A computing system comprising: processor(s) and memory; at least one network interface communicatively coupled to the at least one processor and configured to communicate with at least one remotely located computing device; wherein the at least one network interface is configured to receive a plurality of public encryption keys from the at least one remotely located computing device; wherein the at least one processor is configured to: split at least one secret into a plurality of shares, wherein at least a subset of the plurality of shares is sufficient to reconstruct the at least one secret; encrypt each of the plurality of shares based on a different public encryption key of the plurality of public encryption keys to create a plurality of encrypted shares; wherein the at least one network interface is configured to communicate the encrypted shares to the at least one remotely located computing device.

The present disclosure relates to methods of mining a block of a distributed ledger. The methods include: receiving a block to be mined, the block including a header hash and a plurality of transactions; creating a first signature based on a first function, where inputs to the first function include the header hash and the plurality of transactions; and creating a second signature based on a second function, where an input to the second function is the first signature. In one example, the second function is a multiplicative inverse function and the method further includes creating the second signature that is a multiplicative inverse value of the first signature with respect to a first irreducible polynomial. The method additionally includes creating a chain of signatures, where each of the signatures is a multiplicative inverse value of a previous output with respect to a respective irreducible polynomial.

Systems and methods are provided for obtaining data to be secured based on a secret sharing technique, the data being associated with a file identifier and a split specification that includes at least a number of splits n and a minimum number of splits m required for reconstructing the data, and a Repeatable Random Sequence Generator (RRSG) RRSG scheme. An RRSG state can be initialized based at least in part on a given data transformation key to provide repeatable sequence of random bytes. For every m bytes of data: a polynomial whose coefficients are determined based at least in part on m bytes of the data and a portion of the repeatable sequence of random bytes can be determined; the polynomial can be evaluated at n unique values determined by a portion of repeatable sequence of random bytes to generate n bytes. Each byte can be stored into one of the n split stores.

An encryption device includes one or more hardware processors functioning as the following units. A unit acquires, as a public key, n-variable indeterminate equations X having coefficients with a predetermined degree of a univariate polynomial ring F.sub.p[t] on a finite field F.sub.p. A unit embeds a plaintext m into coefficients of n-variable plaintext polynomial factors m having coefficients with a predetermined degree of the F.sub.p[t]. A unit generates an n-variable plaintext polynomial M by multiplying the n-variable plaintext polynomial factors m.sub.i whose number is one or more. A unit randomly generates n-variable polynomials s.sub.k (k=1, 2), n-variable polynomials r.sub.k, and noise polynomial e.sub.k, each having coefficients with a predetermined degree of the F.sub.p[t]. A unit generates a ciphertext c.sub.k by executing an operation including at least one of adding, subtracting, and multiplying the s.sub.k, the r.sub.k, the e.sub.k, and the X to, from, or by the M.

A system, method, and computer program product are provided for sending and receiving messages using a noisy cryptographic system. To send a message, N secret keys are negotiated using a noisy cryptographic system, where K secret keys are expected to be noiseless. A secret polynomial that includes the N secret keys is generated, and K points on the secret polynomial are derived. For each of the N secret keys, a secret key MAC key is derived and a secret key MAC is calculated using the derived secret key MAC key. A secret key MAC header is generated that includes an array of each of the secret key MACs and possibly a corresponding public key. Message integrity plaintext is generated that includes an encrypted message, the secret key MAC header, and an array of the K points on the secret polynomial. A final message that includes the message integrity plaintext is generated for being sent.

Disclosed is a method and apparatus for modulus refresh, where the method for modulus refresh of a ciphertext in homomorphic encryption includes receiving a first ciphertext corresponding to a first modulus, generating a second ciphertext by performing a blind rotation on the first ciphertext, and generating a target ciphertext corresponding to a second modulus greater than the first modulus based on the first ciphertext and the second ciphertext.

A secret sharing scheme in which a trust structure of the parties receiving a share of the secret is encoded in the shares. In this regard, an access structure defining an authorized set of participants may be based, at least in part, on the encoded trust structures. The secret sharing scheme includes a secret generator that generates the shares distributed to the parties. In turn, an authorized set of participants as defined by the access structure may provide shares to a dealer for reconstruction of the secret. However, if the participants requesting secret reconstruction are not an authorized set of participants, the secret reconstruction fails. In this regard, secret sharing with asymmetrical trust structures may be provided in which the trust structures are not known by other parties in the scheme.

An application or device is authenticated using secure application data validation. A server computer receives an authentication request comprising an application identifier or a user device identifier associated with a user device, the authentication request originating from the user device. The server computer receives a set of behavioral data associated with the application or the user device. Responsive to receiving the application identifier or device identifier, the server computer obtains a fuzzy vault associated with the application identifier or the user device identifier. The server computer determines a reconstructed key value using the fuzzy vault and the set of behavioral data. The application or the user device is authenticated using the reconstructed key value.

Disclosed are an apparatus and method with homomorphic encryption using automorphism. A computing apparatus includes one or more processors and a memory storing instructions configured to cause the one or more processors to, for a blind rotation key for performing a blind rotation operation and an operand ciphertext of the blind rotation operation: generate a preprocessed ciphertext by performing preprocessing on the operand ciphertext based on automorphism, and generate an operation result of the homomorphic encryption by performing the blind rotation operation for the operand ciphertext on a vector component of the preprocessed ciphertext and a vector component of the blind rotation key.

An electronic device including a key generator is disclosed. The key generator acquires a first affine map, a second affine map, and a third map, and generates a public key using the first affine map, the second affine map, and the third map, the third map is a system of multivariate quadratic polynomials having n variables and m equations, at least one of the multivariate quadratic polynomials has oil-oil quadratic terms with non-zero coefficients, and the third map includes at least one set for defining vinegar variables used in an Oil and Vinegar method and index sets for defining oil variables used in the Oil and Vinegar method, and each of the first affine map, the second affine map, and the third map is a finite field.