FRI-Binius: Polynomial Commitments for Tiny Binary Fields

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" summary

A new polynomial commitment scheme packs tiny-field coefficients into larger embeddings using a tensor-algebra reduction from F2 to a working field and combines the FRY protocol with a sum-check fold to avoid 32‑bit padding. Implementation in the open-source Bas Rust code shows 10× faster commit than Plonky3 for single‑bit coefficients. FPGA evaluation reports a binary field tower that is about 5× more efficient than 32‑bit primes and ~20× cheaper than 256‑bit prime multipliers; vanishing-argument cost remains the main optimization target.

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" chapters (13)

1. 0:00FRI-Binius introduction
2. 1:08Hardware-software codesign
3. 3:15Small field techniques
4. 5:22SNARK computation steps
5. 7:29Padding efficiency loss
6. 8:11Binary vs prime fields
7. 11:00Bas: FRI + binary fields
8. 12:25FRI protocol basics
9. 15:17Small field challenges
10. 16:42Packing tiny elements
11. 17:46Plonky3 performance gains
12. 18:49FPGA hardware efficiency
13. 20:15Future research directions

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