Add Kurihara n-of-m threshold XOR mnemonic backup (core + tests + docs) - #366
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Add Kurihara n-of-m threshold XOR mnemonic backup (core + tests + docs)#366CaverneCrypto wants to merge 1 commit into
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Adds the pure, GUI-less core of an n-of-m threshold backup for BIP39 mnemonics. Any n of m shares reconstruct the seed; strictly fewer than n reveal nothing (perfect, information-theoretic confidentiality up to the threshold). Each share is exactly the size of the secret and re-encodes to a valid BIP39 mnemonic. - src/kurihara.py: scheme (split / reconstruct / regenerate lost share) via Gaussian elimination over GF(2). The arithmetic core has no external dependency (embit imported lazily for the BIP39 glue; rng injectable). - test/tests/test_kurihara.py: 15 unit tests (every coalition reconstructs, sub-threshold rejected, lost-share regeneration is bit-identical, BIP39 round-trip, deterministic known-answer vector). - docs/threshold-backup.md + mkdocs nav entry. Underlying scheme: Kurihara, Kiyomoto, Fukushima, Tanaka, ISC 2008 (https://eprint.iacr.org/2008/409). BIP39 adaptation, derivation, security verification and templates: https://doi.org/10.5281/zenodo.20734041 (CC BY 4.0). GUI/app wiring is intended as a follow-up PR so the security-critical math can be reviewed in isolation first. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Summary
Adds an
n-of-mthreshold backup for BIP39 mnemonics, based on the ideal threshold XOR secret-sharing scheme of Kurihara et al. (ISC 2008). A seed is split intomshares such that anynreconstruct it, while anyn − 1reveal nothing (perfect, information-theoretic confidentiality up to the threshold). Reconstruction reduces to XORs of hex strings — no finite-field arithmetic — so it is also a pen-and-paper procedure. Each share is exactly the size of the secret and re-encodes to a valid BIP39 mnemonic (plausible deniability).There is currently no share-based backup in Specter-DIY (no SeedXOR / Shamir / SLIP-39); this fills that gap.
Scope of this PR
Audited arithmetic core + unit tests + docs only — no on-device GUI yet. Wiring it into an app/menu is intended as a follow-up PR, so the security-critical math can be reviewed in isolation first.
src/kurihara.py— the scheme: split / reconstruct / regenerate a lost share, via Gaussian elimination over GF(2) (coefficient rows as column-index sets, no big-int bitmasks → MicroPython-friendly). The arithmetic core has no external dependency;embitis imported lazily only for the BIP39 glue, and the randomness source is injectable (defaults torng.get_random_bytes).test/tests/test_kurihara.py— 15 unit tests: everyn-coalition reconstructs; every(n − 1)-coalition is rejected; lost-share regeneration is bit-for-bit identical and usable; each share encodes to a valid mnemonic and the secret round-trips through the mnemonics; a deterministic known-answer vector guards the construction.docs/threshold-backup.md(+ mkdocs nav entry).Profiles
Testing
All 15 tests pass. They are written for the simulator suite (
make test) and also run under the project's native CPython harness (realembit).make testwill exercise them in CI.References
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