diff --git a/whitepaper/Dissertation.pdf b/whitepaper/Dissertation.pdf index 50102d2..851def7 100644 Binary files a/whitepaper/Dissertation.pdf and b/whitepaper/Dissertation.pdf differ diff --git a/whitepaper/Dissertation.tex b/whitepaper/Dissertation.tex index d9729fe..a26a70b 100644 --- a/whitepaper/Dissertation.tex +++ b/whitepaper/Dissertation.tex @@ -8,7 +8,6 @@ % requirements spec, clear evaluation of security with links to proofs etc. % clear achievements of content in regards to goals % reflect on achievemtns, difficulties, novelty etc. -% diagrams maybe \usepackage{algorithmicx} \usepackage{algpseudocode} @@ -1193,12 +1192,20 @@ All measurements were taken on Brave 1.50.114 (Chromium 112.0.5615.49) 64-bit, u \section{Contributions} -This project has contributed an implementation of an optimised form of Paillier that is compatible with modern web browsers. It is evident that, considering current hardware, Paillier in Jurik's form is a viable cryptosystem. +This project has contributed an implementation of an optimised form of Paillier that is compatible with modern web browsers. Benchmarks show that, considering current hardware, Paillier in Jurik's form can be a viable cryptosystem for occasional use. However, additional work is needed to make it efficient enough for large amounts of encryptions, as seen in \hyperref[protocol4]{Protocol~\ref{protocol4}}. -The Paillier implementation provides means for Schnorr-style proofs of knowledge and also multi-round proofs of knowledge, which serialise to JSON. These are made non-interactive by applying the SHAKE cryptographic hash suite to reduce program complexity and communication cost. +The Paillier implementation provides capability for Schnorr-style proofs of knowledge and also multi-round proofs of knowledge, which serialise to JSON. These are made non-interactive by applying the SHAKE cryptographic hash suite. Multi-round proofs combining set membership and graph isomorphism are among the implementations, and have strong zero-knowledge properties once used with the Fiat-Shamir transform. +\section{Domain} + +The protocols devised are effective in the target domain of online games. With multi-round proofs of 24 rounds, players can be confident to a reasonably high probability that other players are not trying to cheat. + +For the most part, the protocols shown run in a time-frame that would not disrupt the experience, with the exception of the bit length proof. With additional work, this proof could be replaced with a Bulletproof \cite{bulletproofs}, which may use less bandwidth and perform faster. + +A large outstanding problem with the implementation is conflict resolution. Currently, if a player submits proofs that do not verify, other players simply ignore the message. However, a better solution should be that the other players can decide to remove a misbehaving player from the protocol. + \section{Wider application} P2P software solutions have many benefits to end users: mainly being greater user freedom. I believe that the content presented here shows clear ways to extend P2P infrastructure, and reduce dependence on centralised services.