Deniability an Alibi for Users in P2P Networks Information Systems Engineering Ben-Gurion University Deniability an Alibi for Users in P2P Networks Ofer Hermoni, Eyal Felstaine, Niv Gilboa and Sharon Shitrit January 1, 2019 ©

Outline Introduction Deniability Conclusion Architecture & Shares Operations Performance Mathematics Conclusion

P2P Network Client-Server model: e.g. web-surfing, email… P2P Network: e.g. File-sharing, instant messaging, VoIP…

The Problem – Anonymity in P2P Reader anonymity Server anonymity 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Deniability Deniability Deniability

Categories All documents are distinguished to two categories: Non-controversial Censored

Architecture 5 1 6 2 7 3 8 4

Publishing Non-Controversial Content 1 2 4 3 f 8553 22 872 455 9953 6663 Pool of shares

Publishing Censored Content 1 2 5 8 6 5 f f 7 8553 22 872 455 9953 6663 Pool of shares

Retrieval Censored Content Needed: “Lord of the Rings” Query the Index Retrieving: “Mars Car” + “Baby” 1 2 5 6 4 3 8 7 Server Share Doc name A, C 1 Mars Car B 2 D, F 3 G 4 A, B 5 Baby 6 C 7 D, G 8 Lord of the Rings

Deniability The reader maintains “Reader Deniability” - why? The reader retrieves only non-controversial documents The server maintains “Server Deniability” - why? Every served share is associated with a non-controversial document Indexing

Performance t - threshold = 2 |d| - Doc. size 4|d| bits 2|d| bits Including Indexing deniability Without Indexing deniability Censored Non-controversial 4|d| bits 2|d| bits 3|d| bits Communication Insert Communication Retrieve |d| bits Storage O(|d|) Computation (Insert / Retrieve) t - threshold = 2 |d| - Doc. size

Shamir’s Secret Sharing (1979) f(x) = 2 degree polynomial f(x) f(2) f(3) f(4) f(1) secret f(5) x 1 2 3 4 5 Minimum 3 points needed to reconstruct f(x) formulas

Function f - Deniable Secret Sharing f(x) f(x) = 2 degree polynomial Without index deniability x 1 2 3 4 5 formulas

Conclusion Deniability – An elegant alternative to anonymity Reader, Server and index deniability Against any adversary Low overhead Storage: x2 at most (x4 including index deniability) Communication: x4 at most Can be a “plug-in” to ubiquitous P2P networks

The End Thank you!!!