| Safe Haskell | None |
|---|---|
| Language | Haskell2010 |
Crypto.Lol.Cyclotomic.Linear
Description
Functions from one cyclotomic ring to another that are linear over a common subring.
- data Linear t z e r s
- type ExtendLinIdx e r s e' r' s' = (Fact r, e ~ FGCD r e', r' ~ FLCM r e', e' `Divides` s', s `Divides` s')
- linearDec :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => [Cyc t s z] -> Linear t z e r s
- evalLin :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => Linear t z e r s -> Cyc t r z -> Cyc t s z
- extendLin :: (ExtendLinIdx e r s e' r' s', CElt t z) => Linear t z e r s -> Linear t z e' r' s'
Documentation
An E-linear function from R to S.
Instances
| NFData (Cyc t s z) => NFData (Linear t z e r s) Source | |
| Additive (Cyc t s z) => C (Linear t z e r s) Source | |
| (CElt t zp, CElt t z, (~) * z (LiftOf zp), Lift zp z, Fact s) => Lift' (Linear t zp e r s) Source | |
| (Reduce z zq, Fact s, CElt t z, CElt t zq) => Reduce (Linear t z e r s) (Linear t zq e r s) Source | |
| type LiftOf (Linear t zp e r s) = Linear t (LiftOf zp) e r s Source |
type ExtendLinIdx e r s e' r' s' = (Fact r, e ~ FGCD r e', r' ~ FLCM r e', e' `Divides` s', s `Divides` s') Source
A convenient constraint synonym for extending a linear function to larger rings.
linearDec :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => [Cyc t s z] -> Linear t z e r s Source
Construct an E-linear function given a list of its output values
(in S) on the relative decoding basis of R/E. The number of
elements in the list must not exceed the size of the basis.
evalLin :: forall t z e r s. (e `Divides` r, e `Divides` s, CElt t z) => Linear t z e r s -> Cyc t r z -> Cyc t s z Source
Evaluates the given linear function on the input.
extendLin :: (ExtendLinIdx e r s e' r' s', CElt t z) => Linear t z e r s -> Linear t z e' r' s' Source
Extend an E-linear function R->S to an E'-linear function
R'->S'. (Mathematically, such extension only requires
lcm(r,e') | r' (not equality), but this generality would
significantly complicate the implementation, and for our purposes
there's no reason to use any larger r'.)