How can you design a consensus algorithm that resists data breaches and privacy violations?

Enumerating threats is not a trivial task. The risk here is that if done improperly, the security of the entire consensus algorithm will be based on unproven assumptions of threats. Building a consensus algorithm is essentially like designing a game (see Crypto-economics, game theory and mechanism design). The first thing you want to do is enumerate the assumptions under which the game will be successful and the knes that will result in a failure. The consensus algorithm should essentially reward those who play the game according to the right assumptions and punish those who go against the assumptions. From here, it is easy to decide the adversarial model you have and the threat landscape is more precise.

The second step is to choose how you will enforce the assumptions in step 1 above. There are several ways of doing this. You can impose an economic cost in exchange for trust. In PoW, you leverage an indirect computational economic cost. In PoS, it is more direct. You can use a Capacity consumption model. Here you use some resource for consensus but does not impose much economic cost on protocol participants.Eg: Prood of History, Proof of capacity, proof of space, etc. You may even use Gossip-based models like BFT, Hashgraph,etc. Or you can build a hybrid model from the 3 above. So in general there are 100s of consensus models. But broadly there are 4 types : Economic cost based, capacity consuming, Gossip based protocols and Hybrid.

Indeed the next steps is to design the protocol rules. If you have already built the right assumptions, validated them, and generated the right threats. The protocol rules should appear intuitively as part of the game we are designing. What you really need to do in this stage is to mathematically define your protocol rules. This allows for more rigurous testing mathematically and cryptographically. By doing this you can weed out critical vulnerabilities and efficiency issues even before you write the first line of code. (See Magic Behind Blockchain series)

Here it is important to make a mathematical test, cryptographic test, adversarial tests. Efficiency tests and general cyber security and privacy tests

This is the stage where you actually implement the already rigurously tested algorithm in code. Optimization possibilities begin to naturally appear during implementation. These should be re-verified to make sure it doesnt break the core assumptions and then improve and continue to implement

In my experience, you have two technical elements to consider: (a) the actual protocol that should be designed as per outcomes and requirements, and its formal verification. If it’s about total data privacy in the public space, then it means it will include some sort of encryption like zk-snarks in the mix which also needs to be thoroughly vetted (b) the implementations thereof: protocol can be perfect, but code may have issues (poor quality code). This also includes different Clients to ensure diversity But then it’s about education: if a blockchain wants to retain its decentralisation (ie full consensus) then it’s necessary to share data for validation. Hence people need to carefully think about what data they share and what it means.

I’d suggest quite extensive testing before to rollout a consensus network in a production environment especially if it handles billions worth of public digital assets and crypto. Once rolled out, two things happen: (a) it sticks and it can be very difficult to change (think about the coordination required to update nodes in a permissionless enviros) and (b) if it has an issue, then the reputation of that network may be jeopardised. Hence it’s worth treating consensus changes of any kind with extra care!