Abstract: Methods, systems and apparatus, including computer programs encoded on computer storage medium, for implementation of secret superposition protocols. In one aspect a method includes, performing, by a sender party, quantum operations on one or more qubits, comprising preparing, according to a predetermined secret superposition protocol, one or more qubits in respective uniform superposition quantum states; transmitting, by the sender party, to a recipient party, and through a secure channel, data indicating use of the predetermined secret superposition protocol; and transmitting, by the sender party and to the recipient party, one or more of the qubits, to wherein the recipient party performs one or more measurements on the qubits to verify use of the predetermined secret superposition protocol.

Abstract: A method for generating a random number comprises selecting a group of at least two servers within a network; receiving a server specific string from at least two servers of the group; and using the server specific strings to generate the random number.

Abstract: The present disclosure is directed to systems and methods of providing the next generation of quantum enabled cyber security systems. Such systems include a quantum network of satellites that will provide global coverage. The quantum satellite network includes quantum subnetworks comprised of LEO satellites. Some of these LEO satellite-based quantum subnetworks are connected to a subnetwork of MEO satellites. The MEO satellite subnetworks may then be interconnected to the global network of GEO satellites. The LEO/MEO satellites may also be used to interconnect terrestrial quantum networks. Each quantum communication subnetwork may be based on the cluster state concept.

Abstract: An approach is provided in which the approach receives a request to upload a file at a server system that includes metadata encoded with a non-invertible key. The metadata includes contact information corresponding to an owner of the file. The approach establishes both a photon channel and a classical channel between the server system and a client system, which are both secured using one or more shared secret keys. The approach interfaces with the client system over the photon channel and the classical channel to decode the contact information at the server system, and sends an upload request from the server system to the owner of the file using the contact information. The approach authorizes the upload request at the server system in response to receiving an upload approval from the owner.

Abstract: The present invention discloses an image encryption method based on an improved class boosting scheme, which comprises the following steps: acquiring parameters of a hyperchaotic system according to plaintext image information; generating weights required by class perceptron networks through the plain text image information; bringing the parameters into the hyperchaotic system to obtain chaotic sequences, and shuffling the chaotic sequences by a shuffling algorithm; pre-processing the chaotic sequences after shuffling to obtain a sequence required by encryption: and bringing a plaintext image and the sequence into an improved class boosting scheme to obtain a ciphertext image, wherein the improved class boosting scheme is realized based on the class perception networks. The method solves the problems that update and prediction functions in an original boosting network are too simple and easy to predict or the like, so as to obtain the ciphertext image with higher information entropy.

Abstract: The present disclosure is directed to methods that provide a secure communication protocol by utilizing one step process of authenticating and encrypting data without having to exchange symmetric keys or needing to renew or re-issue digital identities fundamental to asymmetric encryption methodology.

Abstract: An analog hashing system and method includes: an input port for accepting an input signal; a chaotic circuit including non-linear components and multiple chaotic attractors for generating an unpredictable output responsive to the input signal; a differential output port coupled to the chaotic circuit for producing an analog differential signal from the unpredictable output; and a clock circuit for producing a binary output, as a hash function, generated by the sign of the analog output in every clock cycle.

Abstract: Aspects of associative cryptography key operations are described. In one embodiment, a first cryptographic function is applied to secret data to produce a first encrypted result. The first encrypted result is transmitted by a first device to a second device. The second device applies a second cryptographic function to the first encrypted result to produce a second encrypted result. At this point, the secret data has been encrypted by two different cryptographic functions, each of them being sufficient to secure the secret data from others. The two different cryptographic function can be inversed or removed, in any order, to reveal the secret data. Thus, the first device can apply a first inverse cryptographic function to the second encrypted result to produce a first result, and the second device can apply a second inverse cryptographic function to the first result to decrypt the secret data.

Abstract: Disclosed is a time division quadrature homodyne CV QKD system, and a continuous variable quantum key distribution system which includes: a transmitter generating an optical pulse of quantum state data by using continuous light according to data of a transmission target encryption key; and a receiver separating the optical pulse received from a channel into two paths and fixing phases of two signals having a time difference of one period of the optical pulse to orthogonal phases, and then generating bit information through state detection by a time division homodyne detection from interacted signals.

Abstract: Circuits and methods that implement multiplexing for photons propagating in waveguides are disclosed, in which an input photon received on a selected one of a set of input waveguides can be selectably routed to one of a set of output waveguides. The output waveguide can be selected on a rotating or cyclic basis, in a fixed order, and the input waveguide can be selected based at least in part on which one(s) of a set of input waveguides is (are) currently propagating a photon.

Abstract: Systems, apparatuses, methods, and computer program products are disclosed for post-quantum cryptography (PQC). An example system includes a PQC smartcard. The smartcard may include a PQC cryptographic algorithm selection circuitry configured to select a PQC cryptographic technique from a set of PQC cryptographic techniques for encrypting the data. The smartcard may further include a PQC cryptographic circuitry configured to encrypt data based on a generated set of PQC encryption attributes and the PQC cryptographic technique.

Abstract: A method of sharing address information using quantum states includes storing a number, M, of first qubits in a quantum store at a source node and storing classical information tagged to the M first qubits in a classical store at the source node, where the classical information describes a destination node where the M first qubits share entangled qubits. The M first qubits are measured at the source node and a random number is generated that represents an address of the destination node using the measured M first qubits and the classical information describing the destination node. A packet is sent from the source node that includes the generated random number in a quantum address field and further includes data intended for the destination node in a data field. A number, M, of second qubits is stored in a quantum store at the destination node, wherein each of the M first qubits is entangled with a respective one of the M second qubits.

Abstract: A method for generating digital quantum chaotic orthonormal wavepacket signals includes the following steps: construct a N-dimensional Hermitian matrix ?; calculate N eigen-wavefunctions ?j of a quantum Hamiltonian system with the Hamiltonian ? by some numerical calculation methods, wherein the Hamiltonian is the Hermitian matrix ?; extract some or all of the eigen-functions ?j with obvious chaos features as quantum chaotic eigen-wavefunctions according to a chaos criterion; generate some semi-classical digital quantum chaotic wavepacket signals ?j(n) with the same mathematical form as the quantum chaotic eigen-wavefunctions and length N from the selected quantum chaotic eigen-wavefunctions according to the mathematical correspondence between the classical signal and the wavefunction in quantum mechanics.

Abstract: Aspects of the disclosure provide a technological improvement to a cipher by improving data security of format-preserving encryption (FPE), by, inter alia, embedding specific key identifiers for rotating keys directly into ciphertext. Aspects of the disclosure relate to methods, computer-readable media, and apparatuses for improving data security in a format-preserving encryption (FPE) context by using specific methods of rotating and identifying the appropriate encryption key from among numerous rotating keys stored in a key data store. Specific to FPE, a plaintext of the data and its corresponding ciphertext of the data remain the same in length/size; yet the methods, computer-readable media, and/or apparatuses disclosed herein permit embedding of an identification of a specific key among the plurality of rotating keys for the particular ciphertext without compromising the technical requirements of FPE.

Abstract: Cryptographic circuitry, in operation, performs a calculation on a first number and a second number. The performing of the calculation is protected by breaking the second number into a plurality of third numbers, a sum of values of the third numbers being equal to a value of the second number. The calculation is performed bit by bit for each rank of the third numbers. Functional circuitry, coupled to the cryptographic circuitry, uses a result of the calculation.

Abstract: An optical system, comprising: an emitter configured to output a first optical signal along a first optical path to an interference unit and to output a second optical signal along a second optical path to the interference unit, the interference unit being configured to interfere the first and second optical signals, wherein the coherence length of the optical signal is longer than the path difference between first and second optical paths, and there is a path difference between the first and second paths of at least 1 km.

Abstract: Memristor based chaotic oscillators exhibit complex dynamics. They are often chosen for secure communication owing to their interesting feature. In chaos-based secure communication applications using the master-slave configuration, synchronization is a central issue. Most of the synchronization methods proposed in the literature are asymptotic. In practice, it is desirable that synchronization be established in a predefined time. This invention provides new developments in the design of high-gain observers with an unknown input dedicated for predefined-time synchronization of memristor based chaotic systems. The proposed predefined-time extended high gain observer is constructed on the basis of a time-dependent coordinates transformation based on modulating functions that annihilate the effect of initial conditions on the synchronization time. Both noise-free channel and noisy channel are considered. Simulations performed on a numerical example illustrated the efficiency of proposed approaches.

Abstract: A method for the transition is provided from a Boolean masking of a value to be kept secret to an additive masking of the value to be kept secret. The value to be kept secret is present in the Boolean masking as a representation masked with a first Boolean mask and a second Boolean mask. A first additive mask and a second additive mask are determined for the value to be kept secret. A first masking transition is executed in which the first Boolean mask is converted into the first additive mask. A second masking transition is executed in which the obfuscation value is converted into an additive correction value, and a third masking transition is executed in which the second Boolean mask is converted into the second additive mask.

Abstract: An apparatus can be configured to control a quantum memory of a quantum computer. The quantum memory can have a first qubit. The apparatus can comprise: a first-classical-register; a first-clock; a first-machine-language-buffer, that stores a first-machine-language-circuit; and a first-implementer. The first-machine-language-circuit includes: a first-timestamp; a first-qubit-identifier unique to the first qubit; a first-qubit-control-instruction; and a first-protected-location of the first-classical-register. The first-implementer can be configured to: read the first-machine-language-circuit from the first-machine-language-buffer; and read a first-control-value from the first-protected-location of the first-classical-register, the first-control-value can be configured to encode either a first-execute-instruction or a first-alternate-control-instruction.

Abstract: An optical source including: a phase-randomised light source including a master light source configured to intermittently generate master light pulses; a slave light source optically coupled to the master light source and configured to receive the master light pulses, and that generates a sequence of slave light pulses during each period of time that a master light pulse is received; and an interferometer optically coupled to the slave light source and configured to receive sequences of slave light pulses, delay the received sequences by the first time interval to form delayed sequences of slave light pulses, interfere the received sequences with the delayed sequences, such that pulses from a received sequence interfere with adjacent pulses of the delayed sequence, and output interfered pulses including first and second output pulses that have a first and second predetermined amplitude respectively and a predetermined relative phase between them.

Abstract: A quantum key generation system intended to mitigate the effect of the dead time of the photon detectors, the system including a photon generator, a photon pathway, a channel switch, and a photon detector unit. The photon pathway optically couples the photon generator and the channel switch. The channel switch is disposed between and optically coupled to the photon pathway and the photon detector unit. The photon detector unit includes a plurality of photon detectors and a plurality of detector unit sub-channels. Each detector unit sub-channel of the plurality of detector unit sub-channels optically couples the channel switch with an individual photon detector of the plurality of photon detectors. The channel switch is actuatable between a plurality of optical engagement positions. Further, each optical engagement position of the channel switch optically couples the photon pathway with a photon detector of the plurality of photon detectors.

Abstract: Systems, apparatuses, methods, and computer program products are disclosed for quantum entanglement random number generation (QERNG). An example method for QERNG includes, among other operations, generating a quantum entanglement random number based on a subset of a first set of entangled quantum particles associated with a first computing device. Each entangled quantum particle in the first set of entangled quantum particles may be entangled with a respective entangled quantum particle in a second set of entangled quantum particles associated with a second computing device. In some instances, the example method may further include generating a cryptographic key based on the quantum entanglement random number, encrypting an electronic communication based on the cryptographic key, and transmitting the encrypted electronic communication to the second computing device.

Abstract: A nanoelectromechanical systems (NEMS) oscillator network and methods for its operation are disclosed. The NEMS oscillator network includes one or more network inputs configured to receive one or more input signals. The NEMS oscillator network also includes a plurality of NEMS oscillators coupled to the one or more network inputs. Each of the plurality of NEMS oscillators includes a NEMS resonator and produces a radio frequency (RF) output signal that oscillates at a particular frequency and a particular phase. The NEMS oscillator network further includes a plurality of connections that interconnect the plurality of NEMS oscillators. The NEMS oscillator network further includes one or more network outputs coupled to the plurality of NEMS oscillators and configured to output one or more output signals.

Abstract: A method for sequentially encrypting and decrypting doubly linked lists based on double key stream ciphers comprises: establishing a plaintext set M according to a plaintext file; using the plaintext set M as an initial value and performing iterative decryption to obtain a ciphertext set C, wherein a key set P and an algorithm set A are used during the iterative decryption; for the ciphertext set C, performing multiple decryptions by calling the key set P and keys in the key set P, wherein a key set P and an algorithm set A are used during the decryptions; and, converting the obtained result of decryption into a plaintext file.

Abstract: A method for operating a communications network node, the node including a first amplified optical section, a second non-optical section, and an optical bypass section the method including receiving at the node, a first optical channel at a first wavelength and a second optical channel at a second wavelength; directing the first optical channel to the first amplified optical section; directing the second optical channel to the second non-optical section during a first time period; and directing the second optical channel to the optical bypass section during a second time period.

Abstract: A system and method for encryption key generation by receiving a plaintext message having a fixed character length and receiving, from a source, a plurality of random number. A matrix is created from the plurality random numbers and has at least one of the number of rows or columns equal to or greater than the character length. An array that can be used as an encryption key or a seed for an encryption key is generated by selecting an initial element within the matrix, selecting subsequent elements using a selection technique until a number of elements in the array is equal to the character length and rejecting any previously selected elements from the array.

Abstract: Circuitry and processes are disclosed that use conventional electronic circuits (comprising, for example, phase locked loops, pulse width modulators, phase modulators, digital logic gates, etc.) to enable quantum algorithms. Such circuitry and processes achieve the requirement for non-quantum devices to enable quantum algorithms: the tensor product entanglement of signals representing quantum states. Such circuitry and processes are readily usable by current Electronic Design Automation tools, to design, verify and emulate applications such as fast, very large number factoring for use in decryption. Also, the independent Claims concisely signify embodiments of the claimed inventions.

Abstract: A High-Order PSK Signaling (HOPS) communications system which adapts sequence-based spread spectrum signaling techniques to the needs of low-power commercial standards. A HOPS signal generation apparatus incudes a seed calculator configured to calculate a series of seed vectors in response to a plurality of time-evolving key values wherein each of the seed vectors includes a plurality of index values calculated based upon the current key values. A sequence generator is configured to generate a series of time-evolving spreading sequences using the series of seed vectors. A modulator is operative to generate the communications signal by spreading the data signal using the spreading sequences. A transmitter transmits an analog version of the communications signal.

Abstract: A device and method for quantum key distribution (QKD). The QKD center includes an authentication key sharing unit for sharing authentication keys with QKD client devices; a quantum key generation unit for generating a sifted key for each of the QKD client devices using a quantum state; an error correction unit for generating output bit strings by correcting errors of the sifted keys; and a bit string operation unit for calculating an encryption bit string by performing a cryptographic operation on the authentication keys, the distribution output bit strings and output bit strings received from the QKD client devices. The present invention improves security by preventing the QKD center from being aware of keys shared among users.

Abstract: Aspects of the disclosure provide a technological improvement to a cipher by improving data security of format-preserving encryption (FPE), by, inter alia, embedding specific key identifiers for rotating keys directly into ciphertext. Aspects of the disclosure relate to methods, computer-readable media, and apparatuses for improving data security in a format-preserving encryption (FPE) context by using specific methods of rotating and identifying the appropriate encryption key from among numerous rotating keys stored in a key data store. Specific to FPE, a plaintext of the data and its corresponding ciphertext of the data remain the same in length/size; yet the methods, computer-readable media, and/or apparatuses disclosed herein permit embedding of an identification of a specific key among the plurality of rotating keys for the particular ciphertext without compromising the technical requirements of FPE.

Abstract: An improved method of distributing timing information is provided. The method includes transmitting encrypted timing signals from two or more beacons at different locations. The encrypted timing signals are transmitted at regular intervals and are received by a receiver. The receiver then performs a logic operation on the encrypted timing signals and validates, based on the logic operation, the authenticity of the timing signals. The logic operation also results in a decrypted message from the beacons, which can contain additional information, for example, data to be sent back to the beacons to verify receipt.

Abstract: A true random number generator including a light source configured to produce randomly distributed photons, a plurality of detection channels configured to receive the randomly distributed photons produced by the light source, each detection channel including a photon sensor configured to detect a receipt of at least one photon during successive integration time-periods and generate an output signal by assigning a value for each integration time-period based on whether at least one photon was received during each integration time-period, a signal conditioning unit configured to condition the output signal of each of the plurality of detection channels and generate a conditioned output signal for each of the plurality of detection channels, and a signal processing unit configured to combine the conditioned output signals and generate a true random number based on the combination of the conditioned output signals.

Abstract: A file system stores files in a location base on deterministic nonlinear functions using certain initial conditions of the files creation. The file is chunked and encrypted according to one of a set of encryption algorithms based on the initial conditions. Only the file name and associated initial conditions are stored; the initial location and encryption algorithm are not stored and therefore not retrievable. The file system periodically relocates the files based on one of a set of algorithms based on the initial conditions such that even if the initial location where know, the file would still be irretrievable without knowing the relation between the initial conditions and relocation algorithm. During retrieval, the system uses the stored initial conditions to identify the initial location, relocation algorithm, and encryption algorithm.

Abstract: A system, method and apparatus that uses a quantum event-based, binary data generation apparatus operating in combination with a single-party or two-party, symmetric and/or asymmetric key storage system to create both random numbers and encryption keys to be used for purposes of encryption and decryption of a user's or organization's file data.

Abstract: A data compression system can include a compression unit comprising a single chaotic system having an identified initial condition that produces a desired output sequence of data corresponding to a data set being stored. The single chaotic system can be identified using a chain of controlled nonlinear systems and a dynamical search technique to match the output, in sequence over consecutive time intervals with the chain of the controlled nonlinear systems.

Abstract: In an embodiment, an apparatus includes a first logic to receive from a first node a synchronization portion of a message and to generate a set of state information using the synchronization portion, to synchronize the apparatus with the first node. The apparatus may further include a second logic to decrypt a data portion of the message using the set of state information to obtain a decrypted message. Other embodiments are described and claimed.

Abstract: A transmit signal can be distorted with non-linear distortion, and one or more characteristics of the non-linear distortion can be periodically changed in accordance with a change key. The transmission received at a receiver can thus comprise a severely distorted version of the transmission of the transmit signal. A receiver with the same change key can recognize and decode the transmission, but it can be extraordinarily difficult for receivers that lack the change key to detect and decode the transmission. The transmission can be a communications while jamming (CWJ) transmission. The CWJ transmission can contain a coded message that can be decoded only by friendly RF receivers, and the CWJ transmission can also jam unfriendly RF receivers that lack a change key for decoding the coded message.

Abstract: Apparatus and methods for removing leakage from a qubit. In one aspect, an apparatus includes one or more qubits, wherein each qubit facilitates occupation of at least one of a plurality of qubit levels, the qubit levels including two computational levels and one or more non-computational levels that are each higher than the computational levels, wherein the qubit facilitates transitions between qubit levels associated with a corresponding transition frequency; a cavity, wherein the cavity defines a cavity frequency; one or more couplers coupling each qubit to the cavity; one or more couplers coupling the cavity to an environment external to the one or more qubits and the cavity; a frequency controller that controls the frequency of each qubit such that, for each qubit, the frequency of the qubit is adjusted relative to the cavity frequency such that a population of a non-computational level is transferred to the cavity.

Abstract: A method for deducing a quantity (?), in two distinct locations, from further distinct measurable quantities. The method comprises the steps of observing with a first device (CD) the quantity (?) from an intercepted signal, whereby the device is placed in a location with first coordinates (Xi, Yi, Zi); providing a second device (AS) in a location with second coordinates (Xs, Ys, Zs); causing the second device to transmit a signal to be intercepted by the first device (CD); whereby the second device (AS) needs to know the second coordinates and be informed of the first coordinates of the first device (CD) to calculate the quantity (?) that can be obtained from measurements by the first device (CD); the quantity (?) thereby being known by the second device (AS) and the first device (CD) without the need to communicate the quantity or any other value that is sufficient for a third device to deduce the quantity (?).

Abstract: A system, method, and device for stochastically processing data. There is an architect module operating on a processor configured to manage and control stochastic processing of data, a non-deterministic data pool module configured to provide a stream of non-deterministic values that are not derived from a function, a plurality of functionally equivalent data processing modules each configured to stochastically process data as called upon by the architect module, a data feed configured to feed a data set desired to be stochastically processed, and a structure memory module including a memory storage device and configured to provide sufficient information for the architect module to duplicate a predefined processing architecture and to record a utilized processing architecture.

Abstract: The invention relates in particular to a method for securing the execution of a cryptographic algorithm (ALG) against passive sniffing, the method implementing masking (MSK) of data processed by the cryptographic algorithm. The masking (MSK) of said data includes a linear encoding step such as x?=x·L+c, in which x is the data to be masked, x? is the corresponding masked data, c is a code word included in a linear code C, and L is a matrix made up of linearly independent vectors not included in the linear code C. The invention also relates to a device (SC) implementing such a method.

Abstract: A method in an elliptic curve cryptographic system, the method being executed by an electronic device and including a multiplication operation of multiplying a point of an elliptic curve by a scalar number, the point having affine coordinates belonging to a Galois field, the multiplication operation including steps of detecting the appearance of a point at infinity during intermediate calculations of the multiplication operation, and of activating an error signal if the point at infinity is detected and if the number of bits of the scalar number processed by the multiplication operation is lower than the rank of the most significant bit of an order of a base point of the cryptographic system.

Abstract: A quantum cryptographic key distribution system, including: an optical source, which generates a plurality of optical pulses; an optical beam splitter, which generates, starting from each optical pulse, a first and a second optical sub-pulse; a first and a second peripheral device; and an optical path having a first and a second end connected to the optical beam splitter, the optical path extending through the first and second peripheral devices and being traversed in opposite directions by the first and second optical sub-pulses. The peripheral device randomly phase shifts the second optical sub-pulse by a first phase, and the second peripheral device randomly phase shifts the first optical sub-pulse by a second phase. Furthermore, the optical path is such as to cause interference in the first optical beam splitter between the first and second optical sub-pulses, as a function of first and second phases.

Abstract: Various embodiments are provided for fully digital chaotic differential equation-based systems and methods. In one embodiment, among others, a digital circuit includes digital state registers and one or more digital logic modules configured to obtain a first value from two or more of the digital state registers; determine a second value based upon the obtained first values and a chaotic differential equation; and provide the second value to set a state of one of the plurality of digital state registers. In another embodiment, a digital circuit includes digital state registers, digital logic modules configured to obtain outputs from a subset of the digital shift registers and to provide the input based upon a chaotic differential equation for setting a state of at least one of the subset of digital shift registers, and a digital clock configured to provide a clock signal for operating the digital shift registers.

Abstract: A software system which uses a specially designed cellular automaton network to perform symmetric-key encryptions and decryptions of user-supplied input messages. The input messages are in the form of text or images or audio data. A mathematical function based on Fibonacci sequences in the complex domain is used to define interactions among the cells of the cellular automaton network. The outputs of the system are encryptions of the user inputs; a simple key inversion procedure enables the decrypting of the encrypted output. The system permits multiple encryptions of the input and this, in turn, requires multiple decryptions to obtain the original input.

Abstract: In an embodiment, an apparatus includes a first logic to receive from a first node a synchronization portion of a message and to generate a set of state information using the synchronization portion, to synchronize the apparatus with the first node. The apparatus may further include a second logic to decrypt a data portion of the message using the set of state information to obtain a decrypted message. Other embodiments are described and claimed.

Abstract: An optical system for sensing an environmental parameter, comprising: an optical pulse generator for generating an excitation pulse; a pulse splitter for splitting the excitation pulse into a sensing pulse and a reference pulse; a sensing arm for receiving the sensing pulse, the sensing arm comprising an emission sensor for sensing the environmental parameter, the optical emission sensor generating a first measurement pulse having a measurement wavelength; a reference arm for receiving the reference pulse, the reference arm comprising an emission artifact adapted to convert the reference pulse into a second measurement pulse having the measurement wavelength; a time delay line for delaying a relative propagation of the measurement pulses; a light detector for measuring an optical energy of the first and second measurement pulses; and an optical link for optically connecting the pulse generator to the pulse splitter, and the sensing and reference arms to the light detector.

Abstract: The technology includes a method for generating a secret key. The method includes receiving initialization data, the initialization data includes an initialization packet and a transmission path channel response; generating sample data based on the transmission path channel response; and generating a secret key based on the sample data utilizing a chaotic map.

Abstract: Systems and methods for calculating the Lyapunov exponent of a chaotic system are described. In one particular embodiment, a Lyapunov exponent calculating method includes obtaining a value indicative of a condition of a chaotic system and assigning the value to first and second precision levels, the second precision level having a higher level of precision than the first precision level. The method also includes iterating the chaotic system over time and comparing the value at the first precision level with the value at the second precision level. From the comparison of values at the first and second precision levels, the method calculates the Lyapunov exponent for the chaotic system.

Abstract: Techniques and tools for implementing protocols for secure multi-party communication after quantum key distribution (“QKD”) are described herein. In example implementations, a trusted authority facilitates secure communication between multiple user devices. The trusted authority distributes different quantum keys by QKD under trust relationships with different users. The trusted authority determines combination keys using the quantum keys and makes the combination keys available for distribution (e.g., for non-secret distribution over a public channel). The combination keys facilitate secure communication between two user devices even in the absence of QKD between the two user devices. With the protocols, benefits of QKD are extended to multi-party communication scenarios. In addition, the protocols can retain benefit of QKD even when a trusted authority is offline or a large group seeks to establish secure communication within the group.