Abstract:
Homomorphic encoding allows to perform certain mathematical operations with the encoded text and to get the encoded outcome that corresponds to the result of operations processed with a plaintext. There exist both fully homomorphic and partially homomorphic options (with respect to one or more operations). For practical use of such an encoding it is necessary to have a homomorphism with respect for at least one operation. Using non-associative operations, we construct in this paper an example of a cryptosystem based on the El-Gamal system that is homomorphic with respect to two on-going operations: a group and a quasigroup ones.