the privacy computation language. Curve type system for anonymous operations over the cybergraph.
computation in Sec uses the commutative group action on supersingular curves: the genies algebra. the Curve type carries this semantics — the Trident compiler sees Curve operands and routes to genies regime automatically. no annotations needed.
types
Curve supersingular elliptic curve over F_q
Secret exponent vector (secret key)
StealthAddress receiver-anonymous address
RingSignature one-of-n anonymous signature
BlindSignature signer-blind signed message
VRFOutput verifiable random value + proof
SharedSecret derived shared secret (hemera digest)
operations
| operation | Trident | what it computes |
|---|---|---|
| group_action(sk, pk) | Secret, Curve → Curve | isogeny walk |
| agree(sk, pk) | Secret, Curve → SharedSecret | non-interactive key exchange |
| stealth_send(sk, pk) | Secret, Curve → StealthAddress | anonymous addressing |
| ring_sign(msg, ring, sk) | Hash, [Curve], Secret → RingSignature | anonymous signing |
| vrf_eval(sk, input) | Secret, Hash → VRFOutput | verifiable randomness |
| vdf_prove(prev, T) | Hash, u64 → VDFProof | time proof |
regime
Curve type → genies regime → Isogeny lens → zheng proves via F_q Brakedown
jets: jet_group_action, jet_isogeny_walk, jet_vrf_eval, jet_vdf_step, jet_secret_hash
why a language
every time a neuron transacts without revealing identity, proves membership without revealing which member, delegates authority without exposing the chain, or generates verifiable randomness — it thinks in Sec. privacy is not a feature — it is a computation domain with its own algebra, its own lens, and its own jets.
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