Consensus-Dependent Integrity and Fairness

• Consensus-Dependent Integrity and Fairness (CDIF) is a principle that links the correctness of outputs and fairness in outcome distribution directly to consensus among distributed participants.
• It ensures that any deviation or adversarial behavior triggers immediate detection and atomic abort, preventing partial or biased results in protocols.
• CDIF underpins practical applications in secure data aggregation, blockchain consensus, and fair ranking by enforcing collective verification at critical protocol steps.

Consensus-Dependent Integrity and Fairness (CDIF) is a formal security and correctness principle dictating that the achievement of integrity (correctness of outputs) and fairness (equitable outcome distribution or participation) in a distributed protocol is inextricably linked to the agreement—explicit or implicit—of distributed participants. CDIF arises in systems and protocols where individual or adversarial deviations can only be tolerated if they are detected and either rectified or atomically aborted, ensuring that security and correctness are maintained only when consensus is preserved across key operations. This principle underpins security, trust minimization, and auditability in privacy-preserving aggregation, distributed consensus, fair ranking, and blockchain systems.

1. Formal Definition and Theoretical Foundations

CDIF admits formalization in a range of paradigms. In secure multi-client aggregation, as instantiated by the Consensus-Based Privacy-Preserving Data Distribution (CPPDD) framework, CDIF is stated as a theorem:

Let $\mathcal{A}$ be a PPT adversary corrupting up to $f \ge 1$ participants. Then:

1. The protocol completes successfully if and only if every participant follows the specification faithfully.
2. If any corrupted participant deviates, the next honest participant detects the deviation with probability at least $1-2^{-\kappa}$, triggering protocol abort and blocking any data release.
3. The probability that a protocol run both tolerates a deviation and proceeds is at most $2^{-\kappa}$, with perfect correctness under honest execution.

Symbolically: $$\Pr[\text{protocol succeeds with a deviation}] \le 2^{-\kappa},\quad \Pr[\text{honest execution succeeds}] = 1.$$ This all-or-nothing property guarantees that either all correct parties obtain the correct result, or, upon any detected violation, no party obtains any partial output (Panth et al., 1 Jan 2026).

2. CDIF in Secure Data Aggregation and Privacy-Preserving Protocols

The CPPDD framework introduces CDIF in the context of scalable, verifiable data sharing among $N$ clients contributing $D$-dimensional data over a finite field $\mathbb{F}_p$ (Panth et al., 1 Jan 2026). The principal components enforcing CDIF are:

• Per-Client Affine Masking: Each input $D_i$ is transformed to a masked share $O_i = \lambda_i D_i + r_i$ using PRF-generated keys, ensuring computational indistinguishability from random vectors and providing IND-CPA semantic security under standard cryptographic assumptions.
• Priority-Driven Sequential Consensus Locking: Masked states are sequentially unblinded by clients following a fixed priority order, creating distinct protocol layers $L^{(j)}$. Any tampering at each step is checked before protocol advances.
• Step and Data Checksums: For every blinding layer, a collision-resistant hash function records the checksum $\sigma_{S,j} = H(\sum_{d=1}^D L^{(j)}_d)$. Any mismatch on recomputation signals deviation, with abort enforced atomically and immediately.
• Atomic Abort: Detection of deviation (with probability at least $1-2^{-\kappa}$) halts all further progress; no honest client can recover any partial data, guaranteeing fairness and integrity.

The protocol’s correctness and fairness depend critically on unanimous cooperation at each stage and are robust to collusion up to $N-1$ corrupted clients. The design is computationally and communicationally efficient: $O(N \cdot D)$ total cost, supporting both scalability and practical deployment.

3. CDIF in Consensus Protocols and Fault-Tolerant Blockchain Systems

MonadBFT and Tendermint-core provide contrasting models of CDIF in Byzantine fault-tolerant consensus for blockchains and distributed ledgers.

MonadBFT

In MonadBFT, integrity is realized by ensuring no two conflicting states are committed at the same slot by honest validators, formalized by the invariant that for any two honest validators and any two committed values at the same height, those values must be equal. Fairness is achieved by bounding a leader’s power to reorder or censor pending transactions to the leader's protocol share; any transaction visible to a sufficient subset of validators must be included in a bounded number of subsequent slots.

Key mechanisms enforcing CDIF in MonadBFT include:

• Speculative Finality: Early execution and confirmation underpins rapid liveness but retains a finality check ("no two QCs at the same height on different blocks"), ensuring speculative results are rolled back if consensus diverges.
• Optimistic Responsiveness: Leaders proceed after $2f+1$ votes without fixed timeouts, preventing malicious leaders from extending censorship windows.
• MEV-Tail-Forking Mitigation: The protocol requires blocks to extend the highest-tip QC or re-propose it, preventing speculative forks aimed at extractable value.
• Accountability: Leader equivocation is provably slashable, ensuring faulty leaders cannot indefinitely impede fairness; equivocation proof enforces their exclusion.

MonadBFT thus enforces CDIF: any adversarial attempt to violate integrity or fairness is detectable and accounted for within bounded windows, relying on consensus at crucial protocol steps (Jalalzai et al., 28 Feb 2025).

Tendermint-core

Tendermint-core employs a repeated PBFT-style consensus with proof-of-stake validator selection. Integrity (correctness) holds under eventual synchrony and $f<n/3$. That is, one-shot and repeated consensus achieve agreement, guaranteed termination, and validity if the network eventually provides bounded delay and the proportion of Byzantine participants remains below threshold. Fairness, defined as proper reward allocation to correct participating validators, is more subtle:

• A reward mechanism is fair if all correct values are rewarded and no faulty or non-validator is.
• Under full synchrony, perfect fairness holds; under eventual synchrony, only eventual fairness is attainable, provided the protocol dynamically adjusts timeout parameters and includes proofs of participation.
• If the network is fully asynchronous, neither integrity nor fairness can be guaranteed.

This illustrates the dependence of both correctness and fairness guarantees on the system’s capacity to reach timely consensus at specified points—a paradigmatic CDIF scenario (Amoussou-Guenou et al., 2018).

4. CDIF in Fair Rank Aggregation and Social Decision-Making

In aggregation of rankings from multiple stakeholders, as in the FairFuse system (Shrestha et al., 2022), CDIF is encoded by requiring both integrity (proximity to underlying stakeholder rankings) and group fairness (statistical parity for protected classes).

• Integrity: Measured via Kendall-tau distances between the consensus and input rankings.
• Fairness: Quantified using Favored-Pair Representation (FPR) per group and Attribute-Rank Parity (ARP) across groups. The optimization goal is to minimize aggregate distance to stakeholder rankings subject to fairness constraints $ARP(R)\le \tau$.

The Fair-Copeland algorithm operationalizes these constraints, modifying the tournament construction to maintain group-fair intervals, and the interactive system provides real-time feedback on fairness upon any consensus alteration. The property is inherently consensus-dependent: the final ranking is only both close to participant input and fair to all protected groups if the aggregation process does not violate explicit consensus thresholds on either objective.

5. Relationships to Other Security and Social Objectives

CDIF is distinct yet overlaps with several other key notions:

• Unanimous-Release Confidentiality: As in CPPDD, CDIF ensures outputs are not revealed unless all required parties have contributed valid (and untampered) inputs.
• IND-CPA Security: In cryptographic aggregation, CDIF complements semantic security by preventing partial or adversarially biased output exposure.
• Eventual and Strong Fairness: In blockchain and consensus protocols (Tendermint-core), CDIF provides a precise bridge between network assumptions and obtainable fairness, explicitly characterizing when event-driven fairness can be guaranteed.

A plausible implication is that any distributed protocol requiring auditability, trust minimization, or regulatory compliance must explicitly implement (or approximate) CDIF to ensure adversarial actions cannot differentially impact integrity or fairness.

6. Performance, Scalability, and Limitations

The architectural implications of enforcing CDIF are critical for scalability:

• Computational and Communication Overheads: In protocols such as CPPDD, adding CDIF (through step checksums and enforced sequentialism) incurs $O(N)$ extra hashes over an otherwise linear protocol, a negligible cost for the integrity and fairness guarantees attained (Panth et al., 1 Jan 2026).
• Sequentiality and Latency: CDIF protocols often require sequential progress (e.g., layer removal in data aggregation or pipelined leader rotation in consensus), which, while necessary for auditability, can impact efficacy in high-latency or large-$N$ settings.
• Relaxation and Extension: For large-scale or cross-jurisdictional deployments—such as federated learning or multi-jurisdictional voting—distributed protocols may need to employ pipelining, batching, or multi-tree extensions to maintain practical throughput without eroding CDIF’s guarantees.

In protocols dependent on timing assumptions (blockchains), full fairness is only attainable under strict synchrony. Protocol modifications (dynamic timeouts, commit proofs) ameliorate but cannot eliminate this dependence (Amoussou-Guenou et al., 2018).

7. Applications and Domain-Specific Instantiations

CDIF principles underpin a wide spectrum of modern distributed computing and social choice applications:

Domain	Protocol Example	CDIF Manifestation
Secure Aggregation	CPPDD	Atomic abort, unanimous-release, malicious deviation detection (Panth et al., 1 Jan 2026)
Blockchains	MonadBFT, Tendermint	Fork-resistance, MEV mitigation, accountability, fair rewards (Jalalzai et al., 28 Feb 2025, Amoussou-Guenou et al., 2018)
Social Choice	FairFuse	Fair rank aggregation, group parity constraints (Shrestha et al., 2022)

These frameworks extend CDIF from purely technical realms (cryptographic confidentiality, Byzantine consensus) to complex social and regulatory contexts, where both outcome correctness and participant equity are mandated. In all cases, the property operationalizes the fundamental insight that distributed system goals of security, integrity, and fairness fundamentally depend on the consensus structure and the ability to detect and mitigate deviations before any irreversible state transition or output emerges.