API Reference

Submodules

cryptomite.circulant module

The Circulant extractor [For2024] takes an input of `n_1’ bits and a (weak) seed of `n_1 + 1’ bits, where `n_1 + 1’ is prime.

class cryptomite.circulant.Circulant(n_1: int, m: int)[source]

Bases: object

Circulant extractor based on [For2024].

__init__(n_1: int, m: int)[source]

Initialize a Circulant extractor.

Parameters

n_1int: The length of the first input (in bits). Note: n_1 + 1 must be prime.
mint: The length of the extractor output (in bits).

extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]

Perform randomness extraction.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n_1 bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’), consisting of n_2 = n_1 + 1 bits.

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

static from_params(n_1: int, k_1: float, n_2: int, k_2: float, log2_error: float, q_proof: bool, verbose: bool = True) → cryptomite.circulant.Circulant[source]

Generate a Circulant extractor with valid parameters based on input constraints.

Parameters

n_1int: The length of the first input (in bits).
k_1float: The min-entropy of the first input.
n_2int: The length of the second input (in bits).
k_2float: The min-entropy of the second input.
log2_errorfloat: The logarithm (base 2) of the acceptable extractor error. Must be negative, as the extractor error is 2^log2_error.
q_proofbool: If True, adjusts parameters to ensure quantum-proof extraction in the Markov and product sources models (see [For2024]).
verbosebool: If True, prints the parameters used for extraction (default: True).

Returns

Circulant: A configured Circulant extractor.

Raises

ValueError: If the output length is non-positive.

Notes

If n_2 is not prime, the function selects the closest prime and adjusts the other parameters accordingly.
For this extractor, the output length remains the same when it is classical-proof, quantum-proof in the product sources model, and quantum-proof in the Markov model (see [For2024]).

cryptomite.dodis module

The Dodis et al. extractor [Dodis2004] takes two equal length inputs, each of length `n = n_1 = n_2’. This implementation is based on the improved cyclic shift matrices construction from [For2020], which requires n to be prime with primitive root 2.

class cryptomite.dodis.Dodis(n: int, m: int)[source]

Bases: object

Dodis et al. extractor [Dodis2004], with implementation based on [For2020, For2024]_.

__init__(n: int, m: int)[source]

Initialize a Dodis extractor.

Parameters

nint: The length of the first input (in bits). Note: n must be prime with primitive root 2.
mint: The length of the extractor output (in bits).

extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]

Perform randomness extraction.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’), consisting of n bits.

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

static from_params(n_1: int, k_1: float, n_2: int, k_2: float, log2_error: float, q_proof: bool, verbose: bool = True) → cryptomite.dodis.Dodis[source]

Generate a Dodis et al. extractor with valid parameters based on input constraints.

Parameters

n_1int: The length of the first input (in bits).
k_1float: The min-entropy of the first input.
n_2int: The length of the second input (in bits).
k_2float: The min-entropy of the second input.
log2_errorfloat: The logarithm (base 2) of the acceptable extractor error. Must be negative, as the extractor error is 2^log2_error.
q_proofbool: If True, adjusts parameters to ensure quantum-proof extraction in the Markov and product sources models (see [For2024]).
verbosebool: If True, prints the parameters used for extraction (default: True).

Returns

Dodis: A configured Dodis et al. extractor.

Raises

ValueError: If the output length is non-positive.

Notes

If n is not prime with primitive root 2, the function selects the closest prime with primitive root 2 and adjusts the other parameters accordingly.

cryptomite.toeplitz module

The Toeplitz extractor takes an input of `n_1’ bits and a (weak) seed of `n_2 = n_1 + m - 1’ bits, where `m’ is output length. This implementation is based on the efficient implementation presented in [For2024].

class cryptomite.toeplitz.Toeplitz(n_1: int, m: int)[source]

Bases: object

Toeplitz extractor with implementation based on [For2024].

__init__(n_1: int, m: int)[source]

Initialize a Toeplitz extractor.

Parameters

n_1int: The length of the first input (in bits).
mint: The length of the extractor output (in bits).

extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]

Perform randomness extraction.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n_1 bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’), consisting of n_2 = n_1 + m - 1 bits.

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

static from_params(n_1: int, k_1: float, n_2: int, k_2: float, log2_error: float, q_proof: bool, verbose: bool = True) → cryptomite.toeplitz.Toeplitz[source]

Generate a Toeplitz extractor with valid parameters based on input constraints.

Parameters

n_1int: The length of the first input (in bits).
k_1float: The min-entropy of the first input.
n_2int: The length of the second input (in bits).
k_2float: The min-entropy of the second input.
log2_errorfloat: The logarithm (base 2) of the acceptable extractor error. Must be negative, as the extractor error is 2^log2_error.
q_proofbool: If True, adjusts parameters to ensure quantum-proof extraction in the Markov and product sources models (see [For2024]).
verbosebool: If True, prints the parameters used for extraction (default: True).

Returns

Toeplitz: A configured Toeplitz extractor.

Raises

ValueError: If the length of the first source is great than or equal to that of the second.
ValueError: If the output length is non-positive.

Notes

For this extractor, the output length remains the same when it is classical-proof, quantum-proof in the product sources model, and quantum-proof in the Markov model (see [For2024]).

cryptomite.trevisan module

The Trevisan extractor [Trev2001] takes an input of `n_1’ bits and a seed of `n_2 = O(log n_1)’ bits. This implementation is based on the implementation in [Mauer2012] and [For2024].

class cryptomite.trevisan.Trevisan(n: int, k: float, error: float)[source]

Bases: object

Trevisan extractor [Trev2001] with implementation based on [Mauer2012] and [For2024].

__init__(n: int, k: float, error: float)[source]

Initialize a Trevisan Extractor.

Parameters

nint: The length of the input bits.
kfloat: The min-entropy of the input bits.
errorfloat: The maximum acceptable extractor error.

extract(input1: list[bool], input2: list[bool]) → list[bool][source]

Extract randomness.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’).

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

cryptomite.utils module

This is a module.

cryptomite.utils.closest_na_set(k: int) → int[source]

Finds the closest prime number to the given input.

kint: The input value to find the closest prime with primitive root 2 to.

Returns

int: The closest prime number with primitive root 2 to k.

cryptomite.utils.closest_prime(k: int) → int[source]

Finds the closest prime number to the given input.

kint: The input value to find the closest prime number to.

Returns

int: The closest prime number to k.

cryptomite.utils.is_prime(n: int) → bool[source]

Checks whether an integer is prime.

Parameters

nint: The integer to check for primality.

Returns

bool: Whether n is prime.

cryptomite.utils.next_na_set(k: int) → int[source]

Finds the smallest prime number with primitive root 2 greater than or equal to the given input.

Parameters

kint: The lower limit for checking prime numbers with primitive root 2.

Returns

int: The smallest prime number with primitive root 2 greater than or equal to k.

cryptomite.utils.next_prime(k: int) → int[source]

Finds the smallest prime number greater than or equal to the given input.

Parameters

kint: The lower limit for checking prime numbers.

Returns

int: The smallest prime number greater than or equal to k.

cryptomite.utils.previous_na_set(k: int) → int[source]

Finds the largest prime number with primitive root 2 less than or equal to the given input.

Parameters

kint: The upper limit for checking prime numbers with primitive root 2.

Returns

int: The largest prime number with primitive root 2 less than or equal to k.

cryptomite.utils.previous_prime(k: int) → int[source]

Finds the largest prime number less than or equal to the given input.

Parameters

kint: The upper limit for checking prime numbers.

Returns

int: The largest prime number less than or equal to k.

cryptomite.utils.prime_facto(n: int) → tuple[list[int], list[int]][source]

Factorizes an integer into its prime factors and their powers. It is required for the later function: na_set.

Parameters

nint: The integer to check.

Returns

list: A list representing the prime factorization of n.

cryptomite.utils.suggest_extractor(n_1: int, exchangeable_sequence: bool, efficiency_required: bool) → str[source]

Suggests the best extractor for a user, based on Fig.2 from the technical paper.

Parameters

n_1int: The length of the first input (in bits).
exchangeable_sequencebool: Boolean input indicating whether the source forms an exchangeable sequence.
efficiency_requiredbool: Boolean input indicating whether the user requires efficient extraction.

Returns

string: The suggested extractor.

cryptomite.utils.von_neumann(bits: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]: Perform extraction using Von-Neumann extractor.

Module contents

class cryptomite.Circulant(n_1: int, m: int)[source]

Bases: object

Circulant extractor based on [For2024].

__init__(n_1: int, m: int)[source]

Initialize a Circulant extractor.

Parameters

n_1int: The length of the first input (in bits). Note: n_1 + 1 must be prime.
mint: The length of the extractor output (in bits).

extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]

Perform randomness extraction.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n_1 bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’), consisting of n_2 = n_1 + 1 bits.

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

static from_params(n_1: int, k_1: float, n_2: int, k_2: float, log2_error: float, q_proof: bool, verbose: bool = True) → cryptomite.circulant.Circulant[source]

Generate a Circulant extractor with valid parameters based on input constraints.

Parameters

n_1int: The length of the first input (in bits).
k_1float: The min-entropy of the first input.
n_2int: The length of the second input (in bits).
k_2float: The min-entropy of the second input.
log2_errorfloat: The logarithm (base 2) of the acceptable extractor error. Must be negative, as the extractor error is 2^log2_error.
q_proofbool: If True, adjusts parameters to ensure quantum-proof extraction in the Markov and product sources models (see [For2024]).
verbosebool: If True, prints the parameters used for extraction (default: True).

Returns

Circulant: A configured Circulant extractor.

Raises

ValueError: If the output length is non-positive.

Notes

If n_2 is not prime, the function selects the closest prime and adjusts the other parameters accordingly.
For this extractor, the output length remains the same when it is classical-proof, quantum-proof in the product sources model, and quantum-proof in the Markov model (see [For2024]).

class cryptomite.Dodis(n: int, m: int)[source]

Bases: object

Dodis et al. extractor [Dodis2004], with implementation based on [For2020, For2024]_.

__init__(n: int, m: int)[source]

Initialize a Dodis extractor.

Parameters

nint: The length of the first input (in bits). Note: n must be prime with primitive root 2.
mint: The length of the extractor output (in bits).

extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]

Perform randomness extraction.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’), consisting of n bits.

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

static from_params(n_1: int, k_1: float, n_2: int, k_2: float, log2_error: float, q_proof: bool, verbose: bool = True) → cryptomite.dodis.Dodis[source]

Generate a Dodis et al. extractor with valid parameters based on input constraints.

Parameters

n_1int: The length of the first input (in bits).
k_1float: The min-entropy of the first input.
n_2int: The length of the second input (in bits).
k_2float: The min-entropy of the second input.
log2_errorfloat: The logarithm (base 2) of the acceptable extractor error. Must be negative, as the extractor error is 2^log2_error.
q_proofbool: If True, adjusts parameters to ensure quantum-proof extraction in the Markov and product sources models (see [For2024]).
verbosebool: If True, prints the parameters used for extraction (default: True).

Returns

Dodis: A configured Dodis et al. extractor.

Raises

ValueError: If the output length is non-positive.

Notes

If n is not prime with primitive root 2, the function selects the closest prime with primitive root 2 and adjusts the other parameters accordingly.

class cryptomite.Toeplitz(n_1: int, m: int)[source]

Bases: object

Toeplitz extractor with implementation based on [For2024].

__init__(n_1: int, m: int)[source]

Initialize a Toeplitz extractor.

Parameters

n_1int: The length of the first input (in bits).
mint: The length of the extractor output (in bits).

extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]

Perform randomness extraction.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n_1 bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’), consisting of n_2 = n_1 + m - 1 bits.

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

static from_params(n_1: int, k_1: float, n_2: int, k_2: float, log2_error: float, q_proof: bool, verbose: bool = True) → cryptomite.toeplitz.Toeplitz[source]

Generate a Toeplitz extractor with valid parameters based on input constraints.

Parameters

n_1int: The length of the first input (in bits).
k_1float: The min-entropy of the first input.
n_2int: The length of the second input (in bits).
k_2float: The min-entropy of the second input.
log2_errorfloat: The logarithm (base 2) of the acceptable extractor error. Must be negative, as the extractor error is 2^log2_error.
q_proofbool: If True, adjusts parameters to ensure quantum-proof extraction in the Markov and product sources models (see [For2024]).
verbosebool: If True, prints the parameters used for extraction (default: True).

Returns

Toeplitz: A configured Toeplitz extractor.

Raises

ValueError: If the length of the first source is great than or equal to that of the second.
ValueError: If the output length is non-positive.

Notes

For this extractor, the output length remains the same when it is classical-proof, quantum-proof in the product sources model, and quantum-proof in the Markov model (see [For2024]).

class cryptomite.Trevisan(n: int, k: float, error: float)[source]

Bases: object

Trevisan extractor [Trev2001] with implementation based on [Mauer2012] and [For2024].

__init__(n: int, k: float, error: float)[source]

Initialize a Trevisan Extractor.

Parameters

nint: The length of the input bits.
kfloat: The min-entropy of the input bits.
errorfloat: The maximum acceptable extractor error.

extract(input1: list[bool], input2: list[bool]) → list[bool][source]

Extract randomness.

Parameters

input1list of bits (0s and 1s): The first input (the ‘weak input’), consisting of n bits.
input2list of bits (0s and 1s): The second input (the ‘(weak) seed’).

Returns

list of bits (0s and 1s): The extractor output bits, of length m.

cryptomite.von_neumann(bits: Sequence[Literal[0, 1]]) → Sequence[Literal[0, 1]][source]: Perform extraction using Von-Neumann extractor.