In this paper, we explore the feasibility of reliable and private communication in dynamic networks, where in each round the adversary can choose which direct peer-to-peer links are available in the network graph, under the sole condition that the graph is k-connected at each round (for some k). We show that reliable communication is possible in such a dynamic network if and only if k > 2t. We also show that if k = cn > 2 t for a constant c, we can achieve reliable communication with polynomial round and communication complexity. For unconditionally private communication, we show that for a passive adversary, k > t is sufficient (and clearly necessary). For an active adversary, we show that k > 2t is sufficient for statistical security (and clearly necessary), while k > 3t is sufficient for perfect security. We conjecture that, in contrast to the static case, k > 2t is not enough for perfect security, and we give evidence that the conjecture is true. Once we have reliable and private communication between each pair of parties, we can emulate a complete network with secure channels, and we can use known protocols to do secure computation.
@InProceedings{damgard_et_al:LIPIcs.ITC.2023.13, author = {Damg\r{a}rd, Ivan and Ravi, Divya and Tschudi, Daniel and Yakoubov, Sophia}, title = {{Secure Communication in Dynamic Incomplete Networks}}, booktitle = {4th Conference on Information-Theoretic Cryptography (ITC 2023)}, pages = {13:1--13:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-271-6}, ISSN = {1868-8969}, year = {2023}, volume = {267}, editor = {Chung, Kai-Min}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2023.13}, URN = {urn:nbn:de:0030-drops-183419}, doi = {10.4230/LIPIcs.ITC.2023.13}, annote = {Keywords: Secure Communication, Dynamic Incomplete Network, Information-theoretic} }
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