{
  "type": "option",
  "name": "Binius and binary-field systems",
  "slug": "binius",
  "section": {
    "id": "proof-systems",
    "number": "01",
    "title": "Choosing a proof system",
    "url": "https://zkpick.com/proof-systems/"
  },
  "url": "https://zkpick.com/proof-systems/binius/",
  "markdown": "https://zkpick.com/md/proof-systems/binius.md",
  "category": "Transparent hash-based, binary fields",
  "summary": "Binius and binary-field systems: Transparent hash-based, binary fields. Setup: None. Proof size: Hash-based scale. On-chain verification: Impractical directly. PQ: Plausibly. Recursion: Developing. Maturity: Early production; fast-moving codebase. Prover cost profile: Binary-field arithmetic maps to hardware bit operations; strongest on hashing and bitwise workloads. Peak prover memory: Low — tiny field elements, no embedding overhead. Off-chain verifier: Milliseconds. Implementations and maintainers: Binius64 (Irreducible); the original binius repository is archived. Where it is measured: Irreducible's published figures; few independent measurements. Assumption: Hash over binary fields. Setup: None. Opening size: Hash-based scale. Verifier cost: Polylogarithmic. Field constraint: Binary field towers. Choose it when: Hash- and bitwise-heavy workloads, and client-side proving, for teams able to track a fast-moving codebase.",
  "description": "SNARKs over towers of binary fields, with a commitment that has no embedding overhead for tiny field elements. The current generation computes natively over 64-bit words with built-in bitwise and multiplication constraints, explicitly targeting client-side proving on commodity CPUs.",
  "notes": [],
  "sections": [],
  "strengths": [
    "Binary-field arithmetic maps directly to hardware bit operations — a strong fit for hashing, ciphers and bit manipulation",
    "No trusted setup; hash-based and plausibly post-quantum",
    "Explicitly targets commodity CPUs rather than GPU clusters"
  ],
  "tradeoffs": [
    "The most volatile family here: the original implementation was archived and superseded, with significant features still on the roadmap at the successor's launch — confirm current capability before designing around it",
    "Small implementation and auditor base",
    "Not directly on-chain verifiable"
  ],
  "bestFit": "Hash- and bitwise-heavy workloads, and client-side proving, for teams able to track a fast-moving codebase.",
  "maintainers": "Diamond and Posen (Irreducible, formerly Ulvetanna, 2023). Implementation: Binius64 (Irreducible)",
  "maturity": "Early production; active development",
  "license": "https://creativecommons.org/licenses/by/4.0/",
  "source": "https://eprint.iacr.org/2023/1784",
  "facts": [
    {
      "table": "Proof system selection matrix",
      "url": "https://zkpick.com/proof-systems/#proof-systems-matrix-binius-binary-fields",
      "name": "Binius (binary fields)",
      "setup": "None",
      "size": "Hash-based scale",
      "verify": "Impractical directly",
      "pq": "Plausibly",
      "recursion": "Developing",
      "maturity": "Early production; fast-moving codebase"
    },
    {
      "table": "Prover profile, implementations and benchmarks",
      "url": "https://zkpick.com/proof-systems/#proof-systems-matrix-2-binius-binary-fields",
      "name": "Binius (binary fields)",
      "prover": "Binary-field arithmetic maps to hardware bit operations; strongest on hashing and bitwise workloads",
      "memory": "Low — tiny field elements, no embedding overhead",
      "offchain": "Milliseconds",
      "impls": "Binius64 (Irreducible); the original binius repository is archived",
      "bench": "Irreducible's published figures; few independent measurements"
    },
    {
      "table": "Commitment schemes — the layer that decides most of it",
      "url": "https://zkpick.com/proof-systems/#proof-systems-matrix-3-binius-commitments",
      "name": "Binius commitments",
      "basis": "Hash over binary fields",
      "setup": "None",
      "opening": "Hash-based scale",
      "verifier": "Polylogarithmic",
      "field": "Binary field towers"
    }
  ],
  "relatedFailureModes": [],
  "sources": [
    {
      "title": "Binius — succinct arguments over towers of binary fields",
      "url": "https://eprint.iacr.org/2023/1784",
      "kind": "paper"
    }
  ],
  "updated": "2026-09-12",
  "version": "1.3",
  "canonical": "https://zkpick.com/proof-systems/binius/",
  "authors": [
    "MarketComp"
  ]
}