{"id":51430491,"url":"https://github.com/oxarbitrage/halo2-formal","last_synced_at":"2026-07-05T03:30:43.046Z","repository":{"id":355228089,"uuid":"1227281725","full_name":"oxarbitrage/halo2-formal","owner":"oxarbitrage","description":null,"archived":false,"fork":false,"pushed_at":"2026-05-02T13:35:15.000Z","size":11,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2026-05-02T15:29:37.335Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Lean","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/oxarbitrage.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null,"notice":null,"maintainers":null,"copyright":null,"agents":null,"dco":null,"cla":null}},"created_at":"2026-05-02T13:16:31.000Z","updated_at":"2026-05-02T13:35:19.000Z","dependencies_parsed_at":null,"dependency_job_id":null,"html_url":"https://github.com/oxarbitrage/halo2-formal","commit_stats":null,"previous_names":["oxarbitrage/halo2-formal"],"tags_count":null,"template":false,"template_full_name":null,"purl":"pkg:github/oxarbitrage/halo2-formal","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/oxarbitrage%2Fhalo2-formal","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/oxarbitrage%2Fhalo2-formal/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/oxarbitrage%2Fhalo2-formal/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/oxarbitrage%2Fhalo2-formal/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/oxarbitrage","download_url":"https://codeload.github.com/oxarbitrage/halo2-formal/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/oxarbitrage%2Fhalo2-formal/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":35142824,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-07-05T02:00:06.290Z","response_time":100,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":[],"created_at":"2026-07-05T03:30:42.375Z","updated_at":"2026-07-05T03:30:43.035Z","avatar_url":"https://github.com/oxarbitrage.png","language":"Lean","funding_links":[],"categories":[],"sub_categories":[],"readme":"# halo2-formal\n\n**Status:** Fully proven — zero `sorry` statements.\n\nLean 4 formalization of core Halo 2 components: PLONKish constraint system, elliptic curve gadgets, Sinsemilla circuit gadget, and Fiat-Shamir transcript.\n\n## What's formalized\n\n**Key results:**\n\n- **`sinsemilla_circuit_pedersen`** — the Sinsemilla circuit gadget computes [2ⁿ]·Q(D) + Σᵢ 2^(n−1−i)·S(mᵢ): the circuit matches the protocol spec.\n- **`fixedBaseMul_eq_smul`**, **`variableBaseMul_eq_smul`** — fixed-base (3-bit windowed) and variable-base (double-and-add) scalar multiplication circuits equal standard scalar multiplication.\n- **`addGate_sound`**, **`mulGate_sound`**, **`boolGate_sound`** — gate satisfaction implies the claimed arithmetic relation.\n- **`range_check_soundness`** / **`range_check_completeness`** — base-b decomposition is sound and complete.\n- **`transcript_separation`** — distinct domain or value → distinct Fiat-Shamir challenge.\n\n## Axioms\n\n| Axiom | Justification |\n|-------|--------------|\n| `permCheck_sound` | Schwartz-Zippel soundness — probabilistic argument, see inline doc comment |\n| `ipaCompleteness` | IPA completeness — deep proof theory, not yet in Mathlib |\n| `poseidon_collision_resistant` | Conjectured; not derivable from `permutation_bijective` |\n| `add_ne_zero_of_nonexceptional` | DLP assumption for EC sum non-zeroness |\n\n## Build\n\n```shell\nlake build\n```\n\n## Dependencies\n\nLean 4 (`v4.30.0-rc2`), [Mathlib4](https://github.com/leanprover-community/mathlib4), [pasta-formal](https://github.com/oxarbitrage/pasta-formal), [poseidon-formal](https://github.com/oxarbitrage/poseidon-formal), [sinsemilla-formal](https://github.com/oxarbitrage/sinsemilla-formal).\n\n## References\n\n- [Halo 2 book](https://zcash.github.io/halo2/)\n- [PLONKish arithmetization](https://zcash.github.io/halo2/concepts/arithmetization.html)\n- [PLONK paper](https://eprint.iacr.org/2019/953)\n\n---\n\n## Part of a series\n\nSix repositories formally verifying the Zcash Orchard cryptographic stack:\n\n| Layer | Repository |\n|-------|-----------|\n| Curves | [pasta-formal](https://github.com/oxarbitrage/pasta-formal) |\n| Hash | [poseidon-formal](https://github.com/oxarbitrage/poseidon-formal) |\n| Hash-to-curve | [sinsemilla-formal](https://github.com/oxarbitrage/sinsemilla-formal) |\n| Signatures | [redpallas-formal](https://github.com/oxarbitrage/redpallas-formal) |\n| Protocol | [orchard-formal](https://github.com/oxarbitrage/orchard-formal) |\n| Proof system | [halo2-formal](https://github.com/oxarbitrage/halo2-formal) |\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Foxarbitrage%2Fhalo2-formal","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Foxarbitrage%2Fhalo2-formal","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Foxarbitrage%2Fhalo2-formal/lists"}