Zexe: Enabling Decentralized Private Computation

01 Claim ledger

What the paper is allowed to say

Each row is a sentence already in the study. The status is the same on every row: a model claim, not a live measurement.

1. Claim 01 · Paper model

   Records, not accounts

   The state is a set of committed records. Spending is the death of some records and the birth of others. There is no public account balance to read.

2. Claim 02 · Paper model

   Two predicates

   A death predicate says when a record may be consumed. A birth predicate says when a new record may appear. Applications are written as those rules, not as arbitrary on-chain bytecode in the paper's model.

3. Claim 03 · Paper model

   Offline proving

   The user does the heavy work and posts a succinct proof. The chain verifies the proof and the nullifiers that stop a record being killed twice.

4. Claim 04 · Paper model

   Zerocash is the payment special case

   A simple transfer is a Zexe program. The paper's ambition is every state transition that can be written as record predicates, which includes trades and votes, and also includes bugs in those predicates.

02 Three cuts

Observation, model, falsifier

A desk does not stop at the summary. Each claim is cut three ways, using only this study's own assumptions and checks. Nothing here is a new figure.

1. 01 Records, not accounts

   Observation

   What the study says

   The state is a set of committed records. Spending is the death of some records and the birth of others. There is no public account balance to read.

   Model

   What has to hold

   Nullifiers are deterministic functions of the record secret, so a double death collides and is rejected.

   Falsifier

   What would retire it

   What is the birth predicate, and what is the death predicate?

2. 02 Two predicates

   Observation

   What the study says

   A death predicate says when a record may be consumed. A birth predicate says when a new record may appear. Applications are written as those rules, not as arbitrary on-chain bytecode in the paper's model.

   Model

   What has to hold

   Nullifiers are deterministic functions of the record secret, so a double death collides and is rejected.

   Falsifier

   What would retire it

   What is the birth predicate, and what is the death predicate?

3. 03 Offline proving

   Observation

   What the study says

   The user does the heavy work and posts a succinct proof. The chain verifies the proof and the nullifiers that stop a record being killed twice.

   Model

   What has to hold

   Nullifiers are deterministic functions of the record secret, so a double death collides and is rejected.

   Falsifier

   What would retire it

   Are nullifiers unique per record, and where are they stored?

4. 04 Zerocash is the payment special case

   Observation

   What the study says

   A simple transfer is a Zexe program. The paper's ambition is every state transition that can be written as record predicates, which includes trades and votes, and also includes bugs in those predicates.

   Model

   What has to hold

   Commitments hide the record data. A commitment that includes a public memo may leak it.

   Falsifier

   What would retire it

   Are nullifiers unique per record, and where are they stored?

03 Sequence

One action, as an operating tape

1. 01A user holds secrets that open one or more records committed on the ledger.
2. 02They compute the new records off-chain, satisfying birth and death predicates.
3. 03They publish nullifiers for the consumed records and commitments for the new ones, plus a proof.
4. 04The ledger rejects a nullifier it has seen before, and rejects a proof that does not verify.
5. 05Observers learn that some valid transition happened, not which records, and not the data inside them.

04 Load-bearing

The argument, and where a pitch drops it

1. The predicates are the program

   The cut

   Privacy does not stop a bad rule. If the death predicate allows a record to be consumed without conserving value, the proof will hide the theft and the ledger will accept it. Review moves to the predicate, which users cannot watch execute in the clear.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   A later client, parameter or reward formula is a different object from this paragraph.

2. Counterparty privacy is not observer privacy

   The cut

   Someone who already knows the secret, because they were the other side of the trade, is not blinded by the proof. The paper hides state from the public ledger. It does not hide a deal from its parties.

   Why it carries weight

   If this cut is skipped, the paper's name is being used without the mechanism that makes the name mean anything.

   Where it is dropped

   Aleo and other later systems are implementations, with their own curves, fees, and failures.

05 Register

What has to be true

• Cryptography · Not re-measured

  The proof system is sound for the predicate circuit. A broken SNARK breaks every application at once.

• Model · Not re-measured

  Nullifiers are deterministic functions of the record secret, so a double death collides and is rejected.

• Data · Not re-measured

  Commitments hide the record data. A commitment that includes a public memo may leak it.

• Cryptography · Not re-measured

  Users can actually produce the proofs on their own hardware, or the 'offline' step quietly becomes a trusted prover.

06 Divergence

What happened after the paper

Aleo and other private-computation projects cite Zexe as the model and then change the proof system, the record format, and the fees. The 2018 paper remains the right picture of birth and death predicates. It is not a description of any of those networks' live circuits.

A later client, parameter set, or reward formula is a different object. Cite this paper for the mechanism. Cite a primary release for the network. This desk has not re-run the proof.

07 Pre-mortem

What to check before you use the idea

1. Kill test 1What is the birth predicate, and what is the death predicate?
2. Kill test 2Are nullifiers unique per record, and where are they stored?
3. Kill test 3Who generates the proof: the user or a service?
4. Kill test 4Which SNARK sits underneath, and does it have a setup?
5. 0 of 4 marked on this browser. A mark is a reading note, not a pass, a rating, or a recommendation.

08 Anatomy

The paper, in the order a builder needs

09 Lexicon

Terms, opened into the record

Record

A committed piece of state with rules for how it may be created and consumed.

Nullifier

A public marker that a record has been consumed, which does not reveal which record.

10 Repository

Every linked record on this page

Underlined words open a page that already exists: a concept, a protocol profile, a failure record, or another paper. If a word is not underlined, this desk does not have a record for it.

11 Related

The next papers, as theses

• Zerocash · 2014

  Zerocash: Decentralized Anonymous Payments from Bitcoin

  The 2014 paper that showed how a payment ledger can hide sender, receiver and amount, while still letting the network check that coins were not created or double-spent. Zcash is an implementation of this line of work, not a co-author of the paper.

• Halo · 2019

  Halo: Recursive Proof Composition without a Trusted Setup

  Recursion for inner-product arguments, without a structured setup. A proof can attest that another proof was checked. That is how a chain can fold a long history into one object. Halo 2 is a later system.

• Groth16 · 2016

  On the Size of Pairing-based Non-interactive Arguments

  A pairing-based argument in three group elements. The proofs are tiny and cheap to verify. Each circuit needs its own setup, and a leaked setup can forge proofs.