Group homomorphic encryption: characterizations, impossibility results, and applications

• Published in: Designs, codes, and cryptography Vol. 67; no. 2; pp. 209 - 232
• Main Authors: Armknecht, Frederik, Katzenbeisser, Stefan, Peter, Andreas
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.05.2013; Springer
• Subjects: Algebraic combinatorics; Applied sciences; Circuits; Coding and Information Theory; Combinatorics; Combinatorics. Ordered structures; Computer Science; Cryptography; Cryptology; Data Structures and Information Theory; Discrete Mathematics in Computer Science; Exact sciences and technology; Information and Communication; Information, signal and communications theory; Mathematics; Sciences and techniques of general use; Signal and communications theory; Telecommunications and information theory; Linear problem; Foundations; 94A60; Public-key cryptography; Homomorphic encryption; IND-CCA1 security; Subgroup membership problem; Shift; Algebraic combinatorics; k-Linear problem; Decryption; Modeling; Linear code; Multilinear function; Cryptanalysis; Public key cryptography; Oracle

We give a complete characterization both in terms of security and design of all currently existing group homomorphic encryption schemes, i.e., existing encryption schemes with a group homomorphic decryption function such as ElGamal and Paillier. To this end, we formalize and identify the basic under...