Abstract: A system for providing notifications to client devices that includes one or more processors and one or more storage devices. The storage devices may store instructions that, when executed, configure the processors to perform operations. The operations include receiving a transaction notification from a third party; identifying a user account associated with the transaction notification; generating a push notification with a payload describing instructions to display a message and an interactive icon, and a resource identifier associated with the interactive icon, where the resource identifier includes a message ID encoding an interactive session and an action ID encoding a requested action. The operations also include transmitting the push notification to a client device associated with the user account; receiving a first indication indicating a user interaction with the interactive icon, the first indication having the resource identifier and updating the user account based on the action request.

Abstract: A system for providing notifications to client devices that includes one or more processors and one or more storage devices. The storage devices may store instructions that, when executed, configure the processors to perform operations. The operations include receiving a transaction notification from a third party; identifying a user account associated with the transaction notification; generating a push notification with a payload describing instructions to display a message and an interactive icon, and a resource identifier associated with the interactive icon, where the resource identifier includes a message ID encoding an interactive session and an action ID encoding a requested action. The operations also include transmitting the push notification to a client device associated with the user account; receiving a first indication indicating a user interaction with the interactive icon, the first indication having the resource identifier and updating the user account based on the action request.

Abstract: The present scheme improves the security of encrypted data or information by using of a practical public-key cryptosystem that is able to resist adaptive attacks. The disclosed scheme does not leak any information about the secret of the used key. Therefor the scheme generates an extended private key and public key. A message m, also referred to as plaintext, is encryptable to a ciphertext t by using the public key. Only a recipient with the right private key is able to decrypt the ciphertext t. But before a decryption starts, a verification of the ciphertext t takes place. Such a verification allows to prove the legitimation of the ciphertext t. That means, the ciphertext t is investigated and either decrypted back to the plaintext or rejected if a chosen ciphertext is fed, ie. the ciphertext is illegitimate or invalid.

Abstract: A method is provided for reducing a known value modulo a shared secret value among network devices exchanging messages in a network. The reduction results in a share of reduced value for each network device of a reduced value. Each network device has its share of known value and its share of shared secret value. It performs an inversion step for deriving from the share of shared secret value a share of the inverse of the shared secret value by using an approximation process, resulting in a share of inverse value; a multiplication step for deriving from the share of inverse value by use of the share of known value a share of multiplied inverse value; a rounding step for rounding the share of multiplied inverse value; and a calculation step for deriving the share of reduced value from the share of known value, the rounded share of multiplied inverse value, and the share of shared secret value.

Abstract: Byzantine Agreement requires a set of parties in a distributed system to agree on a value even if some parties are corrupted. The invention comprises a method for achieving agreement among participating network devices in an asynchronous network is disclosed that makes use of cryptography, specifically of threshold digital signatures and a distributed coin-tossing protocol.

Abstract: Methods and apparatus for achieving agreement among participating network devices in an asynchronous network for deciding on a common value is disclosed, whereby the common value is validated by a justification and both together satisfy a predetermined predicate. Moreover, a method for reliably broadcasting messages in an order within the asynchronous network is described. Up to one third or more of the participating network devices might be faulty in arbitrary ways.

Abstract: The present scheme improves the security of encrypted data or information by using of a practical public-key cryptosystem that is able to resist adaptive attacks. The disclosed scheme does not leak any information about the secret of the used key. Therefor the scheme generates an extended private key and public key. A message m, also referred to as plaintext, is encryptable to a ciphertext t by using the public key. Only a recipient with the right private key is able to decrypt the ciphertext t. But before a decryption starts, a verification of the ciphertext t takes place. Such a verification allows to prove the legitimation of the ciphertext t. That means, the ciphertext t is investigated and either decrypted back to the plaintext or rejected if a chosen ciphertext is fed, ie. the ciphertext is illegitimate or invalid.

Abstract: A method for achieving agreement among n participating network devices to an agree-value in a network is disclosed. The method proposes an optimistic approach to the consensus problem, whereby the number t of faulty devices is less than n/3. It is distinguished between an optimistic and pessimistic case. In the pessimistic case, a fallback agreement protocol is performed that reaches the same agree-value as the method in the optimistic case outputs.

Abstract: The present scheme improves the security of encrypted data or information by using of a practical public-key cryptosystem that is able to resist adaptive attacks. The disclosed scheme does not leak any information about the secret of the used key. Therefor the scheme generates an extended private key and public key. A message m, also referred to as plaintext, is encryptable to a ciphertext t by using the public key. Only a recipient with the right private key is able to decrypt the ciphertext r. But before a decryption starts, a verification of the ciphertext t takes place. Such a verification allows to prove the legitimation of the ciphertext t. That means, the ciphertext t is investigated and either decrypted back to the plaintext or rejected if a chosen ciphertext is fed, ie. the ciphertext is illegitimate or invalid.

Abstract: A method is provided for reducing a known value modulo a shared secret value among network devices exchanging messages in a network. The reduction results in a share of reduced value for each network device of a reduced value. Each network device has its share of known value and its share of shared secret value. It performs an inversion step for deriving from the share of shared secret value a share of the inverse of the shared secret value by using an approximation process, resulting in a share of inverse value; a multiplication step for deriving from the share of inverse value by use of the share of known value a share of multiplied inverse value; a rounding step for rounding the share of multiplied inverse value; and a calculation step for deriving the share of reduced value from the share of known value, the rounded share of multiplied inverse value, and the share of shared secret value.

Abstract: Methods and apparatus for achieving agreement among participating network devices in an asynchronous network for deciding on a common value is disclosed, whereby the common value is validated by a justification and both together satisfy a predetermined predicate. Moreover, a method for reliably broadcasting messages in an order within the asynchronous network is described. Up to one third or more of the participating network devices might be faulty in arbitrary ways.

Abstract: A method for the fair exchange of value items between two parties is presented in which a third party is only involved in exceptional situations. Each party sends initially in an exchange procedure, to the other party a permit which binds its value item in such a way that the receiving party can verify the fact that the value item is bound, but cannot yet extract the expected value item from the permit. If a party can accept a permit as correct, it then sends the actual value item to the other party. Thus, the exchange can be completed without involving the third party if no exceptional situation occurs.

Abstract: Byzantine Agreement requires a set of parties in a distributed system to agree on a value even if some parties are corrupted. The invention comprises a method for achieving agreement among participating network devices in an asynchronous network is disclosed that makes use of cryptography, specifically of threshold digital signatures and a distributed coin-tossing protocol.

Abstract: A method for achieving agreement among n participating network devices to an agree-value in a network is disclosed. The method proposes an optimistic approach to the consensus problem, whereby the number t of faulty devices is less than n/3. It is distinguished between an optimistic and pessimistic case. In the pessimistic case, a fallback agreement protocol is performed that reaches the same agree-value as the method in the optimistic case outputs.