Abstract: According to an aspect of an embodiment operations may include receiving, by a server, message shares. The operations may also include generating, by the server, an aggregate hash share of the message shares. In addition, the operations may include receiving, by the server, a verification vector iteration from another server and generating another verification vector iteration based on: the received verification vector iteration, a permutation that corresponds to the server, and a masking vector that corresponds to the server. The operations may also include obtaining a verification hash that is based on the verification vector and participating in a multiparty computation to determine an aggregate hash. The operations may also include determining, as part of the multiparty computation, whether one or more of the servers is operating in an adverse manner based on whether the verification hash is equal to the aggregate hash.

Abstract: A method of implementing a revocable threshold hierarchical identity-based signature scheme may include receiving an identifier associated with a user. A first secret key based on the identifier may be generated. A string and the identifier may be directed to be posted on a block of a blockchain. A second secret key may be generated using the string, the first secret key, and the identifier. The block that includes the string and the identifier may be signed using the second secret key. A message may be signed using the second secret key to generate a signature. The signature may be provided to a device. The signature may be verifiable by the device using the string and the identifier obtained from the block by the device.

Abstract: According to an aspect of an embodiment operations may include receiving, by a server, message shares. The operations may also include generating, by the server, an aggregate hash share of the message shares. In addition, the operations may include receiving, by the server, a verification vector iteration from another server and generating another verification vector iteration based on: the received verification vector iteration, a permutation that corresponds to the server, and a masking vector that corresponds to the server. The operations may also include obtaining a verification hash that is based on the verification vector and participating in a multiparty computation to determine an aggregate hash. The operations may also include determining, as part of the multiparty computation, whether one or more of the servers is operating in an adverse manner based on whether the verification hash is equal to the aggregate hash.

Abstract: A method may include obtaining a set of tags and a set of items in which each item is pre-sorted into a cluster and each item corresponds to one or more tags. The method may include generating a bipartite graph that includes the set of tags as a first set of nodes and the clusters of items as a second set of nodes. Relationships between tags and items may be represented as edges between the first nodes and the second nodes. The bipartite graph may be modeled as a quadratic programming formulation, and cluster descriptor sets that each include one or more of the tags may be determined by solving the quadratic programming formulation of the bipartite graph, each of the cluster descriptor sets providing an explanation of how one or more clusters of items were pre-sorted. The method may include analyzing the items based on the luster descriptor sets.

Abstract: A method of facilitating an anonymous message board may include receiving a secret key share associated with a published public key. An initial table state may be generated by encrypting, via the public key, an initial table including a table index and table initial values. A user post encrypted via the public key may be received, the user post including a message and a message index value. The initial table state may be updated to an updated table state by replacing an initial table value of the initial table values with the message. In response to a time interval associated with a predetermined length of time expiring after generating the initial table state, the updated table state may be partially decrypted via the first secret key share as a partially decrypted table. The partially decrypted table may be broadcast.

Abstract: According to an aspect of an embodiment, operations include receiving a Quadratic Integer Programming (QIP) problem including an objective function and a set of constraints on integer variables associated with the objective function. The operations further include obtaining an approximation of the QIP problem by relaxing the QIP problem and generating an approximate solution by solving the obtained approximation. The operations further include generating a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the QIP problem based on the generated approximate solution and the received QIP problem. The operations further include submitting the generated QUBO formulation to an optimization solver machine and receiving a solution of the submitted QUBO formulation from the optimization solver machine. The operations further include publishing an integral solution of the received QIP problem on a user device based on the received solution.

Abstract: A method of solving a large scale combinatorial optimization problem including inputting, via at least one processor, an objective function and an initial solution as a mapping from a plurality of n nodes, randomly clustering the plurality of nodes into k clusters of n/k nodes each, for each cluster of the k clusters, assigning binary variables to denote each possible permutation of a label set within the cluster, determining that there are u=k2 variables if k>2, and u=1 variables if k=2, expressing the objective function in terms of the un/k variables, solving the objective function in terms of the un/k variables using a Quadratic Unconstrained Binary Optimization (QUBO) solver to obtain an updated solution, determining whether a convergence criteria is satisfied for the updated solution, and upon a determination that a convergence criteria is satisfied, outputting the updated solution to the objective function.

Abstract: A method may include splitting an original token into a first sub-token and a second sub-token, generating a first hash value of the first sub-token and a first randomness value, and generating a second hash value of the second sub-token and a second randomness value. The method may also include evaluating an NIZKP regarding the split, and sampling first and second signature keys and verification keys associated with the first and second sub-tokens, respectively. The method may additionally include generating first and second signed values of concatenations of the first and second hash values and the first and second verification keys, respectively, and signed using an initial signature key of a current owner of the original token. The method may additionally include sending the NIZKP, the first and second hash values, the first and second signed values, and the first and second verification keys to the blockchain.

Abstract: A method of facilitating an anonymous message board may include receiving a secret key share associated with a published public key. An initial table state may be generated by encrypting, via the public key, an initial table including a table index and table initial values. A user post encrypted via the public key may be received, the user post including a message and a message index value. The initial table state may be updated to an updated table state by replacing an initial table value of the initial table values with the message. In response to a time interval associated with a predetermined length of time expiring after generating the initial table state, the updated table state may be partially decrypted via the first secret key share as a partially decrypted table. The partially decrypted table may be broadcast.

Abstract: A method may include obtaining, by a first entity, a verification key from a second entity to which an asset is to be transferred. The method may also include proving to an administrator of a blockchain that the first entity is a current owner of the asset, the blockchain hosting a token associated with the asset. The method may additionally include providing an updated randomness value and the token to the second entity. The method may also include sending an updated hash value of the token and the updated randomness, a signed indication of the transfer of the asset from the first entity to the second entity, and the verification key of the second entity to an administrator of the blockchain.

Abstract: According to an aspect of an embodiment, operations may include receiving a set of inputs associated with a set of orders, a set of production lines, and timelines for the production. The operations may further include initializing each of a set of intervals to be used for scheduling of the production, based on a first interval size. The operations may further include generating a first Quadratic Unconstrained Binary Optimization (QUBO) formulation. The operations may further include generating a first solution of the first QUBO formulation. The operations may further include updating each of the initialized set of intervals based on a second interval size. The operations may further include generating a second QUBO formulation. The operations may further include generating a second solution by solving the second QUBO formulation and determining a schedule to be used for the production of the set of orders, based on the generated second solution.

Abstract: A method may include exchanging a secret symmetric key (SSK) between a first trusted execution environment (TEE) of a first system, a second TEE of a second system and a third TEE of a third system. The method may also include receiving, by the first system, an encrypted first set of data from the second system. The method may also include decrypting, by the first TEE, the encrypted first set of data using the SSK. The method may also include receiving, by the first system, an encrypted query from the third system. The method may also include decrypting, by the first TEE, the encrypted query using the SSK. The method may also include determining, by the first TEE, a query result to the decrypted query using index sets. The method may also include sending, by the first TEE, the encrypted query result to the third system.

Abstract: A method of implementing a revocable threshold hierarchical identity-based signature scheme may include receiving an identifier associated with a user. A first secret key based on the identifier may be generated. A string and the identifier may be directed to be posted on a block of a blockchain. A second secret key may be generated using the string, the first secret key, and the identifier. The block that includes the string and the identifier may be signed using the second secret key. A message may be signed using the second secret key to generate a signature. The signature may be provided to a device. The signature may be verifiable by the device using the string and the identifier obtained from the block by the device.

Abstract: A method may include obtaining a first matrix that represents data in a data set and obtaining a number of clusters into which the data is to be grouped. The method may further include constructing a second matrix using the first matrix and the number of clusters. The second matrix may represent a formulation of a first optimization problem in a framework of a second optimization problem. The method may further include solving the second optimization problem using the second matrix to generate a solution of the second optimization problem and mapping the solution of the second optimization problem into a first solution matrix that represents a solution of the first optimization problem. The method may further include grouping the data into multiple data clusters using the first solution matrix. A number of the multiple data clusters may be equal to the number of clusters.

Abstract: A method may include exchanging a secret symmetric key (SSK) between a first trusted execution environment (TEE) of a first system, a second TEE of a second system and a third TEE of a third system. The method may also include receiving, by the first system, an encrypted first set of data from the second system. The method may also include decrypting, by the first TEE, the encrypted first set of data using the SSK. The method may also include receiving, by the first system, an encrypted query from the third system. The method may also include decrypting, by the first TEE, the encrypted query using the SSK. The method may also include determining, by the first TEE, a query result to the decrypted query using index sets. The method may also include sending, by the first TEE, the encrypted query result to the third system.

Abstract: A method may include receiving a set of encrypted data and an associated public parameter from a first device. The set of encrypted data may be organized in rows. The method may also include receiving an encrypted query of an underlying query from a second device. The method may also include determining a query result using the set of encrypted data, the associated public parameter, and the encrypted query. The query result may include responsive rows of the set of encrypted data that remain encrypted. The responsive rows may be responsive to the underlying query without exposing the underlying query or the set of encrypted data to the system. The method may also include sending the query result to the second device.

Abstract: According to an aspect of an embodiment, operations include receiving an Integer Linear Programming (ILP) problem including an objective function and a set of constraints on integer variables of the objective function. The operations may further include determining a lower bound vector for the integer variables and determining an upper bound vector for the integer variables. The operations further include obtaining a binary variable representation of each of the integer variables and updating the received ILP problem based on the obtained binary variable representation. The operations further include generating a Quadratic Unconstrained Binary Optimization (QUBO) formulation of the updated ILP problem and submitting the generated QUBO formulation to a first optimization solver machine. The operations further include receiving a solution of the submitted QUBO formulation and determining an integral solution of the received ILP problem.

Abstract: According to an aspect of an embodiment, operations include obtaining a first set of input parameters associated with a modified multi-dimensional knapsack problem. The operations further include determining a lattice representation of the modified multi-dimensional knapsack problem and computing a reduced basis by applying a lattice reduction method on the set of basis vectors of the determined lattice representation. The operations further include determining a first mathematical formulation of the modified multi-dimensional knapsack problem based on the reduced basis and submitting the determined first mathematical formulation as an input to an integer linear programming (ILP) solver. The operations further include receiving a first solution of the submitted mathematical formulation from the ILP solver and determining an integral solution of the modified multi-dimensional knapsack problem. The operations further include controlling a user device to output the determined integral solution.

Abstract: According to an aspect of an embodiment, operations may include receiving a first input associated with a set of orders to be produced at a production facility and receiving a second input associated with a set of production lines. The operations may further include extracting a set of production-related datapoints and receiving a third input associated with a set of constraints. The operations may further include generating a Quadratic Unconstrained Binary Optimization (QUBO) formulation based on the extracted set of datapoints and the third input and submitting the generated QUBO formulation to a first optimization solver machine. The operations may further include receiving a first solution of the submitted QUBO formulation from the first optimization solver machine and determining a schedule to be used for the production of the set of orders on the set of production lines, based on the received first solution.

Abstract: According to an aspect of an embodiment, operations include receiving a set of datapoints for integrated clustering and outlier detection. The operations further include receiving, as a first input, a clustering constraint comprising a number of outlier datapoints to be detected from the set of datapoints and a second input including a distance metric. The operations further include formulating an objective function based on the first and second inputs and transforming the objective function into an unconstrained binary optimization formulation. The operations further include providing such formulation as input to an optimization solver machine and generating a clustering result and an outlier detection result based on output of the optimization solver machine for the input. The clustering result includes a set of datapoint clusters, and the outlier detection result includes a set of outlier datapoints. The clustering result and the outlier detection result are published on a publisher system.