qkd_key_rate.protocols.classical package

Classical protocols

class qkd_key_rate.protocols.classical.CascadeCorrector(alice, bob)

Bases: Corrector

Cascade corrector

summary()

Calculate a summary object for the error correction

• original message

• corrected message

• error rate (before and after correction)

• number_of_exposed_bits

• key_reconciliation_rate

• protocol specific parameters

Return type:

CascadeCorrectorOutput

class qkd_key_rate.protocols.classical.CascadeReceiver(message, permutations, parity_strategy, name=None)

Bases: CascadeSender, ReceiverBase

This class encodes all functions only available to the receiver.

The receiver is assumed to have a string with errors and is thus assumed to correct the errors.

__init__(message, permutations, parity_strategy, name=None)

Parameters:

• message (Message) – Input message of the sender party

• permutations (Permutations) – List containing permutations for each Cascade pass

• name (Optional[str]) – Name of the receiver party

check_match_of_parities(alice, current_pass, current_block, block_size)

Checks if the parity strings of alice and bob match.

This requires communication between the two parties. The parities of multiple blocks can be combined in a single message.

Parameters:

• current_pass (int) – Index of current pass

• current_block (int) – Index of current block

• alice (CascadeSender) – The sending party

Return type:

bool

Returns:

Boolean if the parity strings of alice and bob match

correct_errors(alice)

This is the main routine Errors in the strings alice and bob are found and corrected

An upper bound on the number of communications is estimated. This is however a loose upper bound. The cascade-routine makes it difficult to give tighter bounds

Parameters:

alice (SenderBase) – The sending party to correct errors with

Return type:

None

do_cascade(current_pass, current_block, block_size, alice, size_blocks_parities)

Apply the Cascade error correction technique.

This routine corrects errors in previous passes that become apparent later. It is recursively used as long as new errors are found.

Parameters:

• current_pass (int) – Index of current pass

• current_block (int) – Index of current block

• block_size (int) – Size of current block

• alice (CascadeSender) – The sending party

• size_blocks_parities (Tuple[Tuple[int, int], ...]) – For each pass the size of the block and number of blocks

Return type:

None

get_block_index(index, block_size, index_pass)

Returns the block index corresponding to a certain index in a certain pass

Parameters:

• index (int) – Index of a certain bit

• block_size (int) – Size of current block

• index_pass (int) – Index of the current pass

Return type:

int

Returns:

The block index corresponding to a certain bit index in a certain pass

get_error_index(index_block, index_pass, block_size, alice)

Recursively checks the parity of half of the block of both parties.

Parameters:

• index_block (int) – Index of the block in which we expect an error

• index_pass (int) – Index of the current pass

• block_size (int) – Size of current block

• alice (CascadeSender) – The sending party

Return type:

int

Returns:

The position index of an error

get_error_rate()

Gives the error rate, based on the found errors.

Return type:

float

get_prior_error_rate(alice, index_start=0, index_finish=None)

Determine the initial error rate. This function is mainly for debugging purposes. Usually, the considered bits are private and this value cannot be computed.

Parameters:

• alice (CascadeSender) – The sending party

• index_start (int) – Start index of the message

• index_finish (Optional[int]) – End index of the message

Return type:

float

Returns:

Initial error rate

class qkd_key_rate.protocols.classical.CascadeSender(message, permutations, name=None)

Bases: SenderBase

This class encodes all functions available to both sender and receiver for the Cascade protocol.

__init__(message, permutations, name=None)

Parameters:

• message (Message) – Input message of the sender party

• permutations (Permutations) – List containing permutations for each Cascade pass

• name (Optional[str]) – Name of the sender party

build_parity_string(block_size, pass_number)

Built a string of parities for the given block size.

Parameters:

• block_size (int) – Message block size

• pass_number (int) – Cascade permutation number

Return type:

None

get_parity(index_start, index_end, pass_number)

Get the parity of a specific message block, taking into account the permutation applied in that specific pass.

Parameters:

• index_start (int) – Start index of the message

• index_end (int) – End index of the message

• pass_number (int) – Cascade pass number

Return type:

int

Returns:

Parity of substring

class qkd_key_rate.protocols.classical.PrivacyAmplification(observed_pulses_basis_x, error_rate_basis_x)

Bases: object

The privacy amplification module. A hash of an error corrected string is computed and returned. The length of the hashed string equals the remaining entropy.

__init__(observed_pulses_basis_x, error_rate_basis_x)

Parameters:

• observed_pulses_basis_x (int) – Number of pulses received in the X-basis

• error_rate_basis_x (float) – Error rate in the pulses received in the X-basis

do_hash(message, entropy)

Computes the hash given a message of bits.

The length of the hash equals the secure entropy we have.

Return type:

bytes

get_entropy_estimate(error_correction_loss=0)

Estimate the amount of entropy.

Uses the key-rate estimation functions to determine the key-rate and obtains the number of secure bits by multiplying this by the number of pulses sent. Adjusts the remaining entropy for losses due to the error-correction.

Parameters:

error_correction_loss (int) – Number of corrected errors

Return type:

float

Returns:

The amount of entropy

class qkd_key_rate.protocols.classical.WinnowCorrector(alice, bob)

Bases: Corrector

Winnow corrector

summary()

Calculate a summary object for the error correction

• original message

• corrected message

• error rate (before and after correction)

• number_of_exposed_bits

• key_reconciliation_rate

• protocol specific parameters

Return type:

WinnowCorrectorOutput

class qkd_key_rate.protocols.classical.WinnowReceiver(message, permutations, schedule, name=None)

Bases: WinnowSender, ReceiverBase

This class encodes all functions only available to the receiver.

The receiver is assumed to have a string with errors and is thus assumed to correct the errors.

__init__(message, permutations, schedule, name=None)

Parameters:

• message (Message) – Input message of the sender party

• permutations (Permutations) – List containing permutations for each pass

• name (Optional[str]) – Name of the receiver party

correct_errors(alice)

The main routine, finds all errors and corrects them.

It is assumed that Alice and Bob use one communication round to agree on the used permutations. Afterwards, they use two communication rounds per iteration to communicate the syndromes.

Parameters:

alice (WinnowSender) – The sending party

Return type:

None

fix_errors_with_syndrome(alice)

Corrects errors using the syndrome strings of alice and bob

Parameters:

alice (WinnowSender) – The sending party

Return type:

None

class qkd_key_rate.protocols.classical.WinnowSender(message, permutations, schedule, name=None)

Bases: SenderBase

This class encodes all functions available to both sender and receiver.

It keeps track of the number of exposed bits and can compute syndromes and parities. Furthermore, it keeps track of the blocks with errors

__init__(message, permutations, schedule, name=None)

Parameters:

• message (Message) – Input message of the sender party

• permutations (Permutations) – List containing permutations for each pass

• name (Optional[str]) – Name of the sender party

build_parity_string()

Builds a parity string for all blocks.

Return type:

None

build_syndrome_string(alice)

Create a syndrome string for all disagreeing blocks.

Computes the syndrome for blocks with disagreeing parity.

Parameters:

alice (WinnowSender) – The sending party

Return type:

None

create_parity_check_matrix()

Creates a parity check matrix.

This matrix is used to encode the bit strings.

Return type:

None

disagreeing_block_parities(alice)

Finds the disagreeing block parities.

The found parities of both parties are compared. This can be done with two communication rounds (one both ways). Afterwards, both separately process the results.

Parameters:

alice (WinnowSender) – The sending party

Return type:

None

discard_parity_bits()

The first bit of every parity block is discarded.

Return type:

None

discard_syndrome_bits()

Discards syndrome bits. Bits at indices \(2^j-1\) are removed. These correspond to the linearly independent columns of the parity check matrix.

In this function the number of bad blocks is known.

No communication is needed to discard syndrome bits.

Return type:

None

first_pass()

First pass with initializations and parity determination.

Return type:

None

get_parity(index_start, index_end)

Get the parity of a specific message part between two indices.

Parameters:

• index_start (int) – Start index of the message

• index_end (int) – End index of the message

Return type:

int

Returns:

Parity of substring

get_syndrome(index_block)

Computes the syndrome of a block.

Both parties compute their syndrome individually, hence, no communication is needed here.

Return type:

int

next_pass()

Performs the necessary computations to prepare for the next pass, including permuting the message and creating a new parity string.

Return type:

None

permute_buffer()

Permutes the message string.

Return type:

None

• qkd_key_rate.protocols.classical.cascade module
  • CascadeCorrector
    • CascadeCorrector.summary()
  • CascadeCorrectorOutput
    • CascadeCorrectorOutput.number_of_passes
    • CascadeCorrectorOutput.sampling_fraction
    • CascadeCorrectorOutput.switch_after_pass
  • CascadeReceiver
    • CascadeReceiver.__init__()
    • CascadeReceiver.check_match_of_parities()
    • CascadeReceiver.correct_errors()
    • CascadeReceiver.do_cascade()
    • CascadeReceiver.get_block_index()
    • CascadeReceiver.get_error_index()
    • CascadeReceiver.get_error_rate()
    • CascadeReceiver.get_prior_error_rate()
  • CascadeSender
    • CascadeSender.__init__()
    • CascadeSender.build_parity_string()
    • CascadeSender.get_parity()
• qkd_key_rate.protocols.classical.privacy_amplification module
  • PrivacyAmplification
    • PrivacyAmplification.__init__()
    • PrivacyAmplification.do_hash()
    • PrivacyAmplification.get_entropy_estimate()
• qkd_key_rate.protocols.classical.winnow module
  • WinnowCorrector
    • WinnowCorrector.summary()
  • WinnowCorrectorOutput
    • WinnowCorrectorOutput.schedule
  • WinnowReceiver
    • WinnowReceiver.__init__()
    • WinnowReceiver.correct_errors()
    • WinnowReceiver.fix_errors_with_syndrome()
  • WinnowSender
    • WinnowSender.__init__()
    • WinnowSender.build_parity_string()
    • WinnowSender.build_syndrome_string()
    • WinnowSender.create_parity_check_matrix()
    • WinnowSender.disagreeing_block_parities()
    • WinnowSender.discard_parity_bits()
    • WinnowSender.discard_syndrome_bits()
    • WinnowSender.first_pass()
    • WinnowSender.get_parity()
    • WinnowSender.get_syndrome()
    • WinnowSender.next_pass()
    • WinnowSender.permute_buffer()