Series → #ZK SNARKs in production
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Range proofs in 80 lines: Pedersen commitments and a tiny Bulletproof
How a Bulletproof actually compresses a range proof to logarithmic size. Derive the inner-product argument from scratch, run a toy prover/verifier in the browser, and pick the right range-proof primitive for 2026.
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Why BN254, and when to switch off it
BN254 is the default curve for production ZK in 2026. The 128-bit security claim is no longer 128 bits, and BLS12-381 is gaining ground. Here is the math, the deployment reality, and the migration path.
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Poseidon, by hand and by code
Why one of the cheapest hashes in zero-knowledge cryptography also has the strangest insides. Derive the S-box, count the constraints, and run a 30-line implementation in the browser.
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Merkle inclusion proofs over compressed account state on Solana
How a 32-byte hash and a logarithmic path replace a multi-kilobyte account. Walk the tree-height math, the Light Protocol compressed-account model, and an inclusion-proof construction you can run in Node.
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Proving in the browser, by the numbers
What is actually feasible inside a browser tab in 2026 — Groth16 prover times for Poseidon, Range, and Merkle circuits, the WASM threading story, and where the main thread stops being a viable home for your prover.
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Circom, by example
A DSL primer told through one circuit — proving knowledge of a Poseidon pre-image. Every Circom keyword annotated as it appears, the constraint graph drawn out, and the R1CS fall-through to a witness.
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Halo2 in 2026: what changed since the Zcash era
A survey of the Halo2 ecosystem six years after the Zcash team published it — what stayed the same (PLONKish, lookups, IPA), what evolved (KZG, gadget libraries, fork landscape), and what we ship today.
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Recursive proof composition without the abyss: Halo to Nova
The path from Halo's accumulation scheme to Nova's folding scheme, derived from the recurrence relation. Where Halo2, Nova, SuperNova, and HyperNova actually differ, and which one to reach for in 2026.
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Plonky3, the small-fast-cheap revolution
Why plonky3 — small fields, FRI commitments, no trusted setup — is the proof system to watch in 2026. The Mersenne31 / BabyBear / Goldilocks landscape, the FRI folding step, and why your laptop is suddenly a viable prover.
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On the death of the trusted setup
Universal SRS, transparent FRI, and why Groth16's per-circuit ceremony feels anachronistic in 2026 — even when, as ZERA does, you're still using one. A history of the ceremonies that worked, the ones that didn't, and what comes next.