In this paper we introduce new primitives to authenticate computation on data expressed as elements in (cryptographic) groups. As for the case of homomorphic authenticators, our primitives allow to verify the correctness of the computation without having to know of the original data set. More precisely, our contributions are two-fold. First, we introduce the notion of linearly homomorphic authe...

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...

We prove that for any integers m; k, there is an integer n 0 such that if G is a graph of girth n 0 then any partial k-tree homomorphic to G is also homomorphic to C 2m+1. As a corollary, every non-bipartite graph does not have bounded treewidth duality.

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...

A pseudorandom function F : K ×X → Y is said to be key homomorphic if given F (k1, x) and F (k2, x) there is an efficient algorithm to compute F (k1 ⊕ k2, x), where ⊕ denotes a group operation on k1 and k2 such as xor. Key homomorphic PRFs are natural objects to study and have a number of interesting applications: they can simplify the process of rotating encryption keys for encrypted data stor...

An algorithm for non-parametric estimation of one-dimensional ul-trasound pulses in echo sequences from human tissues is derived. The technique is a variation of the homomorphic ltering technique using the real cepstrum, and the underlying basis of the method is explained. The algorithm exploits a priori knowledge about the structure of rf line echo data and can employ a number of adjacent rf l...

Introduction: Hydronephrosis is one of the major causes of referring infants for nuclear medicine investigation. Renal dynamic study is the most reliable investigation for such children. However direct evaluation of renogram leads to generation of parameters that have no physiological interpretation. The configuration of renogram is very much dependent upon the rate at which radiopharmace...

Group homomorphic encryption represents one of the most important building blocks in modern cryptography. It forms the basis of widely-used, more sophisticated primitives, such as CCA2-secure encryption or secure multiparty computation. Unfortunately, recent advances in quantum computation show that many of the existing schemes completely break down once quantum computers reach maturity (mainly...