genies specification
canonical reference for isogeny group action arithmetic: F_q field operations, supersingular curves, isogeny computation, and class group action.
spec pages
| page |
defines |
| prime |
CSIDH prime form, selection criteria, concrete parameters, F_q arithmetic |
| curves |
supersingular elliptic curves over F_q, point operations, j-invariant |
| isogeny |
l-isogeny computation, Velu formulas, kernel polynomials |
| class-group |
class group cl(O), ideal representation, mathematical structure |
| action |
class group action algorithm, cost model, constant-time considerations |
| encoding |
F_q element serialization, curve point encoding, secret key format |
| verification |
F_q to F_p folding for zheng proofs |
| vectors |
known-answer test values for all operations |
see also
- nebu — Goldilocks field (proof accumulator)
- kuro — binary field (complementary regime)
- mudra — protocols built on genies (CSIDH, VRF, VDF, threshold, stealth, blind)
Dimensions
lens/specs
lens reference canonical specification for polynomial commitment — five lenses for five algebras. the trait three operations. commit is O(N). open produces a proof. verify checks the proof. all transparent (no trusted setup), all post-quantum. see trait for the full specification. naming convention…
zheng/specs
zheng: polynomial proof system one IOP: SuperSpartan + sumcheck (CCS constraints, O(N) prover, O(log N) verifier). one folding: HyperNova (CCS-native, ~30 field ops per fold, one decider at the end). one hash: hemera (~3 calls per proof — binding, Fiat-Shamir seed, domain separation). five…
trop/specs
trop specification canonical reference for tropical semiring arithmetic: the (min, +) semiring, its matrix algebra, and dual certificate verification. spec pages | page | defines | |------|---------| | [semiring](/trop/specs/semiring) | tropical semiring axioms, (min, +) definition, identity…
bbg/specs
specs
nox/specs
nox reference canonical specification of the nox virtual machine. this is the source of truth — when code and reference disagree, fix reference first, then propagate to code. specifications | page | scope | status | |------|-------|--------| | vm.md | overview, field, hash, algebra polymorphism,…
hemera/specs
Hemera: A Permanent Hash Primitive for Planetary-Scale Collective Intelligence | field | value | |----------|--------------------------------| | version | 2.0 | | status | Decision Record | | authors | mastercyb | | date | March 2026 | Abstract Hemera is the cryptographic hash primitive for cyber,…
nebu/specs
nebu specification canonical reference for the Goldilocks prime field, its arithmetic, and its hardware. spec pages | page | defines | |------|---------| | field | prime, elements, arithmetic, properties, why Goldilocks | | ntt | Number Theoretic Transform, roots of unity, butterfly, Cooley-Tukey |…
jali/specs
jali reference canonical specification for polynomial ring arithmetic R_q = F_p[x]/(x^n+1) over Goldilocks. what jali is jali (जाली — lattice/mesh) is the fifth execution algebra for cyber. polynomial ring elements are structured vectors of n Goldilocks field elements with multiplication defined by…
kuro/specs
kuro specification canonical reference for the F₂ tower field, its arithmetic, packed operations, and hardware targets. spec pages | page | defines | |------|---------| | [field](/kuro/specs/field) | tower levels, all field operations, properties, cost model vs Goldilocks | |…