A functional encryption system includes a key generation device configured to generate a public key and a secret key, based on a master key and a parameter vector, an encryption device configured to generate encrypted data by encrypting an input vector, based on the public key, and a decryption device configured to generate decrypted data corresponding to an approximation value of an inner product of the parameter vector and the input vector by decrypting the encrypted data based on the secret key. Security of data used in machine learning, biometric authentication, etc. may be reinforced and attacks using quantum computers may be blocked by incurring random noise in the decrypted data based on the functional encryption using the LWE problem and the lattice problem.

Processing within a computing environment is facilitated by generating a hybrid security certificate using multiple cryptosystems. The generating includes obtaining data for inclusion in the hybrid security certificate, and generating a first digital signature associated with a first cryptosystem to cover the data, and a second digital signature associated with a second cryptosystem to cover the data. The generating further includes providing the hybrid security certificate, where the hybrid security certificate includes the data, the first digital signature associated with the first cryptosystem, and the second digital signature associated with the second cryptosystem, and where the first digital signature has no dependency on a key of the second cryptosystem or the second digital signature, and the second digital signature has no dependency on a key of the first cryptosystem or the first digital signature.

An encoding method is disclosed. The present encoding method comprises the steps of: receiving a plurality of messages; encoding the plurality of messages into a polynomial expression having been multivariately defined, and encoding the multivariately defined polynomial expression so as to generate a homomorphic cyphertext.

Disclosed is a ciphertext calculation method. The ciphertext calculation method comprises the steps of: receiving a comparative calculation command for a plurality of ciphertexts of the same type; performing a calculation by reflecting the plurality of ciphertexts of the same type on a synthesis function corresponding to the comparative calculation command; and outputting the calculated ciphertexts of the same type.

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.

Cryptographic information is compiled by: (a) determining a first portion of the cryptographic information based on an input and a randomness; (b) checking a rejection criterion based on the first portion; (b1) re-starting step (a) with a different randomness if the rejection criterion is fulfilled; (b2) if not all portions of the cryptographic information have been generated, determining a subsequent portion of the cryptographic information based on the input and the randomness and continuing with step (b) or, otherwise, continuing with step (c); (c) determining the first portion of the cryptographic information based on the input and the randomness; (d) conveying the respective portion of the cryptographic information; and (e) if not all portions of the cryptographic information have been generated, determining a subsequent portion of the cryptographic information based on the input and the randomness and continuing with step (d).

A method for searchable encryption of a system defining a secret key and a public is provided. A data stream cipher can include n elementary data (b.sub.1, b.sub.2, . . . , b.sub.n). The method can include generation of a variate for all elementary data b.sub.j, for values of j from 1 to n, generation of an element function of the public key (g.sup.x(bj),zj) and the variate, the element being associated with a random element of a group of a bilinear environment, the element associated with the random element of the group forming first encryption data (C.sub.j,1). The method can also include generation of a shift factor (g.sup.a.zj−1) function of the variate and the public key, and associated with the random element of the group, the shift factor representing a position of the monomial in the encrypted stream, the shift factor associated with the random element of the group forming second encryption data. The data stream cipher can include the first and second encryption data for all values of j from 1 to n.

Methods and systems described herein authenticate a user and help secure transaction. A display screen presents images that are difficult for malware to recognize but a person can recognize. In at least one embodiment, a person communicates transaction information using visual images received from the service provider system. In at least one embodiment, a user selects a sequence of visual images as a means of authenticating the user and logging into a financial account or other corporate account.

In some embodiments, methods and systems are provided for determining whether to grant access, by generating and displaying visual images on a screen that the user can recognize, and select. In an embodiment, a user presses his or her finger or fingers on a display screen to select images as a method for authenticating and protecting communication from malware.

In an embodiment, non-determinism in hardware helps unpredictably vary the image selected, the image location, generate noise in the image, or change the shape or texture of the image. In some embodiments, visual image authentication helps Alice and Bob detect if Eve has launched a man-in-the-middle attack on their key exchange.

The invention relates to method for adjusting the minimum and maximum number of peer nodes that a node on the blockchain network will connect with. The adjustment takes in to account the bandwidth and processing capability of the node. Bandwidth capacity of a node is determined based on a maximum data amount processable by the node over a time period. Data is monitored passing through interfaces of the node, to and from peer nodes, and a profile factor of the node is determined from the difference between the input data to output data. Over a plurality of time periods monitoring said data the data analysed is used to set a minimum number of peer nodes and a maximum number of peer nodes connectable to the node according to said monitored data and the maximum number of peers connectable to the node. The method enables a node to adjust the number of connections according to performance limitation factors, such as bandwidth availability and processing performance. With the number of peer node connections determined, the node can further determine a correlation matrix between the interfaces and peer nodes to which it is connected. The matrix can be compiled with correlation coefficients representing the correlation between data processed at each interface of said node. The invention also resides in a corresponding computer readable storage medium, electronic device, node of a blockchain network or blockchain network having such a node.

A calculation device is disclosed. The calculation device includes: a memory storing at least one instruction and identity information; and a processor performing the at least one instruction, wherein the processor may randomly sample small elements, generate a function-processed output value by function-processing the stored identity information, and generate an encrypted text for a message by using a master public key computed using a ring having a dimension (d) represented by a power of 2 and an integer multiplication of 3 or more, the sampled small elements and the function-processed output value.