Homomorphic encryption schemes

Title: Homomorphic encryption schemes Author: Anežka Titěrová Department: Department of Algebra Supervisor: RNDr. Alexandr Kazda, Department of Algebra Abstract: Rivest et al. posed in 1978 the cryptographic problem how to correctly compute arbitrary functions over encrypted data without direct decrypting. This problem is solved by using of a fully homomorphic encryp- tion scheme, which was discovered and first described by Craig Gentry in 2009. This work gives a summary of contemporary knowledge in this field. The attention will be restricted to a general overview how to construct the fully homomorphic encryption scheme with respect to the information security. The results will be applied in an implementation of a somewhat homomorphic encryption scheme as a computer program. Fully homomorphic encryption schemes have abundant applications, especi- ally in secure cloud computing. Nevertheless, the greatest challenge for scien- tists is finding out more efficient algorithm because existing implementations are not as effective and fast as required for everyday use. Keywords: homomorphic encryption, fully homomorphic encryption scheme, lattice cryptography, logic circui