commutative group action over supersingular isogenies for cyber. genies is the privacy engine — where nebu proves truth, genies proves that truth was revealed selectively.
the one module with a foreign prime. F_q where q = 4·ℓ₁·ℓ₂·...·ℓₙ - 1. not because the design is incomplete, but because mathematics does not permit post-quantum commutative group actions over Goldilocks.
three properties
- post-quantum security — no known quantum algorithm breaks the class group action
- commutative group action — non-interactive protocols from one primitive
- compact representation — public keys ~64 bytes
all three over Goldilocks — open problem in cryptography.
privacy applications
| application | what it enables |
|---|---|
| stealth addresses | receiver-anonymous payments |
| non-interactive key exchange | shared secret without interaction |
| verifiable random functions | deterministic randomness with proof |
| verifiable delay functions | time proofs (sequential computation) |
| threshold protocols | t-of-n key generation, signing |
| oblivious transfer | sender sends N, receiver gets 1 |
| blind signatures | signer signs without seeing message |
| ring signatures | sign as "one of group" anonymously |
| anonymous credentials | prove attributes without revealing identity |
| updatable encryption | re-encrypt without decrypting |
nox integration
Layer 3 jets: jet_genies_action, jet_genies_dh, jet_genies_vrf, jet_genies_vdf, jet_genies_threshold, jet_genies_blind.
verification: isogeny computation over F_q, zheng proof folds into Goldilocks accumulator. shadow executes in its own field, proof lands in nebu.
dependency graph
nebu (F_p) — proof backbone, accumulator
↓
genies (F_q) ← this repo
↓
nox (jets)
↓
zheng (proof of correct privacy operation)
↓
bbg (private state: UTXO, mutator set)
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