> For the complete documentation index, see [llms.txt](https://polarischain-1.gitbook.io/polarischain/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://polarischain-1.gitbook.io/polarischain/4.-cryptographic-foundations-and-compliance-framework/4.2-crystals-dilithium-ml-dsa-44-implementation.md).

# 4.2 - CRYSTALS-Dilithium (ML-DSA-44) Implementation

All digital signatures in Polarischain use **CRYSTALS-Dilithium2**, standardized by NIST as **ML-DSA-44** in FIPS 204 (2024). Dilithium is a lattice-based signature scheme whose security rests on the **Module Learning With Errors (M-LWE)** and **Module Short Integer Solution (M-SIS)** problems — mathematical foundations with no known efficient quantum algorithms.

**Parameters (Dilithium2 / ML-DSA-44)**

| NIST Security Level | Level 2 (\~128-bit post-quantum) |
| ------------------- | -------------------------------- |
| Public key size     | 1,312 bytes                      |
| Signature size      | 2,420 bytes                      |
| Secret key size     | 2,528 bytes                      |
| Signing speed       | \~100,000 ops/sec (single core)  |
| Verification speed  | \~200,000 ops/sec (single core)  |

**Network Usage**

| Consensus blocks    | Block digest (BLAKE2b-256 hash of block contents) | Validator keypair        |
| ------------------- | ------------------------------------------------- | ------------------------ |
| Wallet transactions | Transaction payload hash                          | User/Institution keypair |
| P2P envelopes       | Inter-validator message content                   | Validator keypair        |
| Identity claims     | Claim data hash (for ERC-3643 compliance)         | Trusted issuer keypair   |

**Implementation Architecture**

Polarischain includes a **pure Rust** implementation of CRYSTALS-Dilithium, ported from the NIST reference C implementation to eliminate FFI dependencies and guarantee memory safety via the Rust compiler. The crate supports Dilithium2, Dilithium3, and Dilithium5 security levels, with **Dilithium2 selected as the default** for its optimal balance of security, bandwidth efficiency, and verification throughput.The consensus layer wraps this implementation behind a typed signing and verification API: validator keypairs sign block digests, and validators verify peer signatures against the committee’s published public keys before accepting any block into the DAG.


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