Abstract: Certain aspects of the disclosure provide a method for performing data verification. The method includes generating a MAC by applying a tagging algorithm indicated by a shared verification key to a data item; appending the MAC to the data item; generating an encrypted dataset comprising an encrypted data item and encrypted message authentication; generating a re-encryption key based on a homomorphic secret key corresponding to the homomorphic public key and a new public key; generating a re-encrypted dataset comprising a re-encrypted data item and a re-encrypted MAC; transmitting the re-encrypted dataset to a first external system configured to perform data verification; receiving, from the first external system, an encrypted verification result based on the shared verification key; and taking an action based on receiving the verification result indicating that the data item is authentic.

Abstract: Systems and methods provide an optionally keyed error-correcting code that is spectrally concentrated. Each codeword of the low dimensional spectral concentration code (LDSC code) typically has very few coefficients of large magnitude and can be constructed even with limited processing resources. Decoding can be performed on low power devices. Error-correcting code is constructed around a key using basic computer arithmetic for computations instead of finite field arithmetic, thus saving energy. A recipient who possesses the key enjoys correction of a relatively high percentage of noise errors. In one implementation, a direct list-decoder iteratively estimates a list of message words directly, instead of a list of codewords. In variations, a unique message word is selected from the list either by applying a randomness test or by using message passing.

Abstract: Systems and methods provide an optionally keyed error-correcting code that is spectrally concentrated. Each codeword of the low dimensional spectral concentration code (LDSC code) typically has very few coefficients of large magnitude and can be constructed even with limited processing resources. Decoding can be performed on low power devices. Error-correcting code is constructed around a key using basic computer arithmetic for computations instead of finite field arithmetic, thus saving energy. A recipient who possesses the key enjoys correction of a relatively high percentage of noise errors. In one implementation, a direct list-decoder iteratively estimates a list of message words directly, instead of a list of codewords. In variations, a unique message word is selected from the list either by applying a randomness test or by using message passing.

Abstract: A method includes searching in the ZN domain, for N greater than 2, for heavy Fourier coefficients of a function. The method may be implemented for any type of signal compression, such as image, video or audio compression. It may also be used to decode corrupted codewords.