---reuf tags: research For simplicity , a multi-signature scheme MS = (Pg, Kg, Sign , Vf) consists of Parameter generation (system wide , runs by central authority , does it have to ?) Key generation (Kg -> (pk,sk) , non-interactive process) Signing Verification ( ($L={pk_1...pk_n}$, m ,$\sigma$) -> 1)

Required Reading 1 https://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=8434214 2 https://eprint.iacr.org/2018/953.pdf 3 https://github.com/flashbots/mev-research/issues/34 4 https://eprint.iacr.org/2016/612.pdf What is ORE? ORE is a cryptographic primitive that enables range queries over encrypted ciphertexts. Its main application is in the database world, where it's used to enable queries over encrypted databases to provide assurances in the case of data breaches. For each of exposition, we will be simply providing a high-level definition.

Definition: An anonymity metric indicates the uncertainty of the identity of a fixed entity is , from the point of view by advarsary A. Objective function This should include two ingredients , i.e. anonymity level and anonymity loss. Anonymity level Anonymity level depends on: 1) distribution of probabilities (see towards measuring anonymity) ; 2) size of anonymity set (see A system for anonymous and unobservable internet access & The disadvantages of free mix routes and how to overcome them in Hannes Federath) Edman et al. orginally propose to count the number of possible perfect matching in G , i.e. computing the permanent of the adjacency matrix A.

[toc] Preliminary Quantify the anonymity (get objective function valued ) : Initial parameter space : x=[x_1,....,x_n] f(x) : performane(anonymity provided) of a particular configuration by running the full application. f(x*) : the best application performance

Motivation Currently in Tendermint, all queries made by light clients in Tendermint are public. In other words, whenever a light client queries Tendermint for application-specific state, anyone listening on the communication can associated a particular light client with certain application state information. There are several instances in which might want to hide what they are querying about to an outside observer, for example: A user wanting to query a block explorer may not want the block explorer service to know exactly what they are querying for. A user wanting to use and interact with a sensitive Tendermint-based application may not want an outside observer to know what they are querying for on that blockchain. Proposal This proposal is to add support for various private information retrieval protocols (PIR) in Tendermint. We propose several additions and changes to the light client, full nodes and ABCI components.