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Dec 4th, 2021
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## min read

Confidential transactions have arrived, a dive into the AZTEC Protocol

Aztec is revolutionizing private transactions on the blockchain, and this is how we're doing it.

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Written by
Zac Williamson
Edited by

Transaction privacy is a fundamental requirement for many kinds of financial services, and the inability to provide this privacy has prevented Ethereum from providing compelling alternatives to traditional financial instruments. There are several blockchains and blockchain projects that use cryptographic techniques to provide this privacy, but this privacy is reserved for the ‘native’ cryptocurrency of the blockchain in question. This transaction privacy is not accessible for digital assets built on top of blockchain protocols. For example, I can’t code up a corporate bond smart contract on Ethereum, where ownership notionals are private.Well, until now, that is.

Maker on Twitter

Whoa. https://t.co/PY4IK0CiaY

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Show and tell: the peculiar case of confidential DAI

Here, take a look at this:

{
   "gamma": "0x20a92d2a4f0dd850314a745719dde20934db69cc8e9b5b84b5819e062d66bb7500",
   "sigma": "0x17d62693c0c9a356e2fd6b0ce877b78c6a1f8a7f195e9db4c0b68e0693d73b3600"
}

This curious jumble of characters is a form of DAI, the dollar-pegged stablecoin created by MakerDAO. But it looks a little odd, doesn’t it? This would normally just be an ethereum address, and a number representing how much DAI that ethereum address has. But this isn’t normal DAI.

You see, when I sent this transaction, my ethereum address (zac.creditmint.eth) became the owner of this DAI, but here’s the thing: nobody can figure out how much DAI I have. Unlike almost every other DAI holder in the world, my DAI balance is encrypted and represented in the form of zero-knowledge AZTEC notes. I can spend this DAI at will by sending some to a different address, but when I do nobody will be able to figure out how much of it I’m sending. For example, I sent a colleague some of my DAI in this transaction and good luck figuring out how much they have.

This is all quite new, and I’m so very excited to be showing this to you and the wider Ethereum community. We’ve been developing this for almost a year now, but we’ve held off on making any formal announcements because I wanted to show you that specific, peculiar, jumble of hexademical characters.

Because this isn’t some imagined technology that will one-day be implemented.

It doesn’t require modifications to the Ethereum protocol.

It is a working demonstration that is live on the Ethereum main-net today, and that AZTEC zero-knowledge note is a real note that encrypts real DAI.

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A breakdown of AZTEC confidential transactions

There are really two questions here: what is the AZTEC protocol and how does it work? I can only answer how by getting into the guts of elliptic curve cryptography, which is a topic for another blog article (you can read a formal description in our paper. For a lightning summary of how this thing works: it’s not a ZK-SNARK, it’s an algebraic zero-knowledge proof that utilizes Boneh-Boyen signatures to create a commitment scheme with a highly efficient range proof embedded into each commitment.

Right, well that’s cleared everything up then. So I’m going to focus on answering what the AZTEC protocol is. What is it doing when transactions are sent to it? To start with, we need to describe what we mean by ‘confidential transaction’.

A confidential transaction is a transfer of value between two or more entities, where the values being transferred are not visible to observers.

Confidential transactions have come in several forms, from ring signatures to ZK-SNARK circuits. Similar to ZCash, the AZTEC protocol uses the concept of encrypted ‘notes’ and join-split transactions.

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Encrypted Digital Assets and the AZTEC note

The AZTEC protocol does not represent ‘value’ like a traditional balance, which maps owners to how much they own. Instead, value is represented by notes. A note contains the following public information:

  • An AZTEC commitment: an encrypted representation of how much ‘value’ the note holds
  • An Ethereum address of the note’s owner

A note has the following private information

  • The value of the note
  • The note’s viewing key. Knowledge of the viewing key enables a person to decrypt the note (but not spend it)

One owner can have multiple notes. A digital asset that conforms to the AZTEC protocol will contain a note registry, which allows a smart contract to recover the public information of every unspent note that currently exists.

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How can AZTEC notes be spent?

An AZTEC note owner can ‘spend’ their notes in a join-split style confidential transaction. In this transaction, the note owner will destroy some unspent AZTEC notes they own. In their place, they will create a set of new notes. The sum of the values of the new notes must be equal to the sum of the values of the old notes, plus a public commitment (I’ll get to that in a bit, but for now let’s assume this is worth 0).

So imagine Alice has two AZTEC notes worth 100 tokens combined. If she wants to send Bob 20 tokens, Alice would create one or more notes owned by Bob, whose values sum to 20. She would then create one or more notes owned by her, the sum of which is 80 tokens.

She would then create an AZTEC zero-knowledge proof that proves this relationship in zero-knowledge (i.e. Alice does not reveal to anybody how much the notes are actually worth, just that the balancing relationship holds). The AZTEC token smart contract will then validate this zero-knowledge proof, destroy Alice’s input notes and then create the output notes in its note registry.

When Alice is creating Bob’s notes, she constructs note viewing keys that Bob will be able to identify, via a non-interactive secret-sharing protocol. Bob is dependent on Alice to act ‘trustfully’ in this regard and not provide viewing keys that can be decoded by observers. This is already implicitly required — after all Alice could broadcast to the world how much she is sending Bob if she did not want the transaction to be confidential.

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How is note ‘ownership’ defined?

Every confidential transaction also requires digital signatures — a signature is required for every input note, signed by the input note’s owner. The message of the signature is a hash of the zero-knowledge proof. This provides an implicit acceptance that the note owners are satisfied with the outcome of the confidential transaction, and want the transaction to be processed.

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How do we get value into AZTEC note form?

Confidentially transfering value is nice, but without a way of getting ‘value’ (let’s call this v) into the AZTEC cryptosystem it all seems a bit academic. This is done via that ‘public commitment’ in a confidential transaction. Assume that the AZTEC token is linked to a public ERC-20 token. If the AZTEC zero-knowledge proof requires a public commitment value v != 0 in order for the balancing equation to be correct, this means one of two things:

1. If v is negative, the output notes are worth -v more than the input notes

2. If v is positive, the input notes are worth v more than the output notes

If Alice issues a confidential transaction where v is negative, the AZTEC token smart contract will transfer -v public ERC-20 tokens from Alice to its own contract address. Effectively, the AZTEC token smart contract acts as a custodian of the ERC-20 tokens while they are in confidential note form. Naturally, if this token transfer is rejected (e.g. Alice doesn’t have enough tokens) then the transaction will be aborted.

If Alice issues a confidential transaction where v is positive, this represents a conversion from AZTEC notes into public ERC-20 tokens. The AZTEC token smart contract will transfer Alice v public ERC-20 tokens.

There’s one small caveat — the amount of tokens being transferred is actually v multiplied by a scaling factor. This is because the range of integers an AZTEC note supports is smaller than that of an ERC-20 token. Our proof of concept deployment to main-net supports numbers from 0 to about 1 million and our full implementation of the AZTEC protocol will support approximately 32-bit integers (more on that in a bit). ERC-20 token balances, on the other hand, are represented by 256-bit integers.

The scaling factor picked depends on the ERC-20 token being linked to. For our proof of concept confidential DAI deployment, an AZTEC note with value 1 is equal to 0.1 DAI.

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What is the cost of all of this?

The AZTEC protocol uses a bespoke commitment scheme that enables highly efficient range proofs. As a result, the amount of computation required by the verification smart contract is much smaller than one might expect. The overwhelming contributor to a confidential transaction’s gas costs is the elliptic curve arithmetic required to validate the AZTEC zero knowledge proof. It costs 3i + 4j elliptic curve scalar multiplications to validate a proof, where i is the number of input notes and j is the number of output notes. Each confidentialTransfer transaction also requires a single elliptic curve bilinear pariing comparison to verify.

The reason I’m using such odd wording is because the gas costs of these arithmetic operations is likely to go down in the future due to protocol upgrades implemented by geth and parity (EIP-1108). It currently costs about 900,000 gas to issue a confidential transaction that contains 4 notes (this is the total gas cost, not just the cost of validating the cryptogrpahy of a transaction). If/when EIP-1108 goes live, the gas costs will fall to about 200,000–300,000.

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What information can be gleaned from confidential transactions?

The AZTEC protocol has been something of a obsession of mine for the past 11 months and I wouldn’t be comfortable releasing this out into the wild without giving a full account of the protocol’s strengths and limitations, I believe that being up-front about this is important.

With that out of the way, any protocol that converts something public into something private will reveal information at the entry and exit points of the cryptosystem.

If you’re adding tokens into note form, an observer will know that the value of the output notes is at least the amount you’ve converted.

Similarly, after redeeming v tokens, an observer will know that the remaining AZTEC notes are worth v less than the input notes.

These problems can be ameliorated by combining public conversions with additional AZTEC notes. For example, imagine Bob has a note worth 100 tokens that he wants to convert into public token form. Instead of just issuing a conversion, Bob should add additional input notes into his transaction and also generate some output notes, even if the extra input and output notes are worth 0. This will prevent an observer from figuring out how much of Bob’s confidential holdings he has converted, even if he has converted all of it and is left with a pile of notes worth nothing.

AZTEC notes have ‘owners’ defined by Ethereum addresses. On the surface, note ownership is not anonymous (e.g. people can see my ethereum address has a zero-knowledge DAI note); the AZTEC protocol includes a Monero-style stealth-address protocol to derive Ethereum addresses that are single-use and cannot be linked to any other Ethereum address (e.g. if you have an AZTEC wallet, I can ‘send’ a note to an Ethereum address you control, but nobody but you and me will know this is the case). The protocol supports both stealth addresses (which require a specific wallet to work; you need two public/private key pairs so a regular Ethereum account won’t work) and regular Ethereum addresses (which are not anonymous — if you own a note everybody will be able to see that).

The more users of a dual public/confidential asset, the greater the privacy provided. For example, when testing our main-net deployment, I converted 50 DAI into AZTEC notes and sent a bunch to my colleagues. Obviously, the sum of all the notes is 50 DAI so a single note can’t encrypt very much. Now imagine that somebody else created 1000 DAI worth of confidential notes, and we split and merged a few of our notes — it would be impossible to identify how much DAI any of these notes had, other than they would have 1050 DAI as a maximum.

To reduce this to extremes — if I converted 10 DAI into a single AZTEC note, this gives no privacy at all. The ability to create notes worth zero is important to maximize privacy — if you were going to convert 10 DAI and wanted a single note for ease-of-use, you should also create a few notes worth 0 DAI to mask how much each note is worth.

Naturally, a ‘lazy’ use of the protocol will leak information. For example, imagine you converted 10 DAI into 5 notes, where 4 were worth 0 DAI. If you then forgot about these notes and never used them in future transactions, it would be fairly obvious to observers that the un-used notes were worth nothing. Always issuing zero-value notes in join-split transactions, and using them in future join-split transactions minimizes the amount of information available to external observers.

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The AZTEC protocol’s trusted setup

The reason the AZTEC protocol is highly efficient is that we combine Boneh-Boyen signature and Pedersen-style commitments into a single commitment scheme with a highly efficient range proof embedded into the commitment. This comes at the cost of requiring a database of elliptic curve points to be generated before the AZTEC protocol can be used. This database is required to construct proofs, but is not needed to verify them.

A bit like ZCash, this trusted setup generates a ‘toxic waste’ private key and if knowledge of that private key is leaked, it can be used to effectively double-spend, and the protocol becomes unusable.

So how do we deal with this? Well, for one we don’t just expect you to trust us. We have developed a scalable multiparty computation protocol that enables anybody to engage in the trusted setup process. If you participate, you generate a piece of ‘toxic waste’ that, naturally, should be destroyed. The trusted setup private key, the thing that must be destroyed at all costs, can only be recovered by piecing together every participant’s toxic waste. So if a single person acts honestly the scheme is completely secure and can only be ‘cracked’ by solving one of the discrete logarithm-based problems (of which the entireity of elliptic curve cryptography rests; if somebody cracks the discrete log problem we’ve all got bigger problems on our hands than the security of the AZTEC protocol!).

We will be announcing the formal description of our trusted setup process in the coming months and will begin to collect participants. It is similar to ZCash’s ‘powers of tau’ ceremony, albeit for a very different end as the AZTEC protocol is not a ZK-SNARK. We want the trusted setup protocol to be simple to take part in and we want to engage the wider Ethereum community in this process, to create a trusted setup database that has the trust and confidence of the community.

Our deployed proof-of-concept smart contracts use a trusted setup that was generated internally, as implementing our multiparty computation trusted setup is going to take several months. Until we have completed this phase the AZTEC protocol is very much use-at-your-own-risk. Whilst I naturally destroyed the toxic waste, there is no way to prove that I did.

One final point (zing…). The size of the trusted setup database grows linearly with the size of the protocol’s range proof. Our proof-of-concept database supports integers between 0 and 1,048,575 because I wanted a database small enough to fit inside a github repo without being a pain to download. Our full implementation will support a much larger range of integers.

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Why is the AZTEC protocol important?

Well of course I’m going to say this is important, I’m the most biased person you could ask on this topic! But here’s why I think this is a real game changer: The AZTEC protocol enables the creation of generic confidential digital assets. We picked DAI to start with but with the press of a button the AZTEC protocol can be applied to any ERC-20 token. It also enables the construction of purely confidential assets that don’t have any kind of ERC-20 token equivalent. No extra cryptographic circuits required, no additional trusted setup processes needed. For the first time ever, it’s possible to create confidential digital assets on Ethereum, obtaining the immutability and decentralization benefits of public blockchains without sacrificing privacy.

AZTEC zero-knowledge proofs are also very efficient to construct, and are well within the capabilities of hardware wallets. This opens up the exciting possibility of issuing confidential transactions directly from hardware wallets and never exposing sensitive private keys.

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What is in the AZTEC protocol’s future?

Of immediate relevance is releasing our AZTEC proof construction API, to accompany our smart contract verifiers and technical paper. We also have several extensions to the AZTEC protocol in the works, and will be releasing our full vision of the AZTEC protocol over the first half of 2019. This includes several important milestones:

1. A confidential decentralized exchange, where people can trade different AZTEC assets in complete confidentiality — neither the quantities or prices of orders can be gleaned from processed orders. The decentralized exchange uses the relayer pattern to acheive this, as well as a bespoke AZTEC DeX zero-knowledge proof (three actually, I’ll be talking about this in depth once our DeX paper is finalized).

2. Confidential weighted voting. Governance mechanics that respect the privacy of a user’s vote are essential a large range of financial applications and the AZTEC protocol’s efficient range proofs make this achievable.

3. Anonymous identity sharing schemes. Being able to prove that you’re part of a group, without revealing who in the group you are is an essential component for many compliance and KYC processes and our AZTEC token standard will support this kind of identity system.

Combined together, this will give builders the tools needed to create the next wave of decentralized financial services; digital assets with implicit privacy and confidential governance mechanics built in from the ground up.

We’re going to be open-sourcing our technology to fully realize this vision — if you want to create private assets on Ethereum, AZTEC will provide the smart contracts, resources and tooling to make it a simple experience.

If you’re interested in building with the AZTEC protocol, drop us a line at hello@aztecprotocol.com. And if you’re a talented developer that wants to work with us on to build the future of decentralized finance, reach out to us because we’re also hiring :).

Cheers,

Zac.

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Aztec Network
Aztec Network
15 Oct
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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).

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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.

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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.