Why Remove `oracle` From `Proof` Structure?

This article delves into the discussion surrounding the proposal to remove the oracle field from the Proof structure, as highlighted in the Google's Longfellow-zk discussion category. The Proof struct currently includes a 32-byte field named oracle, which is described as a "nonce used to define the random oracle." However, there are compelling arguments for its removal, primarily due to redundancy, variable length issues, and inconsistencies within multi-field optimization contexts. Let's explore these reasons in detail.

Redundancy and Security Risks

One of the main reasons to remove the oracle field is the redundancy it introduces. Most protocols employing this proof system already have established methods for communicating transport protocol binding values or liveness nonces, which are essential for hashing into the Fiat-Shamir transcript. Including the oracle field in the serialized proof creates an unnecessary duplication of effort. This redundancy not only increases the size of the proof but also introduces potential security vulnerabilities.

Consider this scenario: if a protocol relies on a verifier-chosen nonce to enforce liveness, sending the same nonce back from the prover is not only redundant but also risky. The prover's copy of the session ID could be used without proper comparison to the verifier's copy, potentially leading to exploitation. Therefore, removing the oracle field mitigates this risk by ensuring that session IDs and nonces are handled through established protocol mechanisms, where they can be managed and validated securely.

To illustrate this further, let's examine the reference verifier service written in Go, which uses ISO 18013-5 with OpenID4VP handoff. In this setup, the Fiat-Shamir transcript is initialized with the serialized SessionTranscript structure. Both the mdoc (mobile document) and the mdoc reader need to agree on this value for the various security features of the protocol. The oracle field, in this context, adds no value and could potentially complicate the process.

Therefore, it's crucial to streamline the data flow and minimize redundancy to enhance both efficiency and security. Removing the oracle field aligns with this principle, ensuring that critical session data is managed in a controlled and validated manner.

Variable Length Considerations

Another compelling argument against the oracle field lies in its fixed size of 32 bytes, which does not accommodate the variable-length nature of session IDs in certain use cases. For instance, in the ISO 18013-5 with OpenID4VP handoff example, the session_id is not a fixed 32 bytes but varies in length depending on the specific session parameters. This discrepancy between the fixed-size oracle field and the variable-length session ID poses a significant challenge for protocols that require flexibility in session management.

This mismatch can lead to several issues:

1. Data truncation: If the session ID exceeds 32 bytes, it would need to be truncated to fit into the oracle field, resulting in a loss of information and potential security vulnerabilities.
2. Padding overhead: Conversely, if the session ID is shorter than 32 bytes, it would need to be padded, leading to inefficient use of space and increased data transmission overhead.
3. Complexity in handling: Managing fixed-size fields for variable-length data adds complexity to the protocol implementation, increasing the risk of errors and security flaws.

To address these issues, removing the fixed-size oracle field and relying on established mechanisms for handling variable-length session IDs is a more practical and secure approach. This ensures that the protocol can accommodate different session requirements without compromising data integrity or efficiency.

By aligning the data structure with the needs of real-world applications, the overall robustness and usability of the proof system can be significantly enhanced. This flexibility is crucial for the widespread adoption of the technology in various domains, including identity verification, secure communication, and decentralized applications.

Multi-Field Optimization Inconsistencies

The third compelling reason to reconsider the inclusion of the oracle field stems from its inconsistency within the context of multi-field optimization, as discussed in section 7.5 of the relevant specifications. Multi-field protocols are designed to enable multiple sub-protocols to share a common Fiat-Shamir transcript, thereby optimizing performance and reducing overhead. In this framework, the session_id argument, which the oracle field is intended to represent, should not be treated as a per-circuit parameter but rather as a higher-level parameter shared across all sub-protocols.

Including the oracle field within the Proof struct contradicts this principle for several reasons:

1. Redundant transmission: If the session_id is transmitted as part of each individual proof within a multi-field protocol, it leads to unnecessary redundancy. The same session ID would be sent multiple times, increasing the data size and computational overhead.
2. Logical separation: The session_id is inherently a parameter that applies to the entire multi-field protocol session, not to individual circuits or sub-protocols. Therefore, it should be stored and managed at a higher level, separate from the Proof struct.
3. Potential for inconsistencies: If each sub-protocol were to transmit its own oracle field, it could lead to inconsistencies and confusion, particularly if the values differ across sub-protocols.

Therefore, to maintain consistency and efficiency in multi-field protocols, the session_id should be managed at the session level, ensuring that it is shared and applied uniformly across all sub-protocols. Removing the oracle field from the Proof struct is a crucial step in aligning the data structure with the logical architecture of multi-field optimization.

By doing so, the proof system becomes more streamlined, efficient, and easier to manage, particularly in complex multi-protocol scenarios. This alignment enhances the overall performance and scalability of the system, making it more suitable for real-world applications that demand high throughput and low latency.

Conclusion

In conclusion, the arguments for removing the oracle field from the Proof structure are substantial and well-founded. The redundancy it introduces, the challenges it poses with variable-length session IDs, and its inconsistencies within multi-field optimization contexts all point to the need for its removal. By streamlining the data structure and aligning it with the logical requirements of various protocols, the security, efficiency, and usability of the proof system can be significantly enhanced. This adjustment is crucial for ensuring the system's robustness and its ability to meet the demands of diverse real-world applications.

For further information on zero-knowledge proofs and related topics, consider exploring trusted resources such as the ZKP MOOC by Dan Boneh.