We present several new constructions of collision-resistant hash-functions (CRHFs) from general assumptions. We start with a simple construction of CRHF from any homomorphic encryption. Then, we strengthen this result by presenting constructions of CRHF from two other primitives that are implied by homomorphic-encryption: one-round private information retrieval (PIR) protocols and homomorphic o...

In cryptography, there has been tremendous success in building various two-party protocols with small communication complexity out of homomorphic semantically-secure encryption schemes, using their homomorphic properties in a black-box way. A few notable examples of such primitives include items like single database Private Information Retrieval (PIR) schemes (introduced in [15]) and private da...

We give a generalization of the Diffie-Hellman key agreement scheme that is based on the hardness of computing homomorphic images from an algebra to another. We formulate computational and decision versions of the homomorphic image problem and devise a key agreement protocol that is secure in the Canetti-Krawczyk model under the decision homomorphic image assumption. We also give an instantiati...

Homomorphic encryption has been used for supporting simple aggregations, numeric calculations on encrypted data as well as for private information retrieval. Recently, theoretical breakthroughs on homomorphic encryption resulted in fully homomorphic encryption, which is able to compute arbitrary functions on encrypted data. As a result, homomorphic encryption is generally believed to be the hol...

Gentry’s bootstrapping technique is the most famous method of obtaining fully homomorphic encryption. In previous work I proposed a fully homomorphic encryption without bootstrapping which has the weak point in the plaintext [1],[15]. I also proposed a fully homomorphic encryption with composite number modulus which avoids the weak point by adopting the plaintext including the random numbers in...

Privacy homomorphisms, encryption schemes that are also homomorphisms relative to some binary operation, have been studied for some time, but one may also consider the analogous problem of homomorphic signature schemes. In this paper we introduce basic definitions of security for homomorphic signature systems, motivate the inquiry with example applications, and describe several schemes that are...

Homomorphic encryption scheme enables computation in the encrypted domain, which is of great importance because of its wide and growing range of applications. The main issue with the known fully (or partially) homomorphic encryption schemes is the high computational complexity and large communication cost required for their execution. In this work, we study symmetric partially homomorphic encry...

This work addresses the characterization of homomorphic encryption schemes both in terms of security and design. In particular, we are interested in currently existing fully homomorphic encryption (FHE) schemes and their common structures and security. Our main contributions can be summarized as follows: – We define a certain type of homomorphic encryption that we call shift-type and identify i...

Homomorphic encryption schemes are malleable by design. In this paper, we find different approaches to practical homomorphic encryption schemes. Partial homomorphic encryption schemes, we observe that the main bottleneck of this scheme is that it is capable of or adapted for turning easily from one to another of various tasks. To solve this problem, we propose general approach to improve the ve...

In this paper we study the feasibility of using homomorphic tallying in the Estonian Internet voting system. The paper analyzes the security benefits provided by homomorphic tallying, the costs introduced and the required changes to the voting system. We find that homomorphic tallying has several security benefits, such as improved ballot secrecy, public verifiability of the vote tallying serve...