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https://github.com/systemslibrarian/crypto-lab-fhe-arena

Browser-based BGV/BFV integer FHE demo — homomorphic addition and multiplication, live noise budget visualizer, relinearization, SIMD batching, and real-world deployments in private genomics and encrypted databases.
https://github.com/systemslibrarian/crypto-lab-fhe-arena

bfv bgv crypto-lab cryptography encrypted-computation fhe homomorphic-encryption microsoft-seal noise-budget privacy-preserving private-genomics relinearization rlwe

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Browser-based BGV/BFV integer FHE demo — homomorphic addition and multiplication, live noise budget visualizer, relinearization, SIMD batching, and real-world deployments in private genomics and encrypted databases.

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README 

          
# crypto-lab-fhe-arena



## What It Is



FHE Arena demonstrates BGV (Brakerski-Gentry-Vaikuntanathan, 2012) and BFV (Fan-Vercauteren, 2012) — the two most widely deployed integer Fully Homomorphic Encryption schemes. Both encrypt integers and support addition and multiplication directly on ciphertexts, allowing a server to compute on encrypted data without ever decrypting it. The central challenge is the noise budget: every operation adds noise to the ciphertext, and when noise exceeds a threshold, decryption fails. BGV manages this via modulus switching; BFV via rescaling. This demo is the integer FHE companion to Blind Oracle (TFHE bit-level FHE).



## When to Use It



- BFV: encrypted integer arithmetic, simple-to-moderate computation depth, most accessible starting point (Microsoft SEAL default)

- BGV: deeper computation requiring more multiplication levels, statistical workloads on encrypted integers

- Both: encrypted database queries, private genomics, encrypted voting tallying, private machine learning inference on integer data

- Neither is suitable for encrypted floating-point / approximate arithmetic — use CKKS for that (see crypto-lab-ckks-lab)

- Neither supports unlimited computation depth without bootstrapping (expensive — plan your circuit depth carefully)

- Not yet practical for real-time applications without GPU acceleration (2024 state of the art for deep circuits)

- Do NOT use this for real encrypted workloads — it runs toy parameters for teaching, not production FHE security.



## Live Demo



**[systemslibrarian.github.io/crypto-lab-fhe-arena](https://systemslibrarian.github.io/crypto-lab-fhe-arena/)**



Every number in the demo is computed by a real (toy-parameter) BFV engine over genuine negacyclic ring arithmetic — nothing is faked. The lab is built to *teach*, so the hidden machinery is made visible:



- **The decryption equation, live.** Exhibit 2 opens up exactly what the secret key recovers: `c0 + c1·s = Δ·m + e`. You see the clean signal `Δ·m`, the actual recovered value, and the noise `e` — so "noise" stops being abstract.

- **Noise budget in bits.** Every meter reports the budget in *bits* (like Microsoft SEAL's `invariant_noise_budget`), color-coded healthy → low → fails, alongside a visual bar.

- **Measured, not asserted.** Exhibit 3 logs the *real measured* noise and budget after each operation and plots it on a live chart — addition steps glide flat, each multiplication drops a cliff. A "multiply until it breaks" button animates the collapse to the decryption-failure floor.

- **Honest about failure.** When the budget is exhausted the demo shows the *actual* (corrupted) decryption and explains that the budget is a guarantee over the whole ciphertext — a single slot may coincidentally survive while the rest is garbage. Nothing is faked to look broken.

- **Semantic security, shown.** Encrypt the same value twice and watch the ciphertexts diverge completely while both still decrypt correctly — a concrete demonstration of IND-CPA randomized encryption.

- **Bootstrapping, shown.** Exhaust the budget, then press *Bootstrap* and watch it snap back to full — with an honest note that real bootstrapping refreshes noise homomorphically (without the key) and must run *before* overflow, not after.

- **The parameter tradeoff, hands-on.** A slider over the real Homomorphic Encryption Standard (128-bit security) shows how a larger degree `n` buys a larger modulus `q` → more multiplicative depth → but slower operations.

- **A live private computation.** Cast ten secret Yes/No ballots, encrypt them, homomorphically sum the ciphertexts, and decrypt *only the tally* — the headline FHE application, verifiable end to end, with no individual vote ever revealed.

- **Verification badges.** Encrypted results are checked against plaintext arithmetic with ✓/✗ badges, so the homomorphic payoff is unmissable.



Six exhibits: the core idea (compute on locked boxes, with a client/server trust diagram); encrypt-add-decrypt with the live `Δ·m + e` reveal and a semantic-security demo; the noise-budget visualizer with a live chart, animated "multiply until it breaks", and a bootstrapping refresh; multiplication, relinearization (2→3→2 ciphertext components) and SIMD batching; a BGV vs BFV vs TFHE comparison table, decision tree, and interactive parameter explorer; and real-world FHE deployments capped by a live encrypted vote tally.



## What Can Go Wrong



- **Noise budget exhaustion.** Every homomorphic operation grows ciphertext noise; exceed the budget and decryption silently returns garbage. Multiplicative depth must be planned before the circuit is built.

- **Wrong scheme for the data.** BGV/BFV are integer schemes. Forcing real-valued or approximate workloads onto them gives poor results — CKKS exists for that, with its own approximation caveats.

- **Insecure parameter selection.** Polynomial degree and modulus must follow the Homomorphic Encryption Standard; ad-hoc parameters can drop below the claimed security level or fail to support the intended depth.

- **No integrity by default.** FHE ciphertexts are malleable by design (that is the whole point), so a malicious server can tamper with results unless you add separate verification. IND-CPA security does not imply CCA security.

- **Bootstrapping cost and timing.** Bootstrapping refreshes noise but is expensive and must run before overflow, not after; treating it as free or as a recovery step after corruption does not work.



## Real-World Usage



- **Private machine learning inference.** Encrypted prediction services let a model run on a client's encrypted inputs without seeing the data, a primary commercial driver for FHE.

- **Encrypted database and analytics queries.** Servers compute sums, counts, and statistics over encrypted records, relevant to regulated medical and financial data.

- **Private genomics.** Encrypted comparison of genomic data is a long-standing FHE research and deployment target where data sensitivity is extreme.

- **Secure voting and aggregation.** Homomorphic summation lets only the final tally be decrypted while individual contributions stay encrypted.

- **Production libraries.** Microsoft SEAL, OpenFHE, HElib, and PALISADE implement BGV/BFV/CKKS and are used in research and industry FHE deployments.



## How to Run Locally



```bash

git clone https://github.com/systemslibrarian/crypto-lab-fhe-arena

cd crypto-lab-fhe-arena

npm install

npm run dev

```



## Related Demos



- [crypto-lab-blind-oracle](https://systemslibrarian.github.io/crypto-lab-blind-oracle/) — TFHE bit-level FHE, the companion scheme to this integer FHE lab.

- [crypto-lab-ckks-lab](https://systemslibrarian.github.io/crypto-lab-ckks-lab/) — CKKS approximate FHE for encrypted real-valued / inference workloads.

- [crypto-lab-paillier-gate](https://systemslibrarian.github.io/crypto-lab-paillier-gate/) — Paillier additive homomorphic encryption for private aggregation.

- [crypto-lab-elgamal-plain](https://systemslibrarian.github.io/crypto-lab-elgamal-plain/) — ElGamal homomorphism and re-randomization.



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*One of 120+ browser demos in the [Crypto Lab](https://crypto-lab.systemslibrarian.dev/) suite.*



*"So whether you eat or drink or whatever you do, do it all for the glory of God." — 1 Corinthians 10:31*