Commitment Opening

Privacy protocols like Tornado Cash use commitment schemes to break the on-chain link between deposit and withdrawal.

• Process: A user deposits funds and generates a secret, creating a cryptographic commitment (e.g., a hash of the secret) that is published. To withdraw, the user must provide a ZK-proof that they know the secret pre-image for a valid commitment without revealing which one, followed by opening the commitment to release funds to a new address.

An attacker can exploit the timing of when a commitment is opened. For example, in a commit-reveal voting scheme, a malicious actor might wait to see others' votes before revealing their own, allowing them to manipulate the outcome. This breaks the fairness and secrecy of the process.

• Front-running: In DeFi, seeing a pending transaction to open a commitment (e.g., a large trade) allows an attacker to submit their own transaction first.
• Mitigation: Use commitment schemes with binding properties and enforce strict, uniform reveal phases.

A participant in a protocol may commit to data but then refuse to open it. This can stall or break systems that require all commitments to be opened to proceed.

• Blockchain Example: In an optimistic rollup, a sequencer may withhold the transaction data batch, preventing anyone from verifying state updates or challenging fraud.
• Consequence: Can lead to liveness failures, where the protocol cannot advance.
• Mitigation: Implement slashing conditions or financial penalties (stake loss) for parties that fail to open their commitments within a specified timeframe.

An attacker opens a commitment to data that is invalid according to protocol rules but still cryptographically consistent with the original commitment hash.

• Example: Committing to a Merkle root of valid transactions, but later revealing a branch containing a double-spend or an invalid signature.
• Risk: The system must have a separate validation step after opening to check the revealed data's integrity and business logic.
• Key Distinction: A binding commitment prevents changing the data, but a hiding commitment does not guarantee the data is correct.

The act of opening a commitment can force the disclosure of sensitive information, leading to privacy breaches. This is a risk even if the commitment scheme itself is cryptographically sound.

• Scenario: A zk-SNARK proof commits to private user data. The proof's validity is verified without opening the data, but a malicious protocol might later demand the raw data be opened for "compliance."
• Threat Model: Distinguish between computational hiding (secure against polynomial-time attackers) and the real-world requirement to keep data secret indefinitely.

In some schemes, an attacker can alter an existing, unopened commitment to create a different but valid commitment to related data, without knowing the original secret.

• Impact: Can break security proofs that assume commitments are unique bindings. In Bitcoin, transaction malleability was a related issue affecting transaction IDs.
• Mitigation: Use non-malleable commitment schemes or include unique nonces/salts to bind the commitment to a specific context.

The value of revealed data often depends on external information (oracles) at the time of opening. Attackers can manipulate these oracles to change the outcome.

• DeFi Example: A commitment is opened to settle a prediction market based on a price feed. An attacker executes a flash loan attack to manipulate the oracle price at the exact moment of settlement.
• Defense: Use time-weighted average prices (TWAPs) or delay revelation so oracle manipulation becomes prohibitively expensive.

A cryptographic protocol where a committer binds to a value without revealing it, later revealing it for verification. It consists of two phases:

• Commit Phase: The committer generates a commitment string (e.g., a hash) from the secret value and a random blinding factor.
• Reveal/Open Phase: The committer provides the original value and blinding factor, allowing a verifier to check the commitment was correctly formed. Core properties are hiding (the commitment reveals nothing about the value) and binding (the committer cannot change the value later).

A Merkle tree is a hash-based data structure used to efficiently commit to a set of data. The Merkle root serves as a succinct commitment to the entire dataset.

• A Merkle proof (or inclusion proof) is the minimal set of sibling hashes needed to verify that a specific piece of data is part of the committed set, without revealing the whole tree.
• The opening for a Merkle commitment involves providing the data leaf and its Merkle proof, allowing a verifier to recompute and match the public root hash.

A cryptographic primitive that allows committing to an ordered list of values. Unlike a Merkle tree, it enables constant-size commitments and openings, regardless of the vector's length.

• Openings can be generated for specific positions (e.g., prove the value at index i).
• Advanced schemes like KZG commitments (used in Ethereum's EIP-4844) allow for efficient openings and are a key component of verkle trees and data availability sampling.

A method by which one party (the prover) can prove to another (the verifier) that a statement is true without revealing any information beyond the statement's validity.

• Commitment schemes are a fundamental building block for ZKPs. The prover often commits to secret witness data.
• The opening of these commitments is typically handled within the proof system itself; the verifier only sees the proof, not the raw openings, maintaining zero-knowledge.

A random value used in commitment schemes to ensure the hiding property. It prevents attackers from guessing the committed value by brute-force.

• During the commit phase, the secret value is combined with this random nonce (e.g., commitment = Hash(value, nonce)).
• The opening must reveal both the original value and the exact blinding factor used. If the nonce is missing or incorrect, the verification will fail, even if the value is correct.

The guarantee that all data necessary to validate a blockchain block is published and accessible to network participants.

• Data availability sampling relies on commitments (like KZG or Merkle roots) to allow light clients to probabilistically verify data is available without downloading it all.
• The opening of these commitments is critical for fraud proofs in rollups or sharding, where a node can challenge a block by proving a specific piece of committed data is unavailable or incorrect.