Exploring Homomorphic encryption
Homomorphic Encryption (HE) is a cryptographic technique that allows computation on encrypted data without decrypting it. In other words, it is possible to perform operations on ciphertexts, generating new ciphertexts that are decrypted to the result of the operation on the plaintexts. HE has the potential to revolutionize data privacy and security, enabling secure computation of sensitive data without revealing the data itself. HE is based on mathematical concepts such as algebraic structures, number theory, and polynomial theory. The most common types of HE are based on the following algebraic structures.
Ring-based
In the context of cryptography, an algebraic structure refers to a set of mathematical operations that can be performed on elements of the set in a specific way. In the case of a ring, the set of elements is closed under addition and multiplication, and the operations satisfy certain properties, such as associativity, commutativity...