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https://github.com/systemslibrarian/crypto-lab-dilithium-reject

Browser-based demo of ML-DSA (FIPS 204) rejection sampling. Live iteration feed, rejection-reason breakdown, acceptance histograms, and the timing side-channel tradeoff — why variable signing time is a feature, not a bug.
https://github.com/systemslibrarian/crypto-lab-dilithium-reject

constant-time crypto-lab cryptography crystals-dilithium digital-signatures dilithium fiat-shamir-with-aborts fips-204 implementation-security lattice-cryptography lattice-signatures lyubashevsky ml-dsa ml-dsa-65 post-quantum-cryptography rejection-sampling timing-side-channel

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Browser-based demo of ML-DSA (FIPS 204) rejection sampling. Live iteration feed, rejection-reason breakdown, acceptance histograms, and the timing side-channel tradeoff — why variable signing time is a feature, not a bug.

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# crypto-lab-dilithium-reject



Browser-based explainer for ML-DSA rejection sampling: the Fiat-Shamir with Aborts loop that makes lattice signatures secure.



[**Live demo →**](https://systemslibrarian.github.io/crypto-lab-dilithium-reject/)



![ML-DSA Rejection Sampling Explorer — dark theme, showing iteration trace and histogram of iterations until acceptance](docs/screenshot.png)



Light theme



![Light theme: same layout, light palette](docs/screenshot-light.png)



> "Whether therefore ye eat, or drink, or whatsoever ye do, do all to the glory of God."

> 1 Corinthians 10:31



## What It Is



This project visualizes the signing rejection loop used by ML-DSA (FIPS 204, August 2024). It walks through what happens iteration by iteration: a candidate is drawn, four norm-bound checks are applied, and either the candidate is accepted or one specific check fails and the loop retries.



The demo targets ML-DSA-65 (NIST level 3) by default and uses strict TypeScript with a browser-only stack (Vite + vanilla CSS, no backend).



Highlights:

- Live iteration feed with explicit rejection reason (`z_too_large`, `r0_too_large`, `ct0_too_large`, `hint_too_dense`)

- Histogram of iterations-until-acceptance over many signatures, per parameter preset

- KS-style distinguishability test for the principle behind sk-independent timing

- Comparison table across Ed25519, ECDSA, ML-DSA, SLH-DSA, FALCON, LMS

- Exhibit explaining why each rejection check exists in FIPS 204



## How This Demo Works (Important)



The iteration feed in Exhibit 1 and the histogram in Exhibit 2 are a **didactic simulation calibrated to ML-DSA's published acceptance distribution**, not a fork of the real signing internals.



- Acceptance per iteration is a coin flip with `p(accept)` set per preset (~0.31 for ML-DSA-44, ~0.26 for ML-DSA-65, ~0.22 for ML-DSA-87). These are **illustrative values calibrated to the order-of-magnitude reported by published ML-DSA implementations**; treat them as the right shape of the distribution, not as measurements. The calibration is asserted by `src/instrumented-sign.test.ts`, which fails the build if mean iterations drift more than ±15% from `1/acceptance`.

- When a candidate is rejected, the specific reason is sampled from the published mix (z dominates, r0 next, ct0 and hint rare). The displayed `||z||∞`, `||r0||∞`, `||c·t0||∞` values are positioned above/below their thresholds to be consistent with that reason; they are not computed from a live `y + c·s1` etc.

- The actual signature shown as "valid" is produced by [`@noble/post-quantum`](https://www.npmjs.com/package/@noble/post-quantum)'s real ML-DSA implementation. The verification check uses the same library. That part is real.

- `src/mldsa-primitives.ts` contains real implementations of `infinityNorm`, `highBits`/`lowBits`, `hintWeight`, and a SampleInBall variant; it is wired into the demo for the per-check explanation exhibit but does not drive the iteration feed.



This separation is deliberate: instrumenting `@noble/post-quantum`'s signing loop from outside the library would require patching internals, while the goal here is pedagogical clarity. The simulation is faithful to the *shape* and *reasons* — not the bit-exact arithmetic — of FIPS 204 § 6.



If you need bit-exact internal traces of real ML-DSA signing, use a reference implementation that exposes per-iteration hooks (e.g. NIST's C reference) rather than this demo.



## When to Use It



Use this demo when you need to:

- teach why ML-DSA signing time is variable by design

- explain Fiat-Shamir with Aborts in lattice signatures

- show that rejection is a security feature, not an implementation bug

- discuss timing side-channel risk tradeoffs in post-quantum signatures

- compare ML-DSA timing behavior with other signature families



Do not use this project as production signing code. For production, use maintained, hardened libraries and platform-specific side-channel countermeasures.



## Install and Run



```bash

npm install

npm run dev       # local dev server with hot reload

npm run build     # type-check + production build to ./dist

npm run preview   # serve the built bundle

```



Requires Node 22+. The build is a static bundle; the GitHub Pages workflow (`.github/workflows/deploy.yml`) publishes `./dist` to `gh-pages` on each push to `main`.



## Live Demo



https://systemslibrarian.github.io/crypto-lab-dilithium-reject/



## What Can Go Wrong (in real deployments)



- Variable signing time can become a side-channel if deployment hardening is weak.

- Worst-case retries matter operationally; FIPS 204 permits bounded loops with failure return.

- Rejection-loop timing is not the only leak source; arithmetic and memory access patterns also matter.

- Deterministic mode has reproducibility benefits but different timing-privacy tradeoffs.

- Different ML-DSA parameter sets shift acceptance distributions; the histogram preset selector illustrates this.



## Real-World Usage



Fiat-Shamir with Aborts was introduced by Vadim Lyubashevsky (ASIACRYPT 2009) and is the core idea behind practical lattice signatures like CRYSTALS-Dilithium and standardized ML-DSA.



NIST selected Dilithium in 2022, then published FIPS 204 in 2024. The standardized ML-DSA design keeps rejection as a deliberate mechanism to preserve signature security, while implementations must manage the operational and side-channel consequences of variable-time signing loops.



## License



MIT — see [LICENSE](LICENSE).