RT info:eu-repo/semantics/doctoralThesis
T1 Algebraic coding theory for private information retrieval
A1 Bodur, Seyma
A2 Universidad de Valladolid. Escuela de Doctorado
K1 Algebra
K1 Algebra
K1 12 Matemáticas
AB Private Information Retrieval (PIR) protocols allow a user to retrieve an entry from a database without revealing to the database server which entry was retrieved. The first part of the thesis focuses on multi-server PIR protocols using binary cyclic codes. We construct PIR schemes with improved privacy guarantees by carefully selecting storage and retrieval codes with optimal or near-optimal parameters, comparing our schemes with known Reed–Muller-based constructions.  Afterward, the thesis proposes a novel single-server PIR scheme based on codes over rings, designed to resist linear algebra attacks. This new construction modifies and strengthens the earlier approach by incorporating cyclic inner codes and matrix-product outer codes, providing both efficiency and resistance to known attacks.  This thesis also focuses on the study of monomial–Cartesian codes and their Schur products. These codes are particularly relevant for the construction of  CSS–T quantum codes, which are capable of fault-tolerantly implementing non-Clifford gates like the T-gate. We generalize previous results and prove that J-affine variety codes support efficient componentwise multiplication and subfield-subcodes.  Moreover, we also consider Cartesian codes and their Schur products in the context of secure multi-party computation protocols. In secure multi-party computation, the subfield subcode of the component-wise square of an evaluation code and its dual code must be taken into account. Controlling the various parameters from a single code can be quite challenging. We will present some strategies for addressing these parameters while constructing codes from well-known families of Cartesian product codes.
YR 2025
FD 2025
LK https://uvadoc.uva.es/handle/10324/79952
UL https://uvadoc.uva.es/handle/10324/79952
LA eng
NO Escuela de Doctorado
DS UVaDOC
RD 21-nov-2025