Cross-Chain Linkage Workflow

• Cross-Chain Linkage Workflow is a systematic process that standardizes on-chain data and uses heuristic algorithms to link related transactions across multiple blockchains.
• It employs address-reuse clustering and transfer graph analysis to identify deposit-withdrawal pairs, enhancing security and compliance investigations.
• The workflow integrates FIFO temporal matching validated by permutation tests, demonstrating its effectiveness in uncovering traceable patterns in multi-chain ecosystems.

A cross-chain linkage workflow is a systematic process for associating, tracing, or auditing related activities and user behaviors across distinct but interoperable blockchain networks. These workflows are critical for security analysis, compliance, privacy evaluation, and operational insights, particularly in multi-chain ecosystems where assets, data, or value can traverse different chains through protocols, bridges, or mixers. Rigorous cross-chain linkage enables detection of behavioral patterns, deanonymization of participants under certain heuristics, and robust investigation of transaction provenance.

1. Data Acquisition and Normalization

The initial stage involves systematic on-chain data extraction and standardization across all relevant blockchains. For empirical cross-chain analysis such as that performed on Tornado Cash mixers, a full-node or archival RPC client is deployed for each blockchain $c$ (e.g., Ethereum, BNB Smart Chain, Polygon) to gather:

• All deposit events $\mathcal{D}_c = \{d_i\}$ and withdrawal events $\mathcal{W}_c = \{w_j\}$ from the corresponding protocol contracts.
• All transfer transactions (native coin and selected ERC-20 tokens) involving addresses present in $\mathcal{D}_c \cup \mathcal{W}_c$.

Data is normalized into a unified format containing chain ID, transaction hash, timestamp, block number, address, denomination, and USD-equivalent value. For protocols with fixed pool denominations, such as Tornado Cash, there is no need for further volume-based normalization, ensuring comparability across pools and chains. This harmonized dataset forms the substrate for subsequent linkage analysis (Cristodaro et al., 10 Oct 2025).

2. Heuristic Clustering Techniques for Deposit-Withdrawal Linkage

To link deposits and withdrawals that may represent the same user or entity across one or more chains, sequential heuristic clustering is performed.

2.1 Address-Reuse Clustering

This approach identifies deposit–withdrawal pairs where the same address appears in both roles:

$$\mathcal{C}_1 = \{(d, w) \mid d \in \mathcal{D}_c,\, w \in \mathcal{W}_c,\, a(d) = a(w) \}$$

where $a(x)$ denotes the address in event $x$ (Cristodaro et al., 10 Oct 2025).

This “gold-standard” heuristic provides high-precision matches, revealing cases of operational address reuse by users despite privacy expectations.

2.2 Transactional Linkage (Transfer Graph Analysis)

A directed graph $G_c = (V, E)$ is constructed per chain, with:

• $$V = \mathcal{A}_{\mathrm{dep},c} \cup \mathcal{A}_{\mathrm{with},c}$$
• $(a_i \to a_j) \in E$ if a transfer occurs from $a_i$ to $a_j$.

Deposits and withdrawals are linked if an edge exists between their respective addresses:

$$\mathcal{C}_2 = \{(d,w) \mid (a(d) \to a(w)) \in E_c \lor (a(w) \to a(d)) \in E_c \}$$

Statistical validation is performed by generating 150 random graphs of equivalent size from the address universe and comparing the observed linkage volume ($X_{H2}$) to the baseline ($X_{\mathrm{rand}}$). A conservative p-value is computed:

$$p = \frac{1}{150} \sum_{k=1}^{150} \mathbf{1}\{ X_{\mathrm{rand}}^{(k)} \geq X_{H2} \}$$

Low p-values ($p \ll 0.01$) confirm that observed linkages are highly non-random (Cristodaro et al., 10 Oct 2025).

2.3 FIFO Temporal Matching

For unmapped events, deposits and withdrawals within each pool denomination are sorted by time. A strict first-in-first-out matching is applied:

Let $D = \{d_1, ..., d_n\}$ and $W = \{w_1, ..., w_m\}$, both time-ordered. Define $f$ by:

$f(1) = \min \{ j : t(w_j) > t(d_1) \}$

$$f(i) = \min \{ j : t(w_j) > t(d_i) \land j \notin \operatorname{Im}(f|_{1\ldots i-1}) \}$$

Each pair $(d_i, w_{f(i)})$ forms a FIFO linkage cluster $\mathcal{C}_3$. Statistical significance is assessed by random temporal shuffling (1,000 permutations), confirming that observed FIFO matches are not explained by chance (p < 0.001) (Cristodaro et al., 10 Oct 2025).

3. Full Cross-Chain Linkage Pipeline and Pseudocode

The stepwise workflow is formalized in high-level pseudocode, orchestrating the three core heuristics:

Input: For each chain c: Deposits D_c, Withdrawals W_c, Transfers T_c Output: Linkage clusters C = C1 ∪ C2 ∪ C3 // Address-reuse for each chain c: for d in D_c: if a(d) ∈ {a(w) : w ∈ W_c}: C1.add((d, w)) Remove mapped events from D_c, W_c // Transactional linkage build graph G_c = (V, E) from T_c for d in D_c, w in W_c: if (a(d)->a(w) in E or a(w)->a(d) in E): C2.add((d, w)) perform null-hypothesis test Remove mapped events from D_c, W_c // FIFO temporal matching for each pool Δ: sort D, W by time for each d_i in D: match to earliest w_j ∈ W with t(w_j) > t(d_i) and unused if match: C3.add((d_i, w_j)) validate via random shuffles return C = C1 ∪ C2 ∪ C3

This pipeline is robust to protocol idiosyncrasies and can be applied uniformly across chains supporting fixed-amount privacy pools (Cristodaro et al., 10 Oct 2025).

4. Validation, Cross-Chain Generality, and Quantitative Outcomes

Each heuristic’s output is statistically validated against random baselines: transactional linkage via random-graph simulation, and FIFO matching via permutation tests. Key parameters:

• Transactional linkage random-graph trials: 150 samples (p < 0.01)
• FIFO randomization: 1,000 trials (p < 0.001)
• No volume thresholds beyond protocol-enforced denominations

The same workflow and validation procedure are applied unchanged on Ethereum, BSC, and Polygon, showing chain-agnostic behavior leakage rather than protocol-specific implementation flaws.

Empirically, integrating all heuristics, up to 34.7% of Tornado Cash withdrawals (across chains) can be linked to deposits, exposing over \$2.3 billion in traceable value flows and demonstrating substantial anonymity erosion in practice (Cristodaro et al., 10 Oct 2025).

5. Interpretation, Implications, and Limitations

The cross-chain linkage workflow described demonstrates that operational heuristics (address reuse, transactional linkage, temporal patterns) can effectively reconstruct substantial proportions of activity that cryptographic protocol design intends to unlink. The universality of these leakages across major blockchains indicates users exhibit similar behavioral lapses independent of chain or contract specifics, underscoring a need for privacy-oriented user education and possibly protocol-level protections against operational traceability.

Limitations include the protocol’s dependency on non-adaptive user behavior (e.g., situations in which users self-reuse addresses or transact rapidly after deposit), and the inability to link perfectly in the face of well-behaved users who strictly adhere to privacy best practices. Nevertheless, the workflow’s chain-general approach renders it an essential tool for real-world privacy and security analysis in multi-chain environments (Cristodaro et al., 10 Oct 2025).

6. Comparative Perspective and Applications

The heuristic-driven cross-chain linkage workflow offers contrast to cryptographic or protocol-enforced approaches (e.g., those relying solely on zero-knowledge proofs or atomicity constraints for linkage prevention). Its application extends to forensic analytics of privacy mixers, compliance monitoring, and incident response, where the ability to reconstruct provenance chains or aggregate address clusters is indispensable.

The methodology is directly relevant for external investigators, compliance teams, and protocol engineers seeking to assess the actual (versus theoretical) privacy guarantees of deployed systems under adversarial observation models across heterogeneous blockchain infrastructures (Cristodaro et al., 10 Oct 2025).