Proofs - Practice 2
Talkat Cryptography 10 Years Later: Obfuscation, Proof Systems, and Secure Computation Boot Camp 2025 · 2025-05-19..05-23·
summary
Explains why the sum-check protocol replaces heavy quotienting: it keeps prover work to field adds/muls, lets verifiers check huge sums by iterated univariate tests, and turns many intermediate polynomials into virtual polynomials so they never get committed. Reports concrete scales: Ethereum blocks are ~a billion RISC‑V cycles; classic GKR costs ~6n field multiplies for prover; Jolt + Shout/Twist cuts proof size by ~5x and speeds prover components by 2–7x. Describes committing inputs via one-hot format and exploiting extreme sparsity and block structure; notes 25 zkVM teams, ~5 using sum-check.
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chapters (15)
- 0:00Polynomial IOPs and sum-check
- 1:09Sum-check in SNARK design
- 5:04Multilinear extensions role
- 6:32Sum-check step-by-step
- 13:48Univariate to multilinear sum-check
- 22:12Sum-check prover gains
- 22:54zkVMs purpose
- 25:51Real-time Ethereum proving
- 31:18zkVMs vs zkDSLs debate
- 34:11Jolt zkVM case study
- 38:20Batch evaluation arguments
- 45:16Lookup arguments comparison
- 50:57Shout protocol commitments
- 1:00:10One-hot vectors handling
- 1:03:48Key takeaways and future
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