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]. In this paper I propose the improved fully homomorphic encryption scheme on non-associative octonion ring over finite field without bootstrapping technique where the p...

Homomorphic signature schemes allow anyone to perform computation on signed data in such a way that the correctness of computation’s results is publicly certified. In this work we analyze the security notions for this powerful primitive considered in previous work, with a special focus on adaptive security. Motivated by the complications of existing security models in the adaptive setting, we c...

Finding interesting tree patterns hidden in large datasets is an central topic in data mining with many practical applications. Unfortunately, previous contributions have focused almost exclusively on mining induced patterns from a set of small trees. The problem of mining homomorphic patterns from a large data tree has been neglected. This is mainly due to the challenging unbounded redundancy ...

By definition, fully homomorphic encryption (FHE) schemes support homomorphic decryption, and all known FHE constructions are bootstrapped from a Somewhat Homomorphic Encryption (SHE) scheme via this technique. Additionally, when a public key is provided, ciphertexts are also re-randomizable, e.g., by adding to them fresh encryptions of 0. From those two operations we devise an algorithm to san...

In this paper we present a key recovery attack to the scale-invariant NTRU-based somewhat homomorphic encryption scheme proposed by Bos et al [BLLN13] in 2013. The attack allows us to compute the private key for t > 2 and when the private key is chosen with coefficients in {−1, 0, 1}. The efficiency of the attack is optimal since it requires just one decryption oracle query, showing that if we ...

In this paper we present an encoding method for xed-point numbers tailored for homomorphic function evaluation. The choice of the degree of the polynomial modulus used in all popular somewhat homomorphic encryption schemes is dominated by security considerations, while with the current encoding techniques the correctness requirement allows for much smaller values. We introduce a generic encodin...

We propose a general framework to develop fully homomorphic encryption schemes (FHE) without using the Gentry’s technique. Initially, a private-key cryptosystem is built over Zn (n being an RSA modulus). An encryption of x ∈ Zn is a randomly chosen vector e such that Φ(e) = x where Φ is a secret multivariate polynomial. This private-key cryptosystem is not homomorphic in the sense that the vect...

Abstract—This paper presents a new enhancement technique for infrared images. This technique combines the benefits of homomorphic image processing and the additive wavelet transform. The idea behind this technique is based on decomposing the image into subbands in an additive fashion using the additive wavelet transform. This transform gives the image as an addition of subbands of the same reso...

Homomorphic encryption (HE) is a cryptosystem that allows the secure processing of encrypted data. One most popular HE schemes Brakerski-Fan-Vercauteren (BFV), which supports somewhat (SWHE) and fully homomorphic (FHE). Since overly involved arithmetic operations are amenable to concurrent computation, GPU devices can be instrumental in facilitating practical use real world applications thanks ...

Server-based collaborative filtering systems have been very successful in e-commerce and in direct recommendation applications. In future, they have many potential applications in ubiquitous computing settings. But today’s schemes have problems such as loss of privacy, favoring retail monopolies, and with hampering diffusion of innovations. We propose an alternative model in which users control...