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Inspired by problems in Private Information Retrieval, we consider the setting where two users need to establish a communication protocol to transmit a secret without revealing it to external observers. This is a question of how large a linear code can be, when it is required to agree with a prescribed code on a collection of coordinate sets. We show how the efficiency of such a protocol is determined by the derived matroid of the underlying linear communication code. Furthermore, we provide several sufficient combinatorial conditions for when no secret transmission is possible.
- Abstract simplicial complex
- Derived matroid
- Linear code
- Private information retrieval
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- 1 Active
01/09/2019 → 31/08/2023
Project: Academy of Finland: Other research funding