Random module¶

Distributions¶

pqlattice.random.distribution.Uniform ¶

Uniform(
    range_beg: int, range_end: int, seed: int | None = None
)

Bases: Distribution

Creates a uniform sampler from range [range_beg; range_end].

Parameters:

Name	Type	Description	Default
`range_beg`	`int`	begin of sampling range. Inclusive	required
`range_end`	`int`	end of sampling range. Inclusive	required
`seed`	`int \| None`	seed for random number generator, by default None	`None`

get_params ¶

get_params() -> dict[str, int]

returns dictionary of parameters of the distribution

Returns:

Type	Description
`dict[str, int]`	dict `d = {"range_beg": self._range_beg, "range_end": self._range_end}`

sample_int ¶

sample_int(seed: int | None = None) -> int

Get uniform random int from range [self.beg_range, self.end_range]

Parameters:

Name	Type	Description	Default
`seed`	`int \| None`	set the new seed, if None does nothing, by default None	`None`

Returns:

Type	Description
`int`	random integer from range [self.beg_range, self.end_range]

sample_matrix ¶

sample_matrix(
    rows: int,
    cols: int | None = None,
    seed: int | None = None,
) -> Matrix

Get a matrix of random uniform ints. Each element of the matrix is sampled from range [self.beg_range, self.end_range].

Parameters:

Name	Type	Description	Default
`rows`	`int`	number of rows	required
`cols`	`int \| None`	number of cols, if None equal to number of rows , by default None	`None`
`seed`	`int \| None`	set the new seed, if None does nothing, by default None	`None`

Returns:

Type	Description
`Matrix`	matrix `m` with shape `(rows, cols)` and random elements from range `[self.beg_range, self.end_range]`

sample_vector ¶

sample_vector(n: int, seed: int | None = None) -> Vector

Get a vector of random uniform ints. Each element of the vector is sampled from range [self.beg_range, self.end_range].

Parameters:

Name	Type	Description	Default
`n`	`int`	dimension of the vector	required
`seed`	`int \| None`	set the new seed, if None does nothing, by default None	`None`

Returns:

Type	Description
`Vector`	vector `v` with shape `(n,)` and random elements from range `[self.beg_range, self.end_range]`

set_params ¶

set_params(
    range_beg: int | None = None,
    range_end: int | None = None,
) -> None

Set the parameters of the distribution

Parameters:

Name	Type	Description	Default
`range_beg`	`int \| None`	if None does nothing, by default None	`None`
`range_end`	`int \| None`	if None does nothing, by default None	`None`

pqlattice.random.distribution.DiscreteGaussian ¶

DiscreteGaussian(
    sigma: float,
    center: int | float = 0,
    tail_cut: float = 6.0,
    seed: int | None = None,
)

Bases: Distribution

Creates DiscreteGaussian sampler that uses rejection sampling method. Samples x are accepted with probability `exp(-((x - center) ** 2) / (2 * sigma ** 2)).

Parameters:

Name	Type	Description	Default
`sigma`	`float`	standard deviation of the distribution	required
`center`	`int \| float`	mean of the distribution, by default 0	`0`
`tail_cut`	`float`	samples outside the range `[center - sigma * tail_cut, center + sigma * tail_cut]` are considered to have probability zero, by default 6.0	`6.0`
`seed`	`int \| None`	seed for random number generator, by default None	`None`

get_params ¶

get_params() -> dict[str, float]

returns dictionary of parameters of the distribution

Returns:

Type	Description
`dict[str, float]`	dict `d = {"sigma": self.sigma, "center": self.center, "tail_cut": self.tail_cut, "bound": self.bound}`

sample_int ¶

sample_int(seed: int | None = None) -> int

Get random int according to the gaussian probability.

Parameters:

Name	Type	Description	Default
`seed`	`int \| None`	set the new seed, if None does nothing, by default None	`None`

Returns:

Type	Description
`int`	random integer sampled from discrete gaussian distribution

sample_matrix ¶

sample_matrix(
    rows: int,
    cols: int | None = None,
    seed: int | None = None,
) -> Matrix

Get a matrix of integers sampled from discrete gaussian distribution.

Parameters:

Name	Type	Description	Default
`rows`	`int`	number of rows	required
`cols`	`int \| None`	number of cols, if None equal to number of rows , by default None	`None`
`seed`	`int \| None`	set the new seed, if None does nothing, by default None	`None`

Returns:

Type	Description
`Matrix`	matrix `m` with shape `(rows, cols)` and random elements from discrete gaussian distribution.

sample_vector ¶

sample_vector(n: int, seed: int | None = None) -> Vector

Get a vector of integers sampled from discrete gaussian distribution.

Parameters:

Name	Type	Description	Default
`n`	`int`	dimension of the vector	required
`seed`	`int \| None`	set the new seed, if None does nothing, by default None	`None`

Returns:

Type	Description
`Vector`	vector `v` with shape `(n,)` and random elements from discrete gaussian distribution.

set_params ¶

set_params(
    sigma: float | None = None,
    center: float | int | None = None,
    tail_cut: float | None = None,
) -> None

Set the parameters of the distribution

Parameters:

Name	Type	Description	Default
`sigma`	`float \| None`	if None does nothing, by default None	`None`
`center`	`float \| int \| None`	if None does nothing, by default None	`None`
`tail_cut`	`float \| None`	if None does nothing, by default None	`None`

Learning with errors¶

pqlattice.random.LWE ¶

LWE(
    n: int,
    q: int,
    sigma: float,
    secret_distribution: str,
    seed: int,
)

Creates LWE sampler with DiscreteGuassianDistribution centered at 0 as noise sampler

Parameters:

Name	Type	Description	Default
`n`	`int`	length of secret vector	required
`q`	`int`	modulus	required
`sigma`	`float`	sigma value for DiscreteGaussianDistribution	required
`seed`	`int`	seed for random number generator	required

secret `property` ¶

secret: Vector

Retrieve underlying secret

Returns:

Type	Description
`Vector`	s: n-vector

next_sample ¶

next_sample() -> tuple[Vector, int]

Generates a single sample pair (a, b).

Returns:

Type	Description
`tuple[Vector, int]`	a (Vector): n-vector (Uniform mod q) b (int): as + e mod q

sample_matrix ¶

sample_matrix(m: int) -> tuple[Matrix, Vector]

Generates a full matrix system (A, b) with 'm' samples.

Parameters:

Name	Type	Description	Default
`m`	`int`	how many samples should the resulting matrix have	required

Returns:

Type	Description
`tuple[Matrix, Vector]:`	A (Matrix): m x n matrix (Uniform mod q) b (Vector): m-vector (As + e mod q)

set_secret ¶

set_secret(secret: Vector) -> None

Set the underlying secret

Parameters:

Name	Type	Description	Default
`secret`	`Vector`	secret vector to set	required

Raises:

Type	Description
`ValueError`	when lenght of the provided vector is not correct with the parameter of the LWE sampler

Miscellaneous¶

pqlattice.random.randlattice ¶

randlattice(
    n: int,
    det_upper_bound: int | None = None,
    seed: int | None = None,
) -> SquareMatrix

Generates lattice basis by, first generating random square matrix in Hermite normal form and then by transforming it using random unimodular matrix.

Parameters:

Name	Type	Description	Default
`n`	`int`	lattice's rank	required
`det_upper_bound`	`int \| None`	upper bound of lattice volume, by default 2 ** n	`None`
`seed`	`int \| None`	seed for random number generator	`None`

Returns:

Type	Description
`SquareMatrix`	n x n matrix representing lattice basis

pqlattice.random.randprime ¶

randprime(kbits: int, seed: int | None = None) -> int

Generates random prime number from range [2 ** (kbits - 1); 2 ** (kbist)]. Uses Miller-Rabin primality test.

Parameters:

Name	Type	Description	Default
`kbits`	`int`	number of bits the prime number should have	required
`seed`	`int \| None`	seed for random number generator, by default None	`None`

Returns:

Type	Description
`int`	prime number

Random module¶

Distributions¶

pqlattice.random.distribution.Uniform ¶

get_params ¶

sample_int ¶

sample_matrix ¶

sample_vector ¶

set_params ¶

pqlattice.random.distribution.DiscreteGaussian ¶

get_params ¶

sample_int ¶

sample_matrix ¶

sample_vector ¶

set_params ¶

Learning with errors¶

pqlattice.random.LWE ¶

secret property ¶

next_sample ¶

sample_matrix ¶

set_secret ¶

Miscellaneous¶

pqlattice.random.randlattice ¶

pqlattice.random.randprime ¶

secret `property` ¶