> For the complete documentation index, see [llms.txt](https://duce.gitbook.io/duce/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://duce.gitbook.io/duce/getting-started/duce-cryptographic-modules-and-rollup-integration.md).
# DUCE Cryptographic Modules and Rollup Integration
**Technical Workflow**
The zkDEFAI FHE system processes data in the following sequence:
1. **Data Encryption:** All deposit and yield data is encrypted using FHE libraries.
2. **FHE Computation:** Investment algorithms execute on ciphertexts, enabling blind computation of yields.
3. **Zero-Knowledge Verification:** zk proofs are generated to confirm that the computations are correct, without revealing the underlying data.
**Performance Benchmarks**
Preliminary benchmarks indicate that:
* Latency remains within acceptable ranges
* Gas costs for on-chain verification via rollups are reduced by up to 70% compared to conventional methods. These benchmarks validate the efficiency of the integrated zkDEFAI FHE system.
#### Superchain Rollup Mechanics Enhancing **Batch Compression and Data Structures**
The rollup layer aggregates transactions into compressed blocks using optimized data structures. Each rollup block contains:
* A Merkle root of all batched transactions.
* Succinct zk proofs attesting to the correctness of off-chain computations. This design minimizes on-chain storage requirements and reduces verification costs.
**Fraud Proof and Dispute Resolution**
In the event of discrepancies, the system allows any party to submit a fraud proof. A sequence diagram outlines
* How a dispute is raised.
* The role of zk proofs in resolving the dispute.
* The final settlement mechanism on the base chain.
---
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