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 published in the literature, 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, the approach of designing symmetric primitives that naturally operate over bits is showing all its limit 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 (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 traditional symmetric primitives such as AES and Keccak/SHA-3 for performing operations over a prime fields or an integer ring represents a significant bottleneck in terms of performances.
As part of this project, your work will consist in designing, implementing, and analyzing dedicated symmetric primitives operating directly over prime fields 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 to improve the current cryptanalytic results, and to develop new innovative security arguments.
You will be supervised by Dr.
Lorenzo Grassi in order to conduct research and publish the results at top-ranked international academic conferences and journals. You will be expected to collaborate with fellow PhD candidates and researchers from
Coding Theory and Cryptology group in the
Department of Mathematics and Computer Science and from other international institutions.
The successful candidate will be an integral part of the prestigious ERC Starting Grant 'Getting SYMmetric CryPtography Out of its Comfort ZONe' (SYMPZON). SYMPZON aims to reshape the process of designing and analyzing symmetric algorithms that operate over the integer rings, by both developing a new theoretical framework, and by constructing concrete cryptographic primitives for practical use cases.
ProfileWe are seeking a highly motivated PhD candidate to join our research team in cryptography. The ideal candidate will have a strong background in mathematics, computer sciences, engineering, or a closely related field. The candidate must be highly motivated and be able to demonstrate their potential for conducting original research in symmetric cryptography.