Lattice module¶

General lattice functions¶

pqlattice.lattice.volume ¶

volume(lattice_basis: SquareMatrix) -> int

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required

Returns:

Type	Description
`int`	description

pqlattice.lattice.rank ¶

rank(lattice_basis: SquareMatrix) -> int

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required

Returns:

Type	Description
`int`	description

pqlattice.lattice.hadamard_ratio ¶

hadamard_ratio(lattice_basis: SquareMatrix) -> float

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required

Returns:

Type	Description
`float`	description

pqlattice.lattice.discriminant ¶

discriminant(lattice_basis: SquareMatrix) -> int

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required

Returns:

Type	Description
`int`	description

pqlattice.lattice.gaussian_heuristic ¶

gaussian_heuristic(lattice_basis: SquareMatrix) -> float

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required

Returns:

Type	Description
`float`	description

pqlattice.lattice.is_lll_reduced ¶

is_lll_reduced(
    lattice_basis: SquareMatrix, delta: float = 0.99
) -> bool

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required
`delta`	`float`	description, by default 0.99	`0.99`

Returns:

Type	Description
`bool`	description

pqlattice.lattice.is_size_reduced ¶

is_size_reduced(lattice_basis: SquareMatrix) -> bool

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required

Returns:

Type	Description
`bool`	description

Lattice reduction algorithms¶

pqlattice.lattice.gso ¶

gso(B: Matrix) -> tuple[Matrix, SquareMatrix]

summary

Parameters:

Name	Type	Description	Default
`B`	`Matrix`	description	required

Returns:

Type	Description
`tuple[Matrix, SquareMatrix]`	description

pqlattice.lattice.lll ¶

lll(
    lattice_basis: SquareMatrix, delta: float = 0.99
) -> SquareMatrix

pqlattice.lattice.bkz ¶

bkz(
    lattice_basis: SquareMatrix,
    block_size: int = 10,
    delta: float = 0.99,
) -> SquareMatrix

pqlattice.lattice.hkz ¶

hkz(
    lattice_basis: SquareMatrix, delta: float = 0.99
) -> SquareMatrix

pqlattice.lattice.glr_2dim ¶

glr_2dim(lattice_basis: SquareMatrix) -> SquareMatrix

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required

Returns:

Type	Description
`SquareMatrix`	description

Raises:

Type	Description
`ValueError`	description

SVP and CVP¶

pqlattice.lattice.shortest_vector ¶

shortest_vector(lattice_basis: SquareMatrix) -> Vector

pqlattice.lattice.babai_closest_vector ¶

babai_closest_vector(
    lattice_basis: SquareMatrix, target_vector: Vector
) -> Vector

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required
`target_vector`	`Vector`	description	required

Returns:

Type	Description
`Vector`	description

pqlattice.lattice.babai_nearest_plane ¶

babai_nearest_plane(
    lattice_basis: SquareMatrix, target_vector: Vector
) -> Vector

summary

Parameters:

Name	Type	Description	Default
`lattice_basis`	`SquareMatrix`	description	required
`target_vector`	`Vector`	description	required

Returns:

Type	Description
`Vector`	description

Lattice embeddings¶

pqlattice.lattice.embeddings.sis_basis ¶

sis_basis(A: Matrix, q: int) -> SquareMatrix

lattice: L = { x | Ax = 0 mod q }

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`q`	`int`	description	required

Returns:

Type	Description
`SquareMatrix`	description

pqlattice.lattice.embeddings.lwe_basis ¶

lwe_basis(A: Matrix, q: int) -> SquareMatrix

lattice: L = { y | y = xA mod q }

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`q`	`int`	description	required

Returns:

Type	Description
`SquareMatrix`	description

pqlattice.lattice.embeddings.kannan ¶

kannan(A: Matrix, b: Vector, q: int) -> SquareMatrix

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`b`	`Vector`	description	required
`q`	`int`	description	required

Returns:

Type	Description
`SquareMatrix`	description

pqlattice.lattice.embeddings.bai_galbraith ¶

bai_galbraith(
    A: Matrix, b: Vector, q: int, M: int
) -> SquareMatrix

summary

Parameters:

Name	Type	Description	Default
`A`	`Matrix`	description	required
`b`	`Vector`	description	required
`q`	`int`	description	required
`M`	`int`	description	required

Returns:

Type	Description
`SquareMatrix`	description

pqlattice.lattice.embeddings.subset_sum ¶

subset_sum(sequence: Vector, S: int) -> SquareMatrix

summary

Parameters:

Name	Type	Description	Default
`sequence`	`Vector`	description	required
`S`	`int`	description	required

Returns:

Type	Description
`SquareMatrix`	description

pqlattice.lattice.embeddings.ntru ¶

ntru(quotient: Vector, q: int, h: Vector) -> SquareMatrix

construct the ntru lattice basis

Parameters:

Name	Type	Description	Default
`quotient`	`Vector`	description	required
`q`	`int`	description	required
`h`	`Vector`	description	required

Returns:

Type	Description
`SquareMatrix`	description