We introduce a homomorphic batching technique that can be used to pack multiple ciphertext messages into one ciphertext for parallel processing. One is able to use the method to batch or unbatch messages homomorphically to further improve the flexibility of encrypted domain evaluations. In particular, we show various approaches to implement Number Theoretic Transform (NTT) homomorphically in FF...

We show how to transform any additively homomorphic privatekey encryption scheme that is compact, into a public-key encryption scheme. By compact we mean that the length of a homomorphically generated encryption is independent of the number of ciphertexts from which it was created. We do not require anything else on the distribution of homomorphically generated encryptions (in particular, we do...

Cloud databases often need client-side encryption. Encryption however impairs queries, especially with numerical SQL value expressions. Fully homomorphic encryption scheme could suffice, but known schemes remain impractical. Partially homomorphic encryption suffices for specific expressions only. The additively homomorphic Paillier scheme appears the most practical. We propose the homomorphic e...

We give an introduction to Fully Homomorphic Encryption for mathematicians. Fully Homomorphic Encryption allows untrusted parties to take encrypted data Enc(m1), . . . ,Enc(mt) and any efficiently computable function f , and compute an encryption of f(m1, . . . ,mt), without knowing or learning the decryption key or the raw data m1, . . . ,mt. The problem of how to do this was recently solved b...

All the currently existing homomorphic e-voting schemes are based on additive homomorphism. In this paper a new e-voting scheme based on multiplicative homomorphism is proposed. In the tallying phase, a decryption is performed to recover the product of the votes, instead of the sum of them (as in the additive homomorphic e-voting schemes). Then, the product is factorized to recover the votes. T...

In this paper we port Brakerski’s fully homomorphic scheme based on the Learning With Errors (LWE) problem to the ring-LWE setting. We introduce two optimised versions of relinearisation that not only result in a smaller relinearisation key, but also faster computations. We provide a detailed, but simple analysis of the various homomorphic operations, such as multiplication, relinearisation and...

Vote validity proof and verification is an efficiency bottleneck and privacy drawback in homomorphic e-voting. The existing vote validity proof technique is inefficient and only achieves honest-verifier zero knowledge. In this paper, an efficient proof and verification technique is proposed to guarantee vote validity in homomorphic e-voting. The new proof technique is mainly based on hash funct...

Received Jul 17 th , 2012 Accepted Aug 26 th , 2012 Recently, many fully-homomorphic encryption schemes have been constructed. However, the issue of the security of these fully homomorphic encryptions has not been carefully studied. By using lattice reduction algorithm, we firstly present an attack on the fully homomorphic encryption based on approximate GCD over the integers. Our result shows ...

We formally define and give the first construction of (leveled) threshold fully homomorphic encryption for any access structure induced by a monotone boolean formula and in particular for the threshold access structure. Our construction is based on the learning with errors assumption and can be instantiated with any existing homomorphic encryption scheme that satisfies fairly general conditions...