zkRollups are a means of achieving higher transaction throughput by batching up to thousands of transactions into a single “rollup” which is included in L1 blocks. The fidelity of the rollup can be secured in various ways. Either through greater hardware requirements with standard rollups (ZKRU) or economic incentives, a variant known as optimistic rollups (ORU). Standard rollups use a zero knowledge proof, this is a small cryptographic proof which can be verified extremely quickly by bakers. This requires at least one specialized node processing these rollups for the chain. Optimistic rollups rely on a game theory approach. Validators post a stake when including the rollup. This rollup can be challenged and through a series of challenges and responses the dispute can result in the execution of a single transaction. This transaction can be re-executed on-chain to adjudicate and the winner of the dispute gets the stake. The Tezos protocol can host multiple rollup implementations and designs. Some can also be permissioned ( only certain parties can add to them ) at the cost of some benefits. All of these options are currently being explored.
An excellent video featuring rollups by Arthur Brietman.
zkChannels is a Lightning-like protocol that enables scalable and anonymous off-chain transactions using a combination of commitments, blind signatures and efficient zero-knowledge proof techniques (in addition to multi-party computation techniques). In particular, for Tezos, zkChannels rely on a randomizable blind signature scheme with efficient zero-knowledge protocols. The randomizable signature scheme is based on Pointcheval-Sanders (PS) and instantiated on the BLS12-381 curve as well.
For some background, zkChannels allows a customer and a merchant to open an asymmetric payment channel (unlike Lightning). The merchant is at most pseudonymous and remains identifiable across all channels; the customer is at most pseudonymous during channel establishment and closure, but has the ability to make payments anonymously as long as they have an open channel with sufficient balance. That is, the customer’s anonymity set for a payment is the set of all customers with whom the given merchant has a channel open.
All payments must be initiated by the customer and the anonymous channels are bi-directional only in the sense that payment values can be positive or negative. At any point while the channel is open, the merchant or customer are able to initiate channel closure.
zkChannels library implementation for Tezos is here
zkChannels is still being actively developed, led by Bolt Labs, Inc.
PVSS and VDFs have both been discussed as ways to improve randomness in Tezos.
Publicly Verifiable Secret Sharing (PVSS)
Secret sharing methods distribute a secret amongst a group of participants. Each individual is allocated a share of the secret. In PVSS, the distributor of the secret posts public proof verifying the validity of the shares of the secret. This can be used to strengthen randomness and to minimize bias in leader and/or committee election in proof-of-stake context
Verifiable Delay Function (VDF)
New cryptographic techniques such as VDFs (Verifiable Delay Functions) have been discussed as a way to improve randomness on Tezos. This is important because baker selection on Tezos relies on randomness. The stronger the randomness, the more difficult it is to "game" the consensus algorithm, either in order to give supernormal profits to other bakers or in order to disrupt the network more generally.
VDF ASIC research is underway, led by Filecoin and the Ethereum Foundation.
One discussed change to mempool management is expected to increase throughput by 2-3x. This would entail including a transactions in a block based on whether its fee can be paid, without computing its effects. Invalid transactions would be included and treated as nops, as already done in Tezos.