A device may receive a set of cryptographic parameters associated with an integer, wherein the set of cryptographic parameters includes a linked list of potential prime integers, in an order, used to generate the integer. The device may determine, iteratively and in the order, whether each potential prime integer included in the linked list of potential prime integers is a prime integer using a primality test or a lookup operation based on a set of proven prime integers. The device may determine whether the integer is a proven prime integer based on determining whether each potential prime integer included in the linked list of potential prime integers is a prime integer. The device may authorize, when the integer is a proven prime integer, the integer for use in a cryptographic protocol.

Scrambling a point cloud (PC), including: receiving the PC in polar coordinates, wherein each point of the PC includes an index; scrambling each point of the PC by translating each point along a radial axis of the polar coordinates by adding a pseudo-random number (PRN) to each point, wherein the PRN is generated using the index and a secret key.

A method of storing data on a blockchain, such as the bitcoin blockchain, is disclosed. The method comprises generating a blockchain transaction having at least one first input and/or at least one first output containing first data (<Content 1>) to be stored on the blockchain, and at least one second input and/or at least one second output containing second data (<Attribute 1>,<Attribute 2>) representing at least one attribute of the first data. At least one second input and/or at least one second output is separate from the or each first input and/or first output.

Disclosed herein are methods, systems, and apparatus, including computer programs encoded on computer storage media, for recovering and verifying a public key. One of the methods includes accepting information encoding parameters of an elliptic curve, a published public key, a hash value of a message, a digital signature, and an identification parameter; generating a recovered public key based on the parameters of the elliptic curve, the hash value of the message, the digital signature, and the identification parameter; comparing the published public key and the recovered public key to verify the published public key.

Methods and systems for secure authentication in an extended reality (XR) environment are described herein. An XR environment may be output by a computing device and for display on a device configured to be worn by a user. A first plurality of images may be determined via the XR environment. The first plurality of images may be determined based on a user looking at a plurality of objects, real or virtual, in the XR environment. The first plurality of images may be sent to a server, and the server may return a second plurality of images. A public key and private key may be determined based on different portions of each of the second plurality of images. The public key may be sent to the server to register and/or authenticate subsequent communications between the computing device and the server.

A method for decrypting encrypted data/message whereby a computing device derives the prime numbers that are used to make up a public key by searching the decimals of the inverse of the quasi-prime number that is the public key. The computing devices designates a search range around a jump point of the decimals of the inverse of the public key and searches within the search range for prime numbers by testing them against the quasi-prime. When the prime numbers are found, the computing device then uses them to derive the private key and decrypt the data.

Device, system, and method of generating and handling cryptographic parameters. A first device and a second device store the same secret seed value, utilize the same deterministic pseudo-random number generation function, and utilize the same deterministic value modification function. The first device generates a candidate value, sequentially modifies its value, and performs primality testing until a confirmed prime number is found. The first device indicates to the second device, how many iterations of value modifications to perform in order to reach and thus re-generate therein the same already-confirmed prime number, without the need to perform any primality testing in the second device.

Disclosed are methods and systems to encrypt data with SomeWhat Homomorphic Encryption (SWHE) properties for submission to a distributed ledger/blockchain that allows further open operations retained in the distributed ledger/blockchain on the encrypted data that will be properly reflected when the encrypted result is decrypted by the data owner. The somewhat homomorphic properties include addition and scalar division. Also disclosed is an ability to update a secret key applied for a ciphertext such that a single piece of data may be provided on the distributed ledger/blockchain by a data owner to a new data owner without also exposing other data encrypted with the original secret key of the original data owner.

A method of storing data on a blockchain, such as the Bitcoin blockchain, is disclosed. The method comprises generating a plurality of blockchain transactions, wherein a plurality of the blockchain transactions each store therein a respective part (<Content chunk 1>, <Content chunk 2>) of first data to be stored on the blockchain and second data (<Metanet Flag>) indicating that the parts of the first data are related to each other.

An anonymous authentication service for an invulnerable secret key authentication and encryption token distribution service. Applications place a small code segment within their communications protocol, thereby allowing network participants the full benefit of perfectly secure authenticated and encrypted message traffic without concern for third party key management. This is the world's first participant-managed, independent-trust secure messaging key distribution capability.