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.

An encryption protocol is provided that can be implemented within a single clock cycle of an integrated circuit chip while still providing unbreakable encryption. The protocol of the present invention is so small that it can co-exist on any integrated circuit chip with other functions, including a general purpose central processing unit, general processing unit, or application specific integrated circuits with other communication related functionality.

A secure computation technique for performing a bit shift operation at high speed using a protocol for performing left shift with a numerical value and a shift amount to be shifted as inputs. A secure shift system for computing a share [[s]].sup.P of a numerical value s obtained by shifting a numerical value a by p bits from a share [[a]].sup.P of the numerical value a and a share <<ρ>>.sup.Q of the shift amount p includes a modulus conversion circuitry for computing a share <<ρ>>.sup.p, a first flag computation circuitry for computing shares [[f.sub.0]].sup.2, . . . , [[f.sub.L]].sup.2, a second flag computation circuitry for computing shares <<f.sub.1>>.sup.p, . . . , <<f.sub.L>>.sup.p, a shift amount computation circuitry for computing shares <<ρ′>>.sup.p, a left shift circuitry for computing a share [[b]].sup.P, a right shift circuitry for computing shares [[c.sub.0]].sup.P, . . . , [[c.sub.d-1]].sup.P, a third flag computation circuitry, and a shift value computation circuitry.

Temporal key generation devices and methods are described. One such device of a first domain receives a “seed” to generate a private key associated with a public key for use in a second domain. The device uses the private key in cryptographic operations with the second domain. When the device loses power or is no longer connected to the second domain, the private key may be erased or no longer stored on the device.

Disclosed are methods and systems to use p-adic numbers to permit a RSA cryptosystem to send rational numbers or to add randomness to the RSA cryptosystem. An embodiment may convert at the source device a rational number to an integer as p-adic based Hensel code representation of the rational number at the source device and then recover the rational number at the destination device by reversing the Hensel code back to the original rational number. Another embodiment may use a g-adic inverse of a message value together with a random number to obtain a different rational number to encrypt for each different random number resulting in different ciphertexts representing the same message value while still recovering the original message value despite having a different ciphertexts for the same message value. The various embodiments further retain the multiplicative homomorphism of the RSA cryptosystem since the p-adic Hensel codes are also multiplicative homomorphic.

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.

The invention provides improved methods and systems for storing, sharing retrieving, writing and accessing data (content) on a blockchain. The invention may form part of a protocol for storing, searching and accessing the data. An embodiment of the invention comprises the step of processing at least one blockchain transaction (Tx) comprising: a protocol flag; a discretionary public key (DPK); and a discretionary transaction ID (DTx ID). These are discretionary in the sense that they are not required as part of the underlying blockchain protocol but in accordance with the present invention. This combination of features enables portions of data to be identified, retrieved and shared on a blockchain, and also to be linked/associated with one another when provided in a plurality of transactions. It enables a graph or tree-like structure to be constructed, which reflects the hierarchical relationships between portions of data, facilitating their processing, searching and sharing.

The invention provides improved methods and corresponding systems for the sharing, storage, creation and accessing of data stored on a blockchain eg the Bitcoin blockchain. It may form part of a protocol for searching the blockchain for content/data. A method in accordance with the invention may be used for associating or linking data stored within (separate/different) blockchain transactions to enable the identification, retrieval and/or sharing of data stored therein. Additionally, or alternatively, it facilitates identification of transactions (TX) in a blockchain which store content/data that needs to be shared, transmitted, stored and/or accessed by a user. Such a method comprises the step of mapping a mnemonic to: 1) a public key (PK) associated with the transaction (TX); and 2) the transaction ID (TX.sub.ID) of the transaction (TX).

A method of encrypting and storing a data item; said method comprising: a data encryption step wherein the data item is encrypted to form an encrypted data item; a mathematical disassembly step wherein the encrypted data item is mathematically disassembled into two or more encrypted data item component parts comprising at least a first component part and a second component part; storing at least a one of the component parts at a location separate from the others of the component parts.

Embodiments are disclosed for fairness in gaming. The techniques include generating a public-private key pair for a bet with a gaming application. The techniques further include encrypting the bet using the generated public-private key pair. Additionally, the techniques include providing the encrypted bet to the gaming application. The techniques also include providing a private key of the public-private key pair in response to a notice from the gaming application indicating whether the bet is won.