API Reference
Submodules
cryptomite.circulant module
Circulant is a seeded extractor that takes an input of n bits and a seed of n + 1 bits, where n + 1 is prime, to produce some error-perfect random bits.
- class cryptomite.circulant.Circulant(n: int, m: int)[source]
Bases:
objectCirculant extractor based on [For2024].
- __init__(n: int, m: int)[source]
Create a Circulant Extractor.
- Parameters
- nint
The length of the input bits. ** n + 1 should be prime. **
- mint
The length of the output bits.
- extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) Sequence[Literal[0, 1]][source]
Extract randomness.
- Parameters
- input1list of bits
The first list of bits, the ‘input’.
- input2list of bits
The second list of bits, the ‘(weak) seed’.
- Returns
- list of bits
The extracted output.
- static from_params(min_entropy1: float, min_entropy2: float, log2_error: float, input_length1: int, input_length2: int, markov_q_proof: bool, verbose: bool = True) cryptomite.circulant.Circulant[source]
Calculate a valid input and output size for this extractor, given the initial lengths and min-entropies of the input sources and generate the associated extractor.
The input_length2 must be prime, else the code will chose a valid input_length2 choice and adjust the other parameters accordingly. The min_entropy inputs are a lower bound on the min-entropy of the related input string.
- Parameters
- min_entropy1float
The min-entropy of input source 1, the ‘input’.
- min_entropy2float
The min-entropy of input source 2, the ‘(weak) seed’.
- log2_errorfloat
The acceptable maximum extractor error, in the form error = b where extractor error = \(2 ^ b\).
- input_length1int
The initial length of input source.
- input_length2int
The initial length of the (weak) seed.
- markov_q_proofbool
Boolean indicator of whether the extractor parameters should be calculated to account for being quantum-proof in the Markov model or not.
- Returns
- Circulant
The Circulant extractor.
cryptomite.dodis module
Dodis is a 2-source extractor that takes two equal length, independent, strings of bits to produce some error-perfect random bits.
- class cryptomite.dodis.Dodis(n: int, m: int)[source]
Bases:
objectDodis extractor based on [Dodis2004].
- __init__(n: int, m: int)[source]
Create a Dodis Extractor.
- Parameters
- nint
The length of the two input bits. ** This should be prime with primitive root 2. **
- mint
The length of the output bits.
- extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) Sequence[Literal[0, 1]][source]
Extract randomness.
- Parameters
- input1list of bits
The first list of bits, the ‘input’.
- input2list of bits
The second list of bits, the ‘(weak) seed’.
- Returns
- list of bits
The extracted output.
- static from_params(min_entropy1: float, min_entropy2: float, log2_error: float, input_length1: int, input_length2: int, markov_q_proof: bool, verbose: bool = True) cryptomite.dodis.Dodis[source]
Calculate a valid input and output size for this extractor, given the initial lengths and min-entropies of the input sources and generate the associated extractor.
The input_length must be prime with primitive root 2, else the code will chose a valid input_length choice and adjust the other parameters accordingly. The min entropy inputs are a lower bound on the min-entropy of the related input string.
- Parameters
- min_entropy1float
The min-entropy of input source 1, the ‘input’.
- min_entropy2float
The min-entropy of input source 2, the ‘(weak) seed’.
- log2_errorfloat
The acceptable maximum extractor error, in the form error = b where extractor error = \(2 ^ b\).
- input_length1int
The initial length of input source.
- input_length2int
The initial length of the (weak) seed.
- markov_q_proofbool
Boolean indicator of whether the extractor parameters should be calculated to account for being quantum-proof in the Markov model or not.
- Returns
- Dodis
The Dodis extractor.
cryptomite.toeplitz module
Toeplitz is a seeded extractor that takes two differing length, independent, strings of bits to produce some error-perfect random bits.
- class cryptomite.toeplitz.Toeplitz(n: int, m: int)[source]
Bases:
objectToeplitz extractor
- __init__(n: int, m: int)[source]
Create a Circulant Extractor.
- Parameters
- nint
The length of the input bits.
- mint
The length of the output bits.
- extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) Sequence[Literal[0, 1]][source]
Extract randomness.
- Parameters
- input1list of bits
The first list of bits, the ‘input’.
- input2list of bits
The second list of bits, the ‘(weak) seed’.
- Returns
- list of bits
The extracted output.
- static from_params(min_entropy1: float, min_entropy2: float, log2_error: float, input_length1: int, input_length2: int, markov_q_proof: bool, verbose: bool = True) cryptomite.toeplitz.Toeplitz[source]
Calculate a valid input and output size for this extractor, given the initial lengths and min-entropies of the input sources and generate the associated extractor.
The min entropy inputs are a lower bound on the min-entropy of the related input string.
- Parameters
- min_entropy1float
The min-entropy of input source 1, the ‘input’.
- min_entropy2float
The min-entropy of input source 2, the ‘(weak) seed’.
- log2_errorfloat
The maximum acceptable extractor error, in the form error = b where extractor error = \(2 ^ b\).
- input_length1int
The initial length of input source.
- input_length2int
The initial length of the (weak) seed.
- markov_q_proofbool
Boolean indicator of whether the extractor parameters should be calculated to account for being quantum-proof in the Markov model or not.
- Returns
- Toeplitz
The Toeplitz extractor.
cryptomite.trevisan module
Trevisan is a seeded extractor that takes two differing length, independent, strings of bits to produce some error-perfect random bits.
- class cryptomite.trevisan.Trevisan(n: int, k: float, error: float)[source]
Bases:
objectTrevisan extractor based on [Trev2001] and [Mauer2012].
cryptomite.utils module
This is a module.
- cryptomite.utils.closest_na_set(k: int) int[source]
Finds the closest integer to the input that is prime with primitive root 2. If both directions are equidistant, outputs the prime with primitive root 2 less than the input.
- Parameters
- kint
number to check is prime with primitive root 2.
- Returns
- int :
prime with primitive root 2.
- cryptomite.utils.closest_prime(k: int) int[source]
Finds the closest integer to the input that is prime. If both directions are equidistant, outputs the prime less than the input.
- Parameters
- kint
number to check is prime.
- Returns
- int :
prime.
- cryptomite.utils.is_prime(n: int) bool[source]
Checks an integer for primality.
- Parameters
- nint
integer to check for primality.
- Returns
- boolWhether n is prime.
- cryptomite.utils.next_na_set(k: int) int[source]
Finds the smallest integer larger than the input that is prime with primitive root 2.
- Parameters
- kint
number to check is prime with primitive root 2.
- Returns
- int :
prime with primitive root 2.
- cryptomite.utils.next_prime(k: int) int[source]
Finds the smallest integer larger than or equal to the input that is prime.
- Parameters
- kint
number to check is prime.
- Returns
- int :
prime.
- cryptomite.utils.previous_na_set(k: int) int[source]
Finds the largest integer smaller than the input that is prime with primitive root 2.
- Parameters
- kint
number to check is prime with primitive root 2.
- Returns
- int :
prime with primitive root 2.
- cryptomite.utils.previous_prime(k: int) int[source]
Finds the largest integer smaller than or equal to the input that is prime.
- Parameters
- kint
number to check is prime.
- Returns
- int :
prime.
- cryptomite.utils.prime_facto(n: int) tuple[list[int], list[int]][source]
Defines the factors of the prime numbers used. It is required for the later function: na_set.
- Parameters
- nint
number to check.
- Returns
- list :
Returns factors and powers.
- cryptomite.utils.suggest_extractor(input_length1: 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
- input_length1int
The initial length of input source.
- 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.
Module contents
- class cryptomite.Circulant(n: int, m: int)[source]
Bases:
objectCirculant extractor based on [For2024].
- __init__(n: int, m: int)[source]
Create a Circulant Extractor.
- Parameters
- nint
The length of the input bits. ** n + 1 should be prime. **
- mint
The length of the output bits.
- extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) Sequence[Literal[0, 1]][source]
Extract randomness.
- Parameters
- input1list of bits
The first list of bits, the ‘input’.
- input2list of bits
The second list of bits, the ‘(weak) seed’.
- Returns
- list of bits
The extracted output.
- static from_params(min_entropy1: float, min_entropy2: float, log2_error: float, input_length1: int, input_length2: int, markov_q_proof: bool, verbose: bool = True) cryptomite.circulant.Circulant[source]
Calculate a valid input and output size for this extractor, given the initial lengths and min-entropies of the input sources and generate the associated extractor.
The input_length2 must be prime, else the code will chose a valid input_length2 choice and adjust the other parameters accordingly. The min_entropy inputs are a lower bound on the min-entropy of the related input string.
- Parameters
- min_entropy1float
The min-entropy of input source 1, the ‘input’.
- min_entropy2float
The min-entropy of input source 2, the ‘(weak) seed’.
- log2_errorfloat
The acceptable maximum extractor error, in the form error = b where extractor error = \(2 ^ b\).
- input_length1int
The initial length of input source.
- input_length2int
The initial length of the (weak) seed.
- markov_q_proofbool
Boolean indicator of whether the extractor parameters should be calculated to account for being quantum-proof in the Markov model or not.
- Returns
- Circulant
The Circulant extractor.
- class cryptomite.Dodis(n: int, m: int)[source]
Bases:
objectDodis extractor based on [Dodis2004].
- __init__(n: int, m: int)[source]
Create a Dodis Extractor.
- Parameters
- nint
The length of the two input bits. ** This should be prime with primitive root 2. **
- mint
The length of the output bits.
- extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) Sequence[Literal[0, 1]][source]
Extract randomness.
- Parameters
- input1list of bits
The first list of bits, the ‘input’.
- input2list of bits
The second list of bits, the ‘(weak) seed’.
- Returns
- list of bits
The extracted output.
- static from_params(min_entropy1: float, min_entropy2: float, log2_error: float, input_length1: int, input_length2: int, markov_q_proof: bool, verbose: bool = True) cryptomite.dodis.Dodis[source]
Calculate a valid input and output size for this extractor, given the initial lengths and min-entropies of the input sources and generate the associated extractor.
The input_length must be prime with primitive root 2, else the code will chose a valid input_length choice and adjust the other parameters accordingly. The min entropy inputs are a lower bound on the min-entropy of the related input string.
- Parameters
- min_entropy1float
The min-entropy of input source 1, the ‘input’.
- min_entropy2float
The min-entropy of input source 2, the ‘(weak) seed’.
- log2_errorfloat
The acceptable maximum extractor error, in the form error = b where extractor error = \(2 ^ b\).
- input_length1int
The initial length of input source.
- input_length2int
The initial length of the (weak) seed.
- markov_q_proofbool
Boolean indicator of whether the extractor parameters should be calculated to account for being quantum-proof in the Markov model or not.
- Returns
- Dodis
The Dodis extractor.
- class cryptomite.Toeplitz(n: int, m: int)[source]
Bases:
objectToeplitz extractor
- __init__(n: int, m: int)[source]
Create a Circulant Extractor.
- Parameters
- nint
The length of the input bits.
- mint
The length of the output bits.
- extract(input1: Sequence[Literal[0, 1]], input2: Sequence[Literal[0, 1]]) Sequence[Literal[0, 1]][source]
Extract randomness.
- Parameters
- input1list of bits
The first list of bits, the ‘input’.
- input2list of bits
The second list of bits, the ‘(weak) seed’.
- Returns
- list of bits
The extracted output.
- static from_params(min_entropy1: float, min_entropy2: float, log2_error: float, input_length1: int, input_length2: int, markov_q_proof: bool, verbose: bool = True) cryptomite.toeplitz.Toeplitz[source]
Calculate a valid input and output size for this extractor, given the initial lengths and min-entropies of the input sources and generate the associated extractor.
The min entropy inputs are a lower bound on the min-entropy of the related input string.
- Parameters
- min_entropy1float
The min-entropy of input source 1, the ‘input’.
- min_entropy2float
The min-entropy of input source 2, the ‘(weak) seed’.
- log2_errorfloat
The maximum acceptable extractor error, in the form error = b where extractor error = \(2 ^ b\).
- input_length1int
The initial length of input source.
- input_length2int
The initial length of the (weak) seed.
- markov_q_proofbool
Boolean indicator of whether the extractor parameters should be calculated to account for being quantum-proof in the Markov model or not.
- Returns
- Toeplitz
The Toeplitz extractor.
- class cryptomite.Trevisan(n: int, k: float, error: float)[source]
Bases:
objectTrevisan extractor based on [Trev2001] and [Mauer2012].