A system and method for communicating over a network, including encrypting and decrypting communications of data over the network for providing enhanced security utilizing a blockchain-encryption process and a global device ledger, and further including systems for device and session initialization, automation, data capture, security, providing alerts, personalization of settings, and other objectives. Methods of establishing and monitoring network communications are further included.

A computer-implemented method and system for computing large-degree isogenies of a base degree raised to a power of form .sup.ak+b and including the steps of providing at least one computer processor resident on an electronic computing device, performing, with the at least one processor, a large-degree isogeny by chaining together a plurality of scalar point multiplications, a plurality of isogeny computations, and a plurality of isogeny evaluations, wherein the large-degree isogeny includes a sequence storing at least one pivot point computed by one of the plurality of scalar point multiplications followed by an isogeny computation of degree .sup.b, performing at least one of the plurality of isogeny evaluations following one of the plurality isogeny computations, and performing an .sup.ak-isogeny through another sequence of .sup.a isogeny computations.

Methods and systems are provided for supporting efficient and secure “Machine-to-Machine” (M2M) communications using a module, a server, and an application. A module can communicate with the server by accessing the Internet, and the module can include a sensor and/or an actuator. The module, server, and application can utilize public key infrastructure (PKI) such as public keys and private keys. The module can internally derive pairs of private/public keys using cryptographic algorithms and a first set of parameters. A server can authenticate the submission of derived public keys and an associated module identity. The server can use a first server private key and a second set of parameters to (i) send module data to the application and (ii) receive module instructions from the application. The server can use a second server private key and the first set of parameters to communicate with the module.

An apparatus for validating an identity of an individual based on biometrics includes a memory and a processor operatively coupled to a distributed database and the memory. The processor is configured to provide biometric data as an input to a predefined hash function to obtain a first biometric hash value. The processor is configured to obtain, using a first pointer to the distributed database, a signed second biometric hash value. The processor is configured to define a certification of the biometric data in response to verifying that a signature of the signed second biometric hash value is associated with the compute device and verifying that the first biometric hash value corresponds with the second biometric hash value. The processor is configured to digitally sign the certification using a private key associated with the processor to produce a signed biometric certification and store the signed biometric certification in the distributed database.

There may be provided a blockchain-implemented security method involving a requestor and a group of nodes, which includes generating a cryptographic key of the requestor based on a password chosen by the requestor and first quantities sent by the group of nodes (which are derived from private key shares of the group of nodes and a generator function of a digital signature scheme employing a bilinear mapping on an elliptic curve). A cryptographic signature for a requestor blockchain transaction can be generated where the signature corresponds to the requestor's cryptographic key. The signature can be based on the password and second quantities sent by the group of nodes (which are also derived from the group private key shares). The method can further include verifying the cryptographic signature of the blockchain transaction using the requestor's cryptographic key. Additionally or alternatively, the method can employ a consensus mechanism involving the group of nodes to allow the requestor to authorise a transaction with a password. The method can be logically partitioned into a sequence of phases, including an initialisation phase, a funding phase, and a payment authorization phase (which involves a pre-spending transaction and a spending transaction).

The present disclosure relates to a cryptographic method comprising: multiplying a point belonging to a mathematical set with a group structure by a scalar by performing: the division of a scalar into a plurality of groups formed of a same number w of digits, w being greater than or equal to 2; and the execution, by a cryptographic circuit and for each group of digits, of a sequence of operations on point, the sequence of operations being identical for each group of digits, at least one of the operations executed for each of the groups of digits being a dummy operation.

An elliptic curve random number generator avoids escrow keys by choosing a point Q on the elliptic curve as verifiably random. An arbitrary string is chosen and a hash of that string computed. The hash is then converted to a field element of the desired field, the field element regarded as the x-coordinate of a point Q on the elliptic curve and the x-coordinate is tested for validity on the desired elliptic curve. If valid, the x-coordinate is decompressed to the point Q, wherein the choice of which is the two points is also derived from the hash value. Intentional use of escrow keys can provide for back up functionality. The relationship between P and Q is used as an escrow key and stored by for a security domain. The administrator logs the output of the generator to reconstruct the random number with the escrow key.

The proposed system employs one or more steps and an architectural arrangement of a plurality of relevant functional element to enable a security. A USB device is arranged to enable secure access of a computing device. A first cloud server is arranged to receive an ID, a cryptographic key, an authentication PIN and a pre-stored data from the computing device. The first cloud server encrypts the received pre-stored data using the received cryptographic key and subsequently transmits the ID, the cryptographic key and the authentication PIN, to a second cloud server. Further, the second cloud server performs a plurality of sequential functional operation, critical to the motive and objective of deploying the proposed system.

A public-key scheme of Homomorphic Encryption (HE) in the framework Quotient Algebra Partition (QAP) comprises: encryption, computation and decryption. With the data receiver choosing a partition or a QAP, [n, k, C], a public key Key.sub.pub=(VQ.sub.en, ) and a private key Key.sub.priv=.sup.†P.sup.\ are produced, where VQ.sub.en is the product of an n-qubit permutation V and an n-qubit encoding operator Q.sub.en, an error generator randomly provides a dressed operator Ē=V.sup.†EV of spinor error E of [n, k, C]. Then, by Key.sub.pub, the sender can encode his k-qubit plaintext |x into an n-qubit ciphertext |ψ.sub.en, which is transmitted to the cloud. The receiver prepares the instruction of encoded computation U.sub.en=PV.sup.†Q.sub.en.sup.† for a given k-qubit action M and sends to cloud, where is the error-correction operator of [n, k, C], =I.sub.2.sub.n−k.Math.M the tensor product of the (n−k)-qubit identity I.sub.2.sub.n−k and M, and V.sup.†Q.sub.en.sup.† and PMETHOD AND SYSTEM FOR KEY AGREEMENT UTILIZING PLACTIC MONOIDS