Zero-knowledge proofs, applied cryptography, and the math behind them — explained without the hand-waving.https://zkcryptographer.example/en-ushttps://zkcryptographer.example/blog/what-zero-knowledge-proofs-actually-prove/https://zkcryptographer.example/blog/what-zero-knowledge-proofs-actually-prove/A plain-language walkthrough of completeness, soundness, and zero-knowledge — the three properties every ZK protocol has to satisfy, with no hand-waving.Fri, 02 Oct 2026 00:00:00 GMTZero-Knowledgehttps://zkcryptographer.example/blog/modular-arithmetic-clock-math/https://zkcryptographer.example/blog/modular-arithmetic-clock-math/Why every cryptographic protocol you'll ever touch secretly runs on clock arithmetic, and how to build the intuition that makes it click.Mon, 28 Sep 2026 00:00:00 GMTMathhttps://zkcryptographer.example/blog/hash-functions-demystified/https://zkcryptographer.example/blog/hash-functions-demystified/SHA-256, Poseidon, and why ZK-friendly hashing is a different design problem entirely — a tour of what makes a hash function 'circuit-friendly.'Thu, 24 Sep 2026 00:00:00 GMTCryptographyhttps://zkcryptographer.example/blog/debugging-a-circuit-that-wont-verify/https://zkcryptographer.example/blog/debugging-a-circuit-that-wont-verify/A field guide to the most common reasons a correct-looking circuit fails verification, from witness mismatches to constraint typos.Sat, 19 Sep 2026 00:00:00 GMTZK Developmenthttps://zkcryptographer.example/blog/groth16-vs-plonk-vs-starks/https://zkcryptographer.example/blog/groth16-vs-plonk-vs-starks/Proof size, prover time, trusted setup requirements, and tooling maturity compared head-to-head for teams shipping production ZK today.Mon, 14 Sep 2026 00:00:00 GMTZK Developmenthttps://zkcryptographer.example/blog/trusted-setups-explained/https://zkcryptographer.example/blog/trusted-setups-explained/What a ceremony actually produces, why it matters, and how transparent setups like STARKs sidestep the problem entirely.Wed, 09 Sep 2026 00:00:00 GMTZero-Knowledgehttps://zkcryptographer.example/blog/lattice-based-cryptography-gentle-on-ramp/https://zkcryptographer.example/blog/lattice-based-cryptography-gentle-on-ramp/The shortest-vector problem, why quantum computers don't break it, and how lattices are becoming the backbone of post-quantum standards.Fri, 04 Sep 2026 00:00:00 GMTPost-Quantum Cryptographyhttps://zkcryptographer.example/blog/this-month-in-zk-ecosystem-roundup/https://zkcryptographer.example/blog/this-month-in-zk-ecosystem-roundup/New proving system releases, protocol upgrades, and the research papers worth your weekend reading time.Sun, 30 Aug 2026 00:00:00 GMTNews/Ecosystemhttps://zkcryptographer.example/blog/formally-verifying-a-zksnark-circuit/https://zkcryptographer.example/blog/formally-verifying-a-zksnark-circuit/Using proof assistants to mechanically check that a circuit's constraints really do encode the statement you think they encode.Tue, 25 Aug 2026 00:00:00 GMTFormal Verificationhttps://zkcryptographer.example/blog/elliptic-curves-without-the-trauma/https://zkcryptographer.example/blog/elliptic-curves-without-the-trauma/Point addition, scalar multiplication, and the discrete log problem — built up visually, one picture at a time.Thu, 20 Aug 2026 00:00:00 GMTMathhttps://zkcryptographer.example/blog/nist-post-quantum-standards-what-changes/https://zkcryptographer.example/blog/nist-post-quantum-standards-what-changes/ML-KEM, ML-DSA, and SLH-DSA are now standardized — here's what migrating a real system actually involves.Sat, 15 Aug 2026 00:00:00 GMTPost-Quantum Cryptographyhttps://zkcryptographer.example/blog/why-formally-verified-doesnt-mean-bug-free/https://zkcryptographer.example/blog/why-formally-verified-doesnt-mean-bug-free/A proof assistant checks your spec against your code — it can't check that your spec means what you think it means.Mon, 10 Aug 2026 00:00:00 GMTFormal Verification