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Homomorphic secret sharing in cryptography, homomorphic secret sharing is a type of secret sharing algorithm in which the secret is encrypted via homomorphic encryption [1][2][3] this shared secret may be directly used as a key, or to derive another key. A homomorphism is a transformation from one algebraic structure into another of the same type so that the structure is preserved.

Homomorphic encryption is a form of encryption with an additional evaluation capability for computing over encrypted data without access to the secret key [3] in secret sharing, a secret is used as a seed to generate a number of distinct secrets, and the pieces are distributed so that some subset of the recipients can jointly authenticate. The result of such a computation remains encrypted

Homomorphic refers to homomorphism in algebra

The encryption and decryption functions can be. The dealer may act as several distinct participants, distributing the shares among the participants. Secret sharing consists of recovering a secret s from a set of shares, each containing partial information about the secret The chinese remainder theorem (crt) states that for a given system of simultaneous congruence equations, the solution is unique in some z/nz, with n > 0 under some appropriate conditions on the congruences

Secret sharing can thus use the crt to produce the shares. [2] openfhe is a successor of palisade and incorporates selected design features of helib, heaan, and fhew libraries. Key exchange (also key establishment) is a method in cryptography by which cryptographic keys are exchanged between two parties, allowing use of a cryptographic algorithm. Key distribution and key storage are more problematic in the cloud due to the transitory nature of the agents on it

[2] secret sharing can be used to store keys at many different servers on the cloud

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