A computer-implemented method can include: constructing and initializing Pseudo Random Generator Resources using a multiplicity of secret seed values or secret data values known to a first and second communication device; deriving a session key based, at least in part, on the secret seed, secret data values, Multi-Factor Authentication methods, or Pseudo Random Number Generator Resource generated output; receiving from the first communications device, at the second communications device, data encrypted with the session key or Deterministic Chaos obfuscation methods; and decrypting the data at the second communications device using the session key or Deterministic Chaos de-obfuscation methods.

A method includes obtaining, from a server, a filter including a set of encrypted identifiers each encrypted with a server key controlled by the server. The method includes obtaining a request that requests determination of whether a query identifier is a member of a set of identifiers corresponding to the set of encrypted identifiers. The method also includes transmitting an encryption request to the server that requests the server to encrypt the query identifier. The method includes receiving, from the server, an encrypted query identifier including the query identifier encrypted by the server key and determining, using the filter, whether the encrypted query identifier is not a member of the set of encrypted identifiers. When the encrypted query identifier is not a member of the set of encrypted identifiers, the method includes reporting that the query identifier is not a member of the set of identifiers.

Disclosed herein are methods and systems for strengthening encryption schemes to side channel attacks. The strengthening of the encryption schemes can involve affine masking of one or more elements of the encryption schemes.

Systems, devices, software, and methods of the present invention provide for homomorphically encrypted (HE) and other data represented as polynomials of degree K−1 to be transformed in O(K*log(K)) time into ‘unique-spiral’ representations in which both linear-time (O(K)) addition and linear-time multiplication are supported without requiring an intervening transformation. This capability has never previously been available and enables very significant efficiency improvements, i.e., reduced runtimes, for applications such as Fully Homomorphic Encryption (FHE), Post-Quantum Cryptography (PQC) and Artificial Intelligence (AI). Other efficient operations, such as polynomial division, raising to a power, integration, differentiation and parameter-shifting are also possible using the unique-spiral representations. New methods are introduced based on the unique-spiral representation that have applications to efficient polynomial composition, inversion, and other important topics.

Disclosed herein are method and systems for transmitting a plurality of ciphertexts to a plurality of users. The systems and methods described herein provide for performing an encryption update comprising a plurality of encryption keys and a multi-ciphertext to a plurality of recipient nodes. Methods and systems for organizing a database are also disclosed herein.

Disclosed is an operation device. The operation device includes a memory storing at least one instruction; and a processor configured to execute the at least one instruction, and the processor, by executing the at least one instruction, may perform encoding or decoding for an approximate homomorphic ciphertext using a predetermined matrix having only a half of an element of a matrix corresponding to a canonical embedding function.

A low latency relinearization process can be performed in an FPGA cluster for accelerating homomorphic encryption. The low-latency process performs an early calculation of matrix rows to make the summation result available earlier in the relinearization to reduce waiting of subsequent operations.

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.

Disclosed is an electronic apparatus. The electronic apparatus includes a memory storing a composite function in which at least two polynomials are composed and a processor configured to, based on a comparison operation command being received for a plurality of homomorphic ciphertexts, perform operation by reflecting the plurality of homomorphic ciphertexts to the composite function, and obtain a comparison result of the plurality of homomorphic ciphertexts based on the operation result, each of the at least two polynomials may output a value in a preset range for a value in a preset domain, and a domain of one of the at least two polynomials may be determined based on a range of a previous polynomial.

A communications system comprises a maximum ratio combining (MRC) circuit for receiving a plurality of input data streams and for processing the plurality of input data streams using maximum ration combining to improve signal to noise ratio. A MIMO transmitter transmits the MRC processed carrier signal over a plurality of separate communications links from the MIMO transmitter, each of the plurality of separate communications links from one transmitting antenna of a plurality of transmitting antennas to each of a plurality of receiving antennas at a MIMO receiver.