), Homomorphic Encryption (HE), and Zero-Knowledge (ZK). These applications are usually defined over prime finite fields, and more recently, even over integer rings. In order to work, such protocols and applications rely on the evaluation of symmetric cryptographic primitives (such as ciphers and hash functions), whose details have a crucial impact on the performances of the considered application/protocol. From this point of view, using a symmetric primitive naturally defines over the bits for performing operations over prime fields or integer rings represents a significant bottleneck in terms of performances.

As part of this project, your work will consist in designing and analyzing dedicated symmetric-key primitives operating directly over prime fields and/or integer rings, that can provide efficient solutions for rising applications of practical importance such as FPE, MPC, HE, and ZK. Due to the novelty of these symmetric primitives, special attention will be given to their security, with the goals of better understanding their security margin, and of proposing new innovative security arguments. (We highlight that the implementation of those schemes will not be part of the tasks of the PhD candidate.)

This PhD project is supported by the ERC Starting Grant "SYMPZON: Getting SYMmetric CryPtography Out of its Comfort ZONe". You will be supervised by Dr. Lorenzo Grassi and Prof. Tanja Lange to conduct research and publish results at top-ranked international academic conferences and journals. You will be expected to collaborate with fellow PhD candidates and researchers from Eindhoven University of Technology (TU/e) and from other international institutions.

A meaningful job in a dynamic and ambitious university, in an interdisciplinary setting and within an international network. You will work on a beautiful, green campus within walking distance of the central train station. In addition, we offer you:

• Full-time employment for four years, with an intermediate assessment after nine months. You will spend a minimum of 10% of your four-year employment on teaching tasks, with a maximum of 15% per year of your employment.
• Salary and benefits (such as a pension scheme, paid pregnancy and maternity leave, partially paid parental leave) in accordance with the Collective Labour Agreement for Dutch Universities, scale P (min. € 3,059 max. € 3,881).
• A year-end bonus of 8.3% and annual vacation pay of 8%.
• High-quality training programs and other support to grow into a self-aware, autonomous scientific researcher. At TU/e we challenge you to take charge of your own learning process.
• An excellent technical infrastructure, on-campus children's day care and sports facilities.
• An allowance for commuting, working from home and internet costs.
• A Staff Immigration Team and a tax compensation scheme (the 30% facility) for international candidates.