How to verify ZK proofs on Bitcoin
L2IV collaborates with Polyhedra on Bitcoin ZK verifier
L2IV and Polyhedra's collaboration on Exploring ZK proofs on Bitcoin
L2IV has collaborated with our portfolio company, Polyhedra ($ZK), on research on verifying ZK proofs on Bitcoin. The research article, contributed by L2IV, was first published in Polyhedra’s tech blog. The full article can be found here.
https://hackmd.io/@l2iterative/bitcoin-polyhedra
In this detailed research, we provide a comprehensive study about Bitcoin script (think “Ethereum smart contracts” but on Bitcoin). Unlike EVM, Bitcoin script has much simpler functionalities, and therefore, while ZK verifier on Ethereum is a solved question (see all the ZK rollups), it has been an open question how to bring the same thing to the Bitcoin network.
The article suggests that a hopeful incoming BIP to Bitcoin, which brings back the OP_CAT opcode, may be the key to an efficient Bitcoin ZK verifier. OP_CAT is a special opcode in the Bitcoin script language that was disabled by Satoshi back in 2010. If this opcode is brought back, one can enable efficient Merkle tree proof verification on Bitcoin, which can significantly improve Bitcoin ZK verifier.
Merkle tree proof verification is just part of the ZK verifier. The other part is related to finite field arithmetic. The article studies extensively on what finite fields are “Bitcoin-friendly” so that they can be handled in Bitcoin without too much overhead.
Lastly, the article offers a discussion on the implementation details. We discuss how to use OP_CAT to enable something called covenants in Bitcoin, which allows us to split the proof verification into several transactions. We also discuss the fraud proof solutions which leverage cryptoeconomics security to lower the prover’s overhead.
Importance of Bitcoin ZK verifier for Polyhedra's future applications
The Bitcoin ZK verifier is important to Polyhedra, as the ability to run a ZK verifier on Bitcoin is crucial to Bitcoin-native layer-2, bridge, restaking, and many other applications. We encourage readers to go through this technical article—though we admit that it is fairly long—but it can bring anyone up to speed with the state of the arts of the Bitcoin ecosystem.
In the rest of the article, we explain Polyhedra's motivation for starting to work on Bitcoin. This is indeed a well-planned strategic move.
The research “How to verify ZK proofs on Bitcoin?” provides a deeper explanation.
Exploring Polyhedra's Strategic Move into Bitcoin
Polyhedra has been working on ZK bridge and became the major player in ZK bridge with a close partnership with LayerZero, while most of the competitors—Succinct, Nil Foundation, Polymer, Lagrange—have given up working on ZK bridge and pivoted into other directions. This matches our prediction in the memo shared with our LPs. Most of the analysis in that memo—including a prediction that Paradigm would eventually invest in Succinct—matched today’s reality well.
In that memo, we briefly mentioned the necessity for Polyhedra to expand beyond the ZK bridge and consider future business plans because Polyhedra, particularly the team, still has a lot of potential. This is even more significant now that they have secured the $ZK ticker, which should not be limited to the ZK bridge.
(extracted from L2IV’s internal memo for Polyhedra)
…Third, we do think Polyhedra needs to start thinking about future business plans… we know, for sure, that there would be a moment when most of the ZK bridges, across all the major chains, have already been established. In that situation, they do need to think about the next chapters… There are other business opportunities, though they might be smaller and are a little bit far away from ZK bridge, that we feel Polyhedra should continue to explore…
Polyhedra moved much faster than what was originally expected, since LayerZero somehow “accelerated” the interoperability part of the modular blockchain. Now is a good time to review Polyhedra, given its recent token listing as well as the expected listings of Wormhole and Layerzero in the coming months.
We participated in two of Polyhedra's rounds. As investors, one of our responsibilities—which is also part of our fiduciary duties to our LPs—is to help Polyhedra grow and enter the next chapter.
Popular trends in the current market
Based on discussions with friends in exchanges and other VCs, many agree that this bull market will have a lot of attention on three topics other than ZK.
Modular Bitcoin infrastructure
Restaking and liquid restaking
AI + Crypto
We have made a number of early-stage investments in these three verticals—Bitcoin (Babylon, Nubit), Restaking (EigenLayer, Babylon), AI (Ritual, Lumino AI). Readers can learn more from three of our articles in this Substack:
We are actively investing in the space, and a few other investments are in process in these sectors as well.
Polyhedra and Bitcoin.
Our fund has been an active participant in exploring and investing in the Bitcoin ecosystem. In our key trends article, we expanded on our bullish support on the emerging Bitcoin ecosystem. Our research partner, Weikeng Chen, has personally contributed a lot of codes to BitVM and saw a lot of potential and practicality in enabling new programmability on Bitcoin.
Polyhedra has been working on Bitcoin since late last year, before this trend was aware by the public. Timing is very important here, as Bitcoin halving is soon.
They published the Medium article, “Introducing the Bitcoin Messaging Protocol with zkBridge”, on Dec 12, 2023.
They announced partnership with a large number of Bitcoin layer-2 projects on Jan 14, 2024. See “Polyhedra Network: Building the Largest Interoperable Bitcoin Ecosystem with zkBridge”.
Especially, Bitcoin + restaking.
They announced with EigenLayer on Bitcoin zkBridge using restaking, “Empowering Bitcoin zkBridge with EigenLayer Restaking and Dual Staking”, on Jan 25, 2024.
This month, Mar 22, 2024, Polyhedra published this Bitcoin research article that we collaborated with them.
Polyhedra has kick-started the restaking collaboration by adding a new partner, Renzo. See this article published today, “zkBridge, EigenLayer Dual-Staking, and Renzo”.
We want to mention that Renzo just flipped Puffer Finance (502k vs. 371k in restaked ETH) and became the 2nd liquid restaking token (LRT) protocol after ether.fi (listed). See this Dune dashboard by Hashed.
L2IV's Conviction in Polyhedra
In our industry, we only have a handful of projects that come out from top universities. We have invested in a few (EigenLayer, Polyhedra, Babylon, Nubit), and these teams demonstrated their potential and capability.
We haven't found another team among ZK, eastern or western, that has cumulatively made so much academic contribution to modern ZK proofs. Three of the cofounders were Ph.D. students in EECS at UC Berkeley.
This is why we feel that the ZK bridge is very likely just a starting point for Polyhedra, and we will help the team go further.
Find L2IV at l2iterative.com and on Twitter @l2iterative
Disclaimer: This content is provided for informational purposes only and should not be relied upon as legal, business, investment, or tax advice. You should consult your own advisors as to those matters. References to any securities or digital assets are for illustrative purposes only, and do not constitute an investment recommendation or offer to provide investment advisory services.