Information-theoretic cryptography is full of open problems with a communication-complexity flavor. We will describe several such problems that arise in the study of private information retrieval, secure multi-party computation, secret sharing, private simultaneous messages (PSM) and conditional disclosure of secrets (CDS). In all these cases, there is a huge (exponential) gap between the best known upper and lower bounds. We will also describe the connections between these problems, some old and some new.
@InProceedings{vaikuntanathan:LIPIcs.FSTTCS.2017.5, author = {Vaikuntanathan, Vinod}, title = {{Some Open Problems in Information-Theoretic Cryptography}}, booktitle = {37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)}, pages = {5:1--5:7}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-055-2}, ISSN = {1868-8969}, year = {2018}, volume = {93}, editor = {Lokam, Satya and Ramanujam, R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2017.5}, URN = {urn:nbn:de:0030-drops-84188}, doi = {10.4230/LIPIcs.FSTTCS.2017.5}, annote = {Keywords: Cryptography, Information-Theoretic Security, Private Information Retrieval, Secret Sharing, Multiparty Computation} }
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