A method and system for storage and retrieval of blockchains with Galois Fields. One or more blocks for a blockchain are securely stored and retrieved with a modified Galois Fields on a cloud or peer-to-peer (P2P) communications network. The modified Galois Field provides at least additional layers for security and privacy for blockchains. The blocks and blockchains are securely stored and retrieved for cryptocurrency transactions including, but not limited to, BITCOIN transactions and other cryptocurrency transactions.

Method and system for storage and retrieval of blockchain blocks using galois fields

A method and system for electronic content storage and retrieval with Galois Fields on cloud computing networks. The electronic content is divided into plural portions and stored in plural cloud storage objects. Storage locations for the plural cloud storage objects are selected using a Galois field and the plural cloud storage objects are distributed across the cloud network. When the electronic content is requested, the plural portions are retrieved and transparently combined back into the original electronic content. No server network devices or target network devices can individually determine locations of all portions of the electronic content on the cloud communications network, thereby providing layers of security and privacy for the electronic content on the cloud communications network.

Method and system for electronic content storage and retrieval with galois fields on cloud computing networks

A method and system for electronic content storage and retrieval using Galois Fields and information entropy on cloud computing networks Electronic content is divided into plural portions and stored in plural cloud storage objects based on determined information entropy of the electronic content thereby reducing location guessing of the electronic content using information gain and mutual information Storage locations for the plural cloud storage objects are selected using a Galois field The plural cloud storage objects are distributed across the cloud network The Galois filed and information entropy providing various levels of security and privacy for the electronic content

Method and system for electronic content storage and retrieval using galois fields and information entropy on cloud computing networks

Computationally implemented methods and systems include acquiring a block of encrypted data that corresponds to an image that has been encrypted through use of a unique device code associated with an image capture device configured to capture the image that includes a representation of a feature of an entity, obtaining a privacy metadata that corresponds to a detection of a privacy beacon in the image, said at least one image captured by the image capture device, said privacy beacon associated with the entity, and determining, at least partly based on the obtained privacy metadata, and partly based on a calculation related to the block of encrypted data that corresponds to the whether to allow one or more processes related to the encrypted data block. In addition to the foregoing, other aspects are described in the claims, drawings, and text.

Devices, methods, and systems for managing representations of entities through use of privacy beacons

A method and system for electronic content storage and retrieval using Galois Fields and geometric shapes on cloud computing networks. Plaintext electronic content is divided into plural portions and stored in plural cloud storage objects based on a created X th dimensional geometric shape and a path through selected components of the geometric shape. Storage locations for the plural cloud storage objects are selected using a Galois field and the geometric shape. The plural cloud storage objects are distributed across the cloud network. When the electronic content is requested, the plural portions are retrieved and transparently combined back into the original electronic content. No server network devices storing the plural cloud storage objects or target network devices requesting the stored electronic can individually determine locations of all portions of the stored electronic content on the cloud communications network, thereby providing various levels of security and privacy for the electronic content without having to encrypt the plaintext electronic content on the cloud network.

Method and system for electronic content storage and retrieval using Galois fields and geometric shapes on cloud computing networks

This invention provides improved security and improved throughput of the McEliece public key encryption system and reduces the public key size. Even though the public key is reduced, in some embodiments of the invention the ensemble of cryptograms produced is identical to the ensemble of cryptograms produced by the original system for a given Goppa code, and the same private key. It is possible using this invention that the encrypted message, the cryptogram is a truly random function, not a pseudo random function of the message so that even with the same message and the same public key, a different, unpredictable cryptogram is produced each time. Other embodiments of the invention use a shortened error correcting code allowing the length of the generated cryptogram to match exactly the available transmission or storage media such as is the case of RFID and packet based radio applications.

Public key encryption system using error correcting codes

This invention provides improved security of the McEliece Public Key encryption system adding features which make full use of random number generation for given message and cryptogram parameters, using this invention the encrypted message (i.e. the cryptogram) is a truly random function, not a pseudo random function of the message so that even with the same message and the same public key, a different, unpredictable cryptogram is produced each time. With the knowledge of the private key, the random function may be determined from the cryptogram and the message decrypted. Different embodiments of the invention are described which enable the level of security to be traded-off against cryptogram size and complexity. A number of different applications are given.

Public key cryptosystem based on goppa codes and puf based random generation

A post-quantum, public key cryptosystem is described which is polynomial based and where the private key polynomial has coefficients from a sub-set of Galois field elements and plain text message polynomials have coefficients from a second sub-set of Galois field elements. The public key polynomial is constructed using the inverse of the private key polynomial and a randomly chosen polynomial having coefficients chosen from a third sub-set of Galois field elements. Cipher texts are constructed using the public key and randomly chosen session key polynomials. Other more complicated embodiments are described. For implementation a small prime base field such as 2, 3 or 5 will usually be used in constructing the prime power Galois field. The system has the advantage of relatively small public key sizes.

Public Key Cryptosystem Based On Partitioning Of Galois Field Elements

Based on the ideas of cyclotomic cosets, idempotents and Mattson-Solomon polynomials, we present a new method to construct GF(2m), where m > 0, cyclic low-density parity-check codes. The construction method produces the dual code idempotent which is used to define the parity-check matrix of the low-density parity-check code. An interesting feature of this construction method is the ability to increment the code dimension by adding more idempotents and so steadily decrease the sparseness of the parity-check matrix. We show that the constructed codes can achieve performance close to the sphere-packing-bound constrained for binary transmission.

GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets

We explore the benefits of implementing Hermitian codes over moderate lengths and compare the hard decision decoding performance in the additive white Gaussian noise (AWGN) channel and performance in the erasure channel of Hermitian codes with shortened non-binary Bose Hocquenghem Chaudhuri (BCH) codes. We implement the Berlekamp-Massey-Sakata (BMSA) decoding and Berlekamp-Massey (BMA) decoding for the hard decision Hermitian and BCH codes respectively, maximum likelihood erasure decoding and ordered reliability soft decision decoding for both.

Martin Tomlinson

Papers

Public key encryption system using error correcting codes

Public key cryptosystem based on goppa codes and puf based random generation

Public Key Cryptosystem Based On Partitioning Of Galois Field Elements

GF(2^m) Low-Density Parity-Check Codes Derived from Cyclotomic Cosets

Performance comparison between Hermitian codes and shortened non-binary BCH codes