Research projects on cryptography
- Sedat Akleylek
The projects are suitable for all degrees (BSc, MSc, PhD)
MDS Matrices over Binary Field Extensions and Their Implementations
Block ciphers have diffusion and confusion layers. Maximum distance separable (MDS) matrices are the core component of the diffusion layers. MDS matrices have the maximum branch number. In this project, the aim is to summarize the search-based methods and direct construction methods to generate MDS matrices over binary field extensions. Another task is to compare the involutory MDS matrices in terms of XOR count after applying optimization methods.
Distributed Storage Blockchain (DSB)
The concept of distributed storage blockchain has been recently studied to reduce the storage cost of traditional blockchain systems. Network coding was adapted to the notion of distributed storage to reduce the storage space for distributed ledger in blockchain systems. One idea is to use Shamir's sharing scheme to decrease the storage of transactions. The task is to summarize the methods of secret sharing algorithms and linear codes for distributed storage with their application areas.
Quantum Secure Digital Signature Schemes
The task is to review the post-quantum digital signature schemes submitted to short signature and fast verification call. The focus will be on multivariate polynomial or lattice-based or code-based signature schemes.
Research projects on coding and communications
- Irina Bocharova
Signal sets indexing for future communications
The development of energy-efficient signal sets for future communication standards requires optimization of signal indexing. Consider a set of signals (points in the Euclidean space) of a small dimension (at most 8). To each point, we assign an index represented by a binary sequence. To each pair of signals corresponds the Hamming distance between indices and the Euclidean distance between points. Good indexing avoids pairs that have a small Euclidean distance but a large Hamming distance. Keeping this in mind, a target function is derived. We need an efficient (maybe, AI) algorithm (program) to minimize the target function over the set of permutations of indices.
- Maiara Francine Bollauf
Oblivious transfer protocol in noisy channels
In an oblivious transfer protocol, a sender has some secret information to be transmitted to the receiver in such a way that it remains unknown which piece of information has been sent. Coding theoretical techniques can be applied to guarantee constant rate oblivious transfer protocols, given that the underlying error-correcting codes satisfy some properties regarding the element-wise multiplication of their codewords. General constructions of such good codes remain an open question in the area and constitute the main objective of this project. Suitable for master's and PhD students interested in security applications of coding theory, with a background in linear algebra.
Mathematics of lattice-based security schemes
In lattice-based cryptography or physical-layer security, some lattice quantities are crucial to define whether a system is secure or not, or more secure than others. This is the case of the theta series, used to characterize the distance profile of all the lattice points. During this project, the objective is not only to study some known theta functions but also to explore some new identities that would translate into substantial improvements in the state of the art in lattice-based security schemes. Suitable for master's and PhD students interested in the mathematical foundations of lattice-based cryptography. Desired background includes number theory and algebra.
Attacks to the lattice isomorphism problem
The lattice isomorphism problem (LIP) has been recently proposed as a foundation for post-quantum cryptographic schemes. It asks if two lattices are isomorphic and if so, to find the isometry between them. The goal of this project is to study the current attacks on LIP, starting with the hull attack, inherited from the code equivalence problem. Suitable for master's and PhD students interested in lattice-based cryptography. Desired background in number theory and algebra.
- Boris Kudryashov
Covering sets for communications and post-quantum cryptology
Some communication systems as well as post-quantum cryptology use error-correction algorithms based on so-called “coverings”. The covering problem is one of the fundamental problems in combinatorics. For a given length n and weight k of covering sequences we need to find the smallest possible set S of covering sequences, such that any w positions are covered (belong to) one of the sequences from S. In practice, we need a fast procedure for constructing S and it is desirable that all sequences in S can be obtained from its small subset by using simple operations such as permutations.
Low-complexity quantum error-correcting coding
The goal is to extend the expertise of the coding theory group in classic coding theory to quantum codes. Some proprietary techniques developed in our projects are good candidates for use in quantum data transmission. We invite students to participate in this research.
- Vitaly Skachek