Aztec Network
May 19th, 2019
•
## min read

Creating, Settling & Streaming Confidential Assets

This is the fourth part, we dive into the creation and management of confidential assets, a breakthrough in private transactions.

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Written by
Joe Andrews
Edited by

This article is in English, you can read a Mandarin(中文) translation here.

This series is split into 4 parts:

  • Part 1 — An introduction to AZTEC
  • Part 2 — Deploying AZTEC on Ganache
  • Part 3 — Constructing Proofs, Signing Flows and Key Management
  • Part 4 — Creating, Settling, & Streaming Confidential Assets

The demo dApp implements a confidential loan on Ethereum. The loan provides for the following functionality :

  1. A borrower can create a loan request with a confidential loan notional.
  2. A lender can request access to see the value of the loan notional.
  3. A lender can settle a loan request by transferring the notional to the borrower, the transfer notional should be confidential. The blockchain should verify that the notional amount and the settlement amount are equal.
  4. The borrower should be able to pay interest into an account that the lender can withdraw from. Any payments to the interest account should be confidential.
  5. The lender should be able to withdraw interest from the interest account as it accrues up to the last block time. The blockchain should verify the amount of interest the lender is withdrawing is correct, and the withdraw amount and the balance of the account should remain confidential.
  6. The lender should be able to mark a loan as defaulting if the interest account does not contain sufficient interest. The blockchain should validate that this is the case whilst keeping the total interest payed, the account balance and the loan’s notional confidential.
  7. The borrower should be able to repay the loan and any outstanding accrued interest at maturity. Both the interest and the notional repayment should remain confidential.

To build the above functionality, the dApp will combine two confidential assets, and the following proofs: Mint Proof, Join Split Proof, Bilateral Swap Proof, Dividend Proof, Private Range Proof.

Creating the Loan ZkAsset

As the loan is intended to be a fully private asset without a public equivalent, it will inherit from the reference EIP1724ZkAssetMintable.sol contract. In this case, the constructor is overridden with to create a fully private asset.

pragma solidity >= 0.5.0 <0.7.0;import "@aztec/protocol/contracts/ERC1724/ZkAssetMintable.sol";import "@aztec/protocol/contracts/libs/NoteUtils.sol";import "@aztec/protocol/contracts/interfaces/IZkAsset.sol";contract Loan is ZkAssetMintable {  using NoteUtils for bytes;constructor(    address _aceAddress,   ) public ZkAssetMintable(_aceAddress, address(0), 1, true, false)          {  } }

All AZTEC toolkits perform logical checks on note values. To perform a logical check, a note must first be created. In order for the loan’s notional to be confidential, it must be represented as a note in the loan’s note registry. As the initial supply of any note registry is zero, in a private asset the Mint Proof must be used to adjust the total supply and create new notes.

Step 1: Constructing the Mint Proof

Firstly, construct a proof using aztec.js.

const {   proofData,} = aztec.proof.mint.encodeMintTransaction({        newTotalMinted: newTotalNote,        oldTotalMinted: oldTotalNote,        adjustedNotes: [loanNotionalNote],        senderAddress: loanDappContract.address,});

Step 2

This proof can now be used to Mint the new notes inside the loan’s note registry. Only the owner of the note registry is permitted to call the confidentialMintmethod. In this case, a smart contract called the constructor of the loan ZkAsset. That contract is the owner of the ZkAsset note registry. This permits it to validate a supplied proof and process the resultant transfer instructions inside ACE.

Loan(loanId).confidentialMint(MINT_PROOF, bytes(_proofData));

The Settlement ZkAsset

The primary functions of the loan (primary settlement, interest payments and repayment) require value transfer. As this value transfer is required to be confidential, the settlement asset also needs to be a ZkAsset that implements EIP1724. The ZkAsset represents the currency the loan counter-parties will use to transact and is redeemable for a public ERC20 token e.g (DAI, CUSD).

Creating the settlement asset requires initialising the ZkAsset constructor with different parameters to the Loan ZkAsset. This tells ACE that this asset is linked to a public ERC20 token and the supply is not adjustable.

pragma solidity >= 0.5.0 <0.7.0;import "@aztec/protocol/contracts/ERC1724/ZkAsset.sol";contract ZKERC20 is ZkAsset {constructor(    address _aceAddress,    address _erc20Address   ) public ZkAsset(_aceAddress, address(_erc20Address), 1, false, true) {  }}

Creating an AZTEC note in the note registry of the Settlement ZkAsset requires a transfer of sufficient ERC20 tokens into ACE equal to the notes value multiplied by a scaling factor. These tokens are owned by ACE in return for creating the desired note.

It is worth noting that creating notes of a ZkAsset with a linked public token has limited confidentiality. An observer of the blockchain can deduce the notes created in any given transaction, sum to the amount of ERC20 consumed. As such it is recommended to create multiple notes in one transaction, in order to help obfuscate the value of individual notes.

If full confidentiality is required for the settlement asset, a private ZkAsset with no public equivalent should be used. Here, AZTEC notes are issued on receipt of funds via bank transfer. The notes are still 1–1 backed with fiat, similar to a stable coin, but the note creation transaction preserves confidentiality as no public ERC20 tokens are consumed. Carbon Money are working on an implementation of this.

This demo assumes a fully private asset is not required and consuming ERC20 tokens is an acceptable solution.

Step 1:

The ACE contract is approved to spend ERC20 tokens on behalf of the token owner.

await settlementToken.approve(aceContract.address, value);

Step 2: Creating the proof

const {      proofData,      expectedOutput} = aztec.proof.joinSplit.encodeJoinSplitTransaction({    inputNotes: [],    outputNotes: [Note1, Note2], // note values sum to kPublic    senderAddress: account.address,    inputNoteOwners: [],    publicOwner: account.address,    kPublic: -value,     validatorAddress: joinSplitContract.address, });

A particular variant of the Join Split proof is required when interacting with public value. The proof has no inputNotes, the input is a public value of ERC20 represented by kPublic. This value is negative as it represents value being converted into an AZTEC note form, (if value was redeemed from note form, the value would be positive). The Join Split proof is validation that the sum of the output notes is equal to the value of kPublic.

The proof construction also requires the Ethereum addresses of the publicOwner (the owner of the tokens spent in this transaction) and the senderAddress (the account that will send this transaction to the ACE for validation), to be set.

Step 3: Approving ACE to spend Tokens

Any proof that results in the transfer of public value has to be first approved by the owner of the public tokens for it to be valid. This allows ACE to transfer the value of the tokens consumed in the proof and acts as an additional security measure when dealing with ERC20s.

await ACE.publicApprove(zkAsset.address, hashProof, kPublic, {      from: accounts[0],});

Step 4: Relaying the transaction

When relaying proofs to ACE, the sender address specified in the proof must match the msg.sender of the account that calls ACE.validateProof().This prevents malicious actors snooping on the transaction pool from front running the execution of this proof.

(bytes memory _proofOutputs) = ACE.validateProof(JOIN_SPLIT_PROOF, address(this), _proofData);

Step 5: Processing Transfer Instructions

Successful proof validation will return an array of proof outputs. These proof outputs contain the state update instructions that allow a dApp to update a note registry.

_loanVariables.settlementToken.confidentialTransferFrom(JOIN_SPLIT_PROOF, _proof2Outputs.get(0));

Settling the loan

Once the loan ZkAsset and the settlement ZkAsset have been created, and each note registry populated with the initial notes, the loan is prepared for settlement. The diagram below shows the state of our dApp at this point and the swap that is required for settlement

The left hand side represents the loan ownership register (currently owned by the borrower) and the right hand side represent all of the notes that make up the lenders balance of the settlement asset.

To settle the loan the Bilateral Swap Proof is required. The borrower wishes to receive a note of the settlement ZkAsset equal to the loans notional multiplied by the loan price. The lender wishes to receive a note that represents 100% of the loan’s ownership register, in this case the notional note. Later on, this note will be used to claim interest and repayment at maturity. The ownership note can also be split and transferred should the lender wish to trade the loan.

Step 1 : Approving the settlement contract to spend notes

As the settlement transaction needs to be atomic, the transaction will be orchestrated by a smart contract. After a proof has been validated, ACE will only process the state updates (create or destroy notes) if the notes destroyed in a transaction have first been approved for spending by the note owner. The validation and processing of the Bilateral Swap proof must occur in an atomic transaction, otherwise, if one side of a transaction fails to approve the notes for spending, there is a chance one party will not receive their required ask in the swap. It is up to the dApp developer to ensure the correct permission logic is in place when calling functions within the AZTEC system. ACE will only validate the mathematical logic of a transaction, but does not know if a transaction should take place. In the case of loan settlement, the dApp should validate that the input notes have been approved by both the buyer and the seller and they are agree to the transfer.

In order for the transaction to process correctly, both the borrower and the lender need to approve the settlement contract to spend their respective notes.

const settlementSignature = signNote(   zkSettlementAsset.address,   settlementNoteHash,   loanId,   lender.privateKey);await zkSettlementAsset.confidentialApprove(   settlementNoteHash,   loanId,   true,   settlementSignature,    {      from: lender.address,  });

Step 2: Constructing the proof

const {     proofData,} = aztec.proof.bilateralSwap.encodeBilateralSwapTransaction({        inputNotes: [takerBid, takerAsk],        outputNotes: [makerAsk, makerBid],        senderAddress: loanId,});

The proof requires 4 notes, and will validate the following logical statements:

  1. The takerBid note is equal to the makerAsk note.
  2. The takerAsk note is equal to the makerBid note.

Step 3: Relaying the Transaction and Updating State

When relaying proofs to ACE, the sender address specified in the proof must match the msg.sender of the account that calls ACE.validateProof().This prevents malicious actors snooping on the transaction pool from front running the execution of this proof.

Once validated, the proof outputs can be used to update the retrospective note registries. This will destroy the takerBid note and create the makerAsk note in the settlement ZkAsset note registry and destroy the makerBid note and create the takerAsk note in the loan ZkAsset note registry.

(bytes memory _proofOutputs) = ACE.validateProof(BILATERAL_SWAP_PROOF, address(this), _proofData);(bytes memory _loanProofOutputs) = _proofOutputs.get(0);(bytes memory _settlementProofOutputs) = _proofOutputs.get(1);settlementZkAsset.confidentialTransferFrom(BILATERAL_SWAP_PROOF, _settlementProofOutputs);loanZkAsset.confidentialTransferFrom(BILATERAL_SWAP_PROOF, _loanProofOutputs);

Thats it! The loan has been settled and all balances remain confidential.

Interest Streaming

AZTEC notes can be owned by smart contracts. This makes it is possible to construct complicated financial instruments using AZTEC. For the loan, we wish to create a system in which the lender can withdraw interest from an account as it accrues. Should the interest account contain insufficient collateral the lender should be able to mark the loan as defaulting and the smart contract transfer any security used as collateral to the lender.

To make interest streaming non-interactive from the borrowers point of view, the blockchain must validate the interest the lender is trying to withdraw is not greater than the currently accrued interest, and use this validation to ensure the correct amount of interest is then withdrawn. This flow is possible by combing the Dividend Proof and the Join Split proof. The Dividend Proof allows us to prove that one note is a ratio of another note plus a residual (to account for the quirks of solidity arithmetic).

Note1 * a = Note2 * b + Residual

If Note2 is set as the withdrawal note, the proof creator is incentivised to pick values of a and b such that the residual note is minimised. This enables Note2 to be expressed as a ratio of Note1 .

Note1 = Note2 * b/a

To apply this to the loan, a ratio must be found that expresses the AccruedInterest with respect to another note supplied by the smart contract in this case the notional.

This is possible with a little algebra:

Interest Steaming with the Dividend Proof

As a smart contract can set the values of ElapsedTime, InterestRate and InterestPeriod. The lender will only be able to construct a proof that will satisfy equation (1) if the value of AccruedInterest picked is correct up to the last block time.

If the Dividend Proof succeeds, the Accrued interest note that is used can be trusted and if supplied inside a subsequent valid Join Split proof, can be used to split the CurrentInterestBalance into the AccruedInterest plus a remainder note.

This process can be repeated for each block allowing the lender to withdraw interest as it accrues by the second. In each case, the blockchain will validate this correctness of the withdrawal.

#moneystreaming

Programatic Default — No Lawyers

Historically, should a borrower fail to pay interest on a loan or fail to pay back the loan at repayment, the lender would have to go through the courts to claim any collateral in lieu of repayment. Interest streaming allows the blockchain to validate a state of default and programatically transfer any collateral to the lender without the need for any arbitration, lawyers or courts.

To achieve this, two proofs are combined the Dividend Proof as used before to validate the currently accrued interest, and the Private Range Proof, to validate that the accrued interest is greater than the available balance inside the interest account.

Putting it all together — DEMO

https://medium.com/media/828f2ee46c391382128652e0eee2b481/href

The Loan dApp is available on github and can be cloned here.

Thanks for reading Part 4 of this series!

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Aztec Network
Aztec Network
15 Oct
•
xx min read

Post-Quantum Aztec

All blockchains today – L1s, L2s, and shielded pools – make use of elliptic curves somewhere in their stack.

Elliptic curves are used in all sorts of places: signing transactions, validator attestations, data availability (such as blobs), zk-snarks, secret sharing, encryption, etc.

No cryptocurrency project today is 100% quantum-proof.

Nobody has a reliable date for when a quantum computer will break the elliptic-curve cryptography we use today, but we know it’s coming.

For a privacy network, some of the work cannot wait for that uncertainty to resolve. An attacker could collect encrypted data today and keep it until they have the means to decrypt it. This is the so-called “Harvest now; decrypt later” attack. Replacing an encryption scheme ten years from now would not protect the data an attacker already harvested under a classical encryption scheme.

Aztec is already quantum resistant against this type of attack. It was designed from the ground up to allow users to bunker-proof their accounts and data against quantum computers.

However, there is work to be done to make Aztec fully quantum secure and able to function with full privacy in the post-quantum world. 

Our roadmap to expand our quantum security has two targets:

  • February 2027: Hardened libraries and better off-the-shelf contract development patterns that protect against harvest-now-decrypt-later attacks
  • 2030: a full post-quantum migration.

The first requires changes to how applications handle private data. The second reaches into the proving system, account authentication, key derivation, validator signatures and Ethereum settlement. Understanding why these need different schedules requires getting into the cryptography.

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The risk of changing cryptography

Years of hard-won experience have taught us that the greatest risk to a network like Aztec is implementation bugs. Our AI audit harness has found critical vulnerabilities, including ones that months of expert human internal and external audits didn’t find. These have been patched in the upcoming v6 Aztec Network release. We have spent the past 18 months hardening our software and cryptography. That work has to continue while we develop their replacements.

AI also changes cryptanalysis. For example, the attack on HAWK (a post-quantum signature scheme) exploited structure specific to that signature scheme and reduced its security enough to end its candidacy for standardization. That is a reason to examine the assumptions and structure of each scheme with care.

Rushing headfirst into new cryptography that has not faced enough scrutiny would expose users to immediate risks, greater than the speculative risks of quantum computers. The Foundation has finite resources, and time spent on the post-quantum migration is time we have to balance against securing the software users depend on today.

Our default approach to changing cryptography is conservative. Any changes to our protocols must be justified, subjected to extraordinary cryptanalysis and have formally-verified implementations.

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Making Aztec post-quantum

To make Aztec post-quantum requires several pieces of cryptography. Aztec has an application layer (smart contracts), the Aztec protocol layer, and it settles on Ethereum itself. All three have responsibilities with respect to post-quantum security.

Protocol layer changes required:

1. Proving System

  • A post-quantum zero-knowledge proving system. Our unique requirements as a decentralized programmable privacy protocol present unique challenges, explained later.

2. Addresses & Keys

  • Changes to Aztec addresses and public keys, which are all elliptic curve points.
  • (These current addresses & keys can be used in a quantum-safe way today, though).
  1. Validator Keys & Signatures:
  • post-quantum digital signature scheme for Aztec’s decentralised validators’ attestations. 
  1. Adoption of the required Ethereum changes outlined below.

Application layer changes required:

  1. Post-quantum digital signature schemes.
  2. Post-quantum KEMs (secret sharing mechanisms).
  3. Post-quantum public-key encryption.

Ethereum changes required:

  1. DA
  • A DA layer that doesn’t use BLS12-381 KZG commitments.
  1. Verification Primitives
  • Cheap post-quantum snark verification primitives, as an alternative to the currently cheap de facto BN254 EVM precompiles.
  1. Public Keys & Signatures
  • Ethereum EoA public keys and signatures
  • Ethereum’s BLS keys.

The latter application layer requirements are not on Ethereum’s post-quantum roadmap as they’re a unique requirement of privacy protocols like Aztec and ZCash.

Notice that the bulk of the changes required for user privacy are dictated by the choices of Aztec smart contract developers at the application layer. Apps can adopt post-quantum encryption and signature schemes today on Aztec, and different Aztec smart contract developers can freely explore differing approaches as the state of the art in post-quantum advances.

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Protecting private data now

If and when quantum computers arrive, Aztec is already (uniquely for privacy protocols) protected in two key categories because of our existing design choices.

  1. A post-quantum proof system can securely use historical state created today 
  2. By default, historical state (including encrypted logs) is not vulnerable to “harvest-now-decrypt-later” attacks

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“Traditional” messaging in privacy protocols 

If I send you private tokens, there’s no onchain public balance update for you to see or query. Private state is stored in notes, so I need to tell you about the existence and contents of your new note for you to be able to use it.

A common solution is for me to publish an encrypted message to a public bulletin board that your wallet can find and decrypt. ZCash pioneered this approach.

Elliptic curve key exchange protocols are well-suited to this, because the amount of data I need to publish to convey “this is for you” and “here’s the ephemeral key you’ll need to decrypt this message” is a single ECDH ephemeral public key; an elliptic curve point; a tiny 32 bytes of info. We like this small communication overhead, because less data means faster tx throughput and cheaper DA costs passed on to users.

But elliptic-curve key exchanges can create a harvest-now-decrypt-later risk. The discrete log of such an ephemeral public key will one day be solvable by a quantum adversary. They could derive all ephemeral secret keys of all messages in the bulletin board. They’d then be able to brute-force combine the resulting list of ephemeral secret keys with a list of all known users’ viewing public keys to effectively derive all decryption keys on the network, to then decrypt all encrypted messages. They’d learn the contents of the note I sent you: the amount and that it belongs to you.

There are a few classical (pre-quantum) solutions to this. They follow from the observation that if an attacker doesn’t know one of: your public key or the ephemeral public key, then they won’t have enough information to decrypt any of your encrypted messages! Wallets are beginning to adopt the following:

  1. Don’t publicly share your public keys.
  • This is easier said than done. It defies the initial design intentions of public key cryptography. After all, you’d need to give me your public key for me to send you money! What if you share it with a dishonest counterparty, or an honest counterparty whose data leaks accidentally? This leads to another protection:
  1. Use a new public key for every new transaction.
  • That way, you stem any leakage if any of those public keys does leak. Some wallets of some privacy protocols already do this.
  1. Don’t broadcast any ephemeral public keys to a public bulletin board.
  • If ephemeral public keys aren’t seen by a quantum adversary, they can’t decrypt your messages, regardless of whether your address is public. Share this data through some private communication channel instead.

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Aztec Public Keys are hashed

Intentionally, most of the public keys in the Aztec protocol are hashed to reduce their leakage to a future post-quantum adversary. The public keys are not even exposed to Aztec smart contracts (which could be malicious).

(Private smart contract protocols even have a niche “harvest now; link later” attack to protect against, whereby a quantum adversary could link all your notes and nullifiers together to reconstruct your entire tx graph. Hashing the nullifier public key resolves this).

‍

Aztec is flexible, today

The Aztec Protocol is agnostic to the way in which users and applications (smart contracts) share private information between each other. It’s a beautifully flexible protocol because we knew times would change. Smart contract developers can adopt the above conventions today, and indeed many are doing so.

Aztec smart contracts can emit arbitrary bytes of data as “private logs”. These private logs are the intended delivery mechanism for sending encrypted notes. It’s up to smart contract developers how they populate those logs. I.e. they can choose:

  • Whether to use these private logs at all;
  • How to get the recipient’s attention;
  • How to convey the decryption key;
  • Which encryption scheme to use.

Aztec also supports offchain note delivery, which gives applications another secure option. A sender delivers the message through an off-chain side channel that is not visible to harvest-now-decrypt-later attackers.

All this flexibility in today’s Aztec Protocol enables Aztec smart contract developers to explore the tradeoff space in a way that best serves their users and use cases. Choices will need to balance: proving speed; DA costs; discovery of pertinent notes; post-quantum threats.

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Better libraries

Of course, most smart contract developers don’t want to think about such things, which is why the Aztec ecosystem has smart contract libraries with off-the-shelf solutions.

Our early 2027 work will focus on hardening these libraries and giving Aztec developers better patterns for protecting their users’ private data, with clear requirements for delivery and secret establishment.

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Post-quantum secret sharing

A more comforting solution to post-quantum worries would be for Aztec smart contracts to instead adopt post-quantum secret sharing and encryption schemes. 

We’re researching the best approaches and working on some tidy libraries. The good thing is, the agnosticism of the Aztec Protocol means multiple libraries for differing post-quantum secret sharing schemes can be written and adopted by different applications on Aztec.

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Constrained Delivery

In most other privacy protocols, the construction of an encrypted note is not constrained by any circuit.

For example, if I send you ZCash tokens, the ‘transfer’ function does not constrain that I have correctly encrypted your note, nor that I have attached the correct ephemeral public key that would enable you to discover and decrypt your encrypted note. I could technically broadcast garbage and you wouldn’t receive your funds. That’s arguably fine in a “simple” transfer protocol. It’s not in my interest to corrupt the encrypted notes that I create for you. After all, you can just claim I didn’t pay you until you do receive a valid and decryptable message. 

But when you generalise beyond simple transfers to private smart contracts, there are use cases whereby a sender might not be incentivised to deliver valid data to a recipient. The sender might actually prefer to corrupt a recipient’s data. Imagine a private swap. The contract should not complete the trade if one party receives a commitment to a note whose contents they cannot recover.

In such cases, the private functions (circuits) need to constrain that a recipient will be capable of discovering and decrypting a sender’s encrypted messages. Aztec’s smart contract libraries have rails for this so-called “constrained delivery”. If a use case assumes distrust between sender and recipient, the smart contract developer can enforce their correct adherence to the rules. The protocol then constrains that all private logs emitted by smart contracts are guaranteed to be broadcast – without tampering – to Ethereum blobs.

With this in mind, the constraints required to support post-quantum encryption then become a very important consideration. We’ll need post-quantum libraries that are efficient to prove.

Key and ciphertext sizes matter, but so does the cost of proving the key exchange, encryption and associated checks. A scheme can be fast as native software and expensive inside a circuit.

MIKE, published on 6 October, illustrates why this remains an active research question. It is an isogeny-based non-interactive key-exchange proposal. Its authors report 80-byte public keys and shared-secret computation, including key validation, in 4.9 milliseconds on a 3.3 GHz AMD CPU at their claimed NIST level 1.

Compact keys are attractive for note delivery. We still need to understand its circuit costs and give its security assumptions time to face scrutiny. Those native timings cannot tell us whether it is the right choice for Aztec.

The encryption and proving-system decisions therefore affect each other. Choosing encryption first and discovering that it is prohibitively expensive in the chosen prover would leave us rebuilding one of them.

Choosing the encryption scheme we will prove inside future post-quantum circuits is a separate, later milestone. Applications that need the contract itself to guarantee delivery impose harder requirements on that choice.

‍

Post-Quantum Proving

Ok, so Aztec provides flexibility for good post-quantum privacy today. And we have plans to roll out even better post-quantum libraries.

But what about the proving system? A post-quantum adversary might be able to forge proofs. Thankfully we have some more time to choose a post-quantum proving system.

Aztec has several proving system requirements that other projects aren’t encumbered by (due to our commitment to both privacy, decentralisation and programmability), which we’ll elaborate on.

  • Low memory and CPU requirements: proving must be possible on a phone, in the browser.
  • Actual zero-knowledge!
  • Fast client-side recursion.
  • Small client-side proof sizes.
  • Cheap L1 verification.
  • Simple, maintainable, and secure.

Common benchmarks for proving system performance don’t take into consideration all these requirements. Fast client-side recursion in particular is often overlooked.

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The problem with recursion

Aztec uses CHONK, an elliptic-curve and pairing-based proving system built around the requirements of private smart contracts. Users generate proofs on their own devices, and a transaction can involve several private contract calls. Recursion lets us combine those calls into a proof of the transaction without requiring the browser to handle the entire computation as one enormous circuit. CHONK’s design puts low memory use and recursive composition at its centre.

There are tradeoffs you can make to get a faster prover. Some give the verifier more work. A custom “precompile” circuit for an expensive operation can save the prover from executing that operation through thousands of VM instructions, but introduces additional commitments and checks that increases Verifier complexity.

The problem is that, in the recursive setting, your verifier is in your prover. The next proof has to establish that the verifier accepted the previous proof.

I have lost count of the conversations about new prover technology where recursion gets a handwave and a “we’ll deal with it later.” It is a complex, messy problem that is easy to postpone until you need users to generate private transaction proofs in a browser.

Some alternative designs might execute an entire function stack within a single VM instance. That might work for some bounded stack depth. But snarks are gaining traction in web2 too (see zkPassport for example). Bridging between chains also often requires snarks. Privacy protocols should be able to verify traditional snarks for as long as we remain in a pre-quantum world. 

Zero knowledge introduces another set of costs. I have heard the same assurances that adding it will be easy and will not affect performance. From personal experience, such claims often disintegrate on contact with reality.

We thought adding zero knowledge to CHONK would be easy. It took us six months and a re-architecture of our recursive proving stack. Modern proof systems have such complexity that throwing randomness into the execution trace and calling it a day almost never works. Adding ZK typically increases proof size and verifier work, which then increases the cost of recursion.

The result is that the real cost of recursion in a production proving system, with all of the edge-cases and exceptions and little additions that pile up, is never as fast as the initial proof-of-concept claims. For Aztec that is a problem because recursion is essential and not an afterthought - we won’t commit to a proving system that can’t meet our extremely tight recursion requirements.

Luckily there are some candidates, and the Ethereum Foundation is doing trailblazing work as one of the few teams that has started to take this problem seriously.

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Getting larger proofs through the network

Proof size matters because Aztec transactions travel through a peer-to-peer network. Every node that receives and forwards a proof pays its bandwidth cost. Aztec’s 20kb proofs are “ok”. If it ever becomes a bottleneck we can make them smaller with little effort because we use elliptic curves.

Post-quantum proof systems (the fast ones), on the other hand, have proofs of ~300KB, which is not ok.

Worse, there are zero post-quantum proving systems whose proofs are small enough to gossip across a p2p network whilst achieving acceptable transaction throughput. There are fundamental constraints which mean this is not likely to change!

Fast recursion offers another path. A node could receive two transaction proofs, produce one proof that establishes the validity of both, and forward the aggregate. Other nodes could repeat the process. Transaction data would still have to travel through the network, but the proof overhead could shrink across a batch.

Ethereum’s post-quantum research faces a related problem. Its proposed hash-based validator signatures lack BLS’s cheap native aggregation, so leanVM supplies a proof that many signatures pass verification. The draft EIP-8292 assigns that proving work to aggregators with suitable hardware. Their longer-term roadmap requires full virtual-machine proof aggregations which presents an extremely similar problem to ours.

For the Aztec approach to work on ordinary nodes, aggregation needs to be cheap. My working estimate is that two-to-one aggregation in roughly 20–100 milliseconds on a modern CPU could make it practical. 

Nodes receive different transactions at different times, so they will duplicate work. An attacker may try to exploit that duplication. We need to establish how many aggregations one malicious transaction can induce and what happens to throughput under that load.

This problem is currently under-explored and poorly parametrised and substantial work needs to occur before a definitive solution can be decided on.

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Which proving systems look promising?

The main candidates are hash-based systems over binary fields and small prime fields, lattice-based systems, and proposals that combine both prime-field and binary-field representations.

The Flock paper gives a good example of the progress in binary-field proving. Its authors report proving 660,000 BLAKE3 hashes per second on an M4 mac on ten cores. 

These are impressive numbers. Hashing is a major part of verifying hash-based proofs, so cheap hashing is good for recursion.

However, binary field systems are weak with regards to integer multiplication. Trustless access to Web2 data is one of the biggest untapped capabilities of blockchain. Private applications should be able to use passport signatures, credit credentials, TLS-based data proofs and signed web tokens without publishing the underlying information. That means dealing with ugly Web2 cryptography: RSA, large-field elliptic curves and integer arithmetic.

Binary-field arithmetic does not behave like integer arithmetic. In particular, integer addition has carries, and multiplication needs a representation and a circuit that handles them. A BLAKE3 benchmark tells us little about the cost of proving a 4096-bit RSA verification. We need to measure the operations our applications will use.

That is what makes hybrid approaches interesting to me: using one commitment both in a binary representation and a prime field representation depending on context. This is an active area of research with limited existing published work, which highlights how rapidly evolving this space is.

Lattice-based proving deserves serious attention too. The Jolt team’s September release replaced the elliptic-curve commitment scheme Dory with Akita, based on Module-SIS. The authors reported faster proving and verification and proofs below 100 KB. Their announcement also described zero knowledge as forthcoming, so those figures do not settle our comparison.

Lattice commitments retain algebraic structure that could be useful for the kinds of composition we rely on. That makes them attractive candidates to investigate, although translating CHONK’s techniques would require work. The field size is a design choice we need to evaluate within each construction; lattices do not impose one universal 128-bit-field requirement.

Much of the suspicion around lattice systems rests on vibes about whether the underlying structure is vulnerable to AI cryptoanalysis. There are good reasons to scrutinize a particular assumption, parameter set or reduction. “It uses lattices” does not supply that scrutiny.

Not all lattice crypto is equal. The fundamental short-integer-solution hardness assumption has had decades of cryptanalysis. Lattice crypto has a degraded reputation because some modern protocols layer on additional, weaker hardness assumptions that have shown to be broken by quantum adversaries. But there is no quantitative evidence to suspect the core harness assumptions of lattice crypto are vulnerable.

Either way, the rate of development gives me confidence that we will have good options. It also makes choosing a winner today premature. We need comparisons that include our applications, recursion, zero knowledge and security parameters together.

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Signatures

In Aztec transactions, digital signatures are private witnesses within private functions of smart contracts (zero-knowledge circuits), which helpfully means we don’t care so much about the size of an individual signature. This gives us more freedom than non-rollups e.g. Ethereum, where signature size directly contributes to their transaction size. This matters because post-quantum digital signatures are typically large.

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Baking Bad

Similar to other privacy protocols such as ZCash Sapling and Orchard, several Aztec keys are baked-into the preimage of an Aztec address. To enable ‘post-quantumification’ of the Aztec protocol, we’re exploring externalising those keys to a canonical keystore registry. An Aztec address would then cease to be an elliptic-curve public key, and instead would simply be a hash which serves as a lookup into this registry. The registry could store all manner of exotic post-quantum public keys for different use cases.

Hash functions belong in the migration too

Aztec uses Poseidon2 throughout the protocol. Poseidon2 is technically post-quantum secure. And while Poseidon2 is secure for our chosen domain, recent breaks over small-field Poseidon signal that we should move to a different hash function in the long-term.

We’re confident that Poseidon2 will remain practically secure for many years, but the writing is on the wall and it would not be wise to use this hash function in Aztec’s future post-quantum system. 

We will likely replace it with either Blake2s or Blake3. The Ethereum Foundation are also considering a canonical hash function for their post-quantum roadmap and we’ll more than likely follow their lead here. Binary-field proof systems can trivially handle BLAKE hashes so the need for Poseidon2 will have run its course.

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Why the roadmap extends to 2030

Our proposed selection milestones are:

  • March 2027: choose a post-quantum signature scheme.
  • July 2027: choose a post-quantum public-key encryption scheme, with constrained note delivery benchmarked in the leading proof systems.
  • November 2027: choose a post-quantum proving system.

The encryption milestone needs circuit measurements before we settle the proving-system choice. The proving-system decision needs working recursion and zero knowledge, alongside representative application workloads. These dates give us a sequence for answering those questions.

After selection, we need to replace the cryptography across the system. That includes addresses and key derivation, application-specific key checks inside the kernels, account authentication, validator authentication and the proof chain that ends on Ethereum. We also need to handle existing private state and give users and applications a migration path.

Ethereum supplies another dependency. Aztec’s final proof verification and blob commitments sit within Ethereum’s cryptographic infrastructure. A full post-quantum migration has to account for Ethereum’s upgrades as well as our own.

The roughly three years between the final selection milestone and end of year 2030 leave room for integration to expose problems that isolated benchmarks cannot. Development and integration of multiple novel post-quantum cryptographic primitives into Aztec will be neither simple nor fast. In addition, the entire tech stack will have to be formally verified due to the incredible threat that AI poses with regards to finding and exploiting bugs.

I think Q-day within four years is unlikely, and the roadmap is designed under the assumption that post-quantum work is not the sole focus and obsession of the Aztec Foundation. If there is evidence of faster progress in quantum hardware that would bring forward Q-day, we will be able to accelerate our roadmap by diverting resources to this project.

Developers will not have to wait for that full migration to make better choices about private data. The January work will provide hardened libraries and documented patterns to build against. A developer building a private application will be able to protect the data they create today to stand the test of time.

Aztec Network
Aztec Network
7 Aug
•
xx min read

Alpha V5 Proving System Vulnerability

Status

Core contributors identified a critical vulnerability affecting the V5 Alpha proving system on 27 July 2026 through internal AI-assisted auditing.

V5 remains Alpha software. Critical findings can arise during this phase, and the audit process exists to identify them before broader deployment. This finding places V5 funds, applications, and contract state at risk.

Treat funds and applications on V5 as exposed to a protocol-level failure until contributors complete incident response work and operators carry out the required network actions.

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What we are disclosing

An attacker may be able to exploit a flaw in the current V5 proving system by constructing a proof that passes verification for a transaction the network should reject. If accepted, that transaction could produce a state transition outside the rules V5 intends to enforce.

Contributors cannot determine whether anyone exploited the flaw before this finding. The affected system lacks the information needed to distinguish ordinary accepted transactions from transactions accepted through the flawed proving path. Historical chain activity cannot establish whether exploitation occurred or quantify its impact.

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Application safeguards

We expect application teams to prepare safeguards in the coming weeks.

Those safeguards may include changes to application controls, deployment procedures, user flows, and migration plans. We expect each team to assess its contracts and determine which protections fit its architecture and users.

We expect teams planning a V5 deployment to pause that work until contributors publish further guidance. We expect teams with live contracts to review their ability to limit user exposure, isolate affected functionality, and move users to fresh deployments if needed.

We expect applications that maintain administrative or emergency controls to assess whether those controls can reduce user risk during the incident timeframe.

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Next steps

Core contributors are working with operators, application teams, and bridge operators as applications add security guards around affected flows.

The findings from this incident will inform the V6 release, including circuit updates that prevent the network from accepting proofs tied to an affected proving system.

V5 launched as Alpha software, with V6 planned for later in 2026. Contributors will publish a security roadmap covering the remaining work and release path.

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Known vulnerability status

Reviewers have not identified other high-severity or critical V5 Alpha vulnerabilities at this time.

Internal and external human audits have completed, and contributors continue AI-assisted auditing. Alpha is the period for identifying faults before production deployment.

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Community
Community
4 Aug
•
xx min read

Dark Forest Aztec Game Goes Live

Dark Forest is a real-time strategy game played across a procedurally generated universe where most of the map is hidden. You cannot see rival players, their planets, or their fleets. You only know what you have explored. Everyone shares one universe, and nobody has the full picture.

In most onchain games, every position and every move is public, because the chain is public. Dark Forest used zero-knowledge proofs to break that assumption: players prove their moves are valid without revealing where those moves came from. The result is a game of hidden information running on a public network.

Dark Forest Aztec ports the original Dark Forest 0.6 to Aztec. It keeps the gameplay from the original and rebuilds the privacy layer on Aztec's programmable privacy.

A note before diving in: this is early, experimental software on Aztec Alpha V5. Treat it as an alpha and play accordingly.

The universe you cannot see

You start on a single home planet with almost the entire map dark. To find anything you mine the universe, running a client that explores coordinates and reveals what sits there: unclaimed planets, resources, and eventually the edges of other players' territory.

You are never handed a view of the board. You earn it one region at a time, and everyone else works under the same fog.

What is hidden on Aztec

Your home coordinates and your fleet movements are private state, expressed as first-class private notes on Aztec. Your location and where you send energy stay hidden, enforced in the contracts by zero-knowledge cryptography.

What sits onchain is a set of cryptographic commitments. Instead of storing every planet's full details in the open, the contracts store Poseidon2 hashes of entity state. When you make a move, your client supplies the full state, the contract checks it against the stored hash, applies the change under zero-knowledge constraints, and writes a new hash back. Full game state lives offchain and gets rebuilt from public logs by an indexer, which is what renders your map without exposing every player's position.

So you can prove you made a legal move from a planet you own without revealing where that planet is. Aztec applies the same principle to private payments and private contracts.

How you play

Four actions carry the game.

Explore. Your explorer sits in the bottom left. Set it running and it uncovers the map around you, surfacing planets, resources, and other players.

Send energy. Most planets produce energy. Click and drag from a planet you own toward a target to capture or weaken it.

Route silver. Asteroid fields produce silver. Move it to your planets and spend it on upgrades, or send it to a Spacetime Rip to convert it into score.

Hunt artifacts. Some planets hold artifacts. Your Gear ship discovers them. Once harvested, you deposit them on planets to boost stats.

Four stats drive most decisions.

Energy is the core resource. Planets generate it over time up to a capacity, and you spend it on everything: claiming planets, reinforcing your own, attacking rivals. Two details matter. Moves are taxed, so a flat percentage of a planet's total capacity burns every time you send energy, which discourages small frequent moves. And energy decays over distance, so send it too far and almost nothing arrives. A common rule of thumb is to let a planet fill to about 75%, then send it down to about 25%.

Defense reduces the damage incoming energy does when it lands. Higher-level planets often have lower defense, but they hold much more energy, so they still take more to capture. Defense matters most on front lines.

Range sets how far a planet can send energy. It governs how fast you expand and how efficiently you move energy inside your own empire, since shorter relative distances mean less decay. Good range also lets you strike deep into an opponent's territory.

Speed sets how quickly a move arrives. Usually secondary, though a fast strike can land before a rival reacts, and some playstyles reward capturing many nearby planets quickly.

Planets can also be upgraded with silver and enhanced with artifacts. Space types carry different multipliers, from mild Nebula to punishing Dead Space, so where a planet sits changes how it plays.

How scoring works

There is a scoreboard, and territory alone does not win it. This round scores two activities: discovering artifacts with your Gear ship, and withdrawing silver through Spacetime Rips.

Point values from the in-game help page:

  • Each unit of silver withdrawn: 1
  • Common artifact: 2,000
  • Rare: 10,000
  • Epic: 200,000
  • Legendary: 3,000,000
  • Mythic: 20,000,000

Silver accrues one point at a time. A single Mythic artifact is worth twenty million of them, so artifact hunting decides rounds and silver withdrawal sets your floor.

Silver has two competing uses. Spend it on upgrades and your planets get stronger, extending range and hardening defense. Withdraw it through a Spacetime Rip and it becomes scored points, but it is gone. Every unit is a choice between building the empire and banking points.

Upgrades tend to win early, since a stronger empire reaches more asteroid fields and finds more artifacts. Late in a round that calculation flips, because a planet you never use is worth less than points already scored.

Artifacts do both jobs at once. They score on discovery, and once deposited they boost a planet's stats, which makes the next expedition easier.

Why you explore

Nothing happens until you find something to act on. Your explorer turns dark space into planets you can capture, asteroid fields you can mine, and artifact-bearing planets you can raid. Sitting still means no new energy, no silver, no score.

Exploring also buys information. The map you have uncovered is an advantage nobody else holds. Knowing where high-level planets sit, which asteroid fields are unclaimed, and where space types shift lets you plan further ahead than someone still working through their starting region.

You find other players as a byproduct. There is no player list. You explore outward until your revealed region touches territory someone already owns: a planet in another player's colors, sitting where you were about to expand. Their home coordinates stay private, so you learn something narrow. Someone is here, roughly this direction, holding this much. You infer the rest, and you have no way of knowing whether they found you first.

What happens when you run into someone

You have three broad options.

Stay quiet and keep growing. Nothing forces you to engage. Keep exploring elsewhere, keep routing silver, keep upgrading. Your positions stay private, so silence costs you only time, which is what you want if they are stronger. The risk is that they are doing the same thing faster.

Fortify the border. If the contact sits somewhere you cannot lose, spend energy hardening the planets facing them. Defense is worth most where an attack will actually land. This keeps the option to fight without committing to one.

Attack. Send enough energy to overwhelm the target's defense and the planet becomes yours, along with its production and its position as a staging post. Higher-level planets are the prize and take proportionally more to crack.

Attacking costs more than energy. A move that lands tells your rival where you strike from, and that you are close enough to be worth answering. Retaliation can then come from directions you have not explored, launched from planets you cannot see.

Multiplayer in practice

Everyone plays one shared universe in real time. No turns, no lobbies. Energy regenerates whether you are watching or not, moves stay in flight while you sleep, and rivals expand while you are away from the screen.

Most strategy games let you watch a threat approach. Here you tend to see the consequences: a planet you owned this morning in someone else's colors, an incoming move you notice once it is already close.

That produces a particular kind of paranoia. You are trying to find everyone else while avoiding being found, and every expansion is a strategic bet that the space ahead is empty.

Information becomes tradeable, because it is scarce. Players compare notes, warn each other about aggressive neighbors, and agree who expands where, then break those agreements when the scoreboard makes it worth breaking.

Why it matters beyond the game

A fully onchain game where players cannot see each other's positions is hard to build, and building it well says something about the platform underneath.

Hidden state, private notes, and client-side proving are the same building blocks behind private applications across Aztec. Dark Forest is a way to watch them work.

Getting started

Dark Forest Aztec is playable now as an alpha. Expect a learning curve; the original was famous for it. DFArchon maintains onboarding material and a community for new players. Round One is live. The universe is dark, and everyone else is out there somewhere. Go find them, quietly.

Play Now

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Follow the Builders

DFArchon on X‍

Source and docs

Aztec Network
Aztec Network
22 Jul
•
xx min read

How Gas Works on Aztec

Gas on Aztec

Gas on Aztec is known as Fee Juice and is used to pay for transaction costs. This is the same as $ETH on Ethereum. Some apps will handle transaction costs for you under the hood, but if you are using a browser extension wallet, you will not be able to send transactions without it. Fee Juice can be obtained by bridging the $AZTEC token on Ethereum to the Aztec Network L2. This means that under the hood, all activity that happens on Aztec is underpinned by the $AZTEC token bridged into the network. Some bridges like Shield (by human.tech) handle this for you, allowing you to allocate a portion of your bridged transaction to convert into Fee Juice and land in your wallet automatically.

Public vs Private Assets

Assets and transactions on the Aztec Network can be either public or private. If you bridge publicly, your tokens will arrive as public, traceable tokens visible to all. Privately bridging, on the other hand, will give you private assets that are visible only to you. These assets can then be sent privately to another user or wallet without ever revealing who you are, what tokens were sent, how many, or who the recipient is.

Public vs Private Gas

Like tokens on the Aztec Network, Fee Juice (gas) can also be public or private. The reason for this is that even if what you are sending is private, the gas you spend to execute that transaction could still be visible if you are using public Fee Juice, potentially revealing transaction patterns and activity. Private Fee Juice keeps your entire transaction footprint hidden. When you send a private transaction, you can use private Fee Juice, and when you send a public transaction, you can use public Fee Juice, which means your transaction costs are always aligned with the type of transaction you're making.

Fee Juice in Apps

Aztec has native fee abstraction, which means apps could let you pay for transactions in any token you want, or cover your fees entirely. Apps like Nyx may choose to cover part or all of a user's transaction costs, or allow you to pay in tokens that are convenient for you. This means you will most likely never see Fee Juice in an app; instead, you'll pay in whatever makes sense for what you're doing, on your terms. Similarly, you might never even see an Aztec wallet at all, because the app itself becomes your interface that you connect to using your MetaMask wallet.

Fee Juice in Browser Wallets

If you're using a browser extension like Azguard, you'll manage Fee Juice directly in your wallet alongside your private and public balances, converting between tokens as needed to cover transaction costs.

When you bridge tokens in, you'll need enough Fee Juice to cover the cost of your first transaction, then you'll need to monitor how much Fee Juice you have available to make transactions. Browser wallets will allow you to send either publicly or privately to other users and will default to using either public or private Fee Juice depending on the type of transaction. Both private Fee Juice and public Fee Juice will appear by default in your token list.

Wrapping up

How you handle Fee Juice depends on where you're transacting: apps can abstract it away entirely and let you pay in any token, while a browser wallet like Azguard puts it in your hands to manage across public and private balances. Match your gas to your transaction, keep private activity private down to the fee, and you move on your terms.