An oblivious linear function evaluation protocol, or OLE, is a two-party protocol for the function f ( x ) = a x + b, where a sender inputs the field elements a, b, and a receiver inputs x and learns f ( x ). OLE can be used to build secret-shared multiplication, and is an essential component of many secure computation applications including general-purpose multi-party computation, private set intersection and more. In this work, we present several efficient OLE protocols from the ring learning with errors (RLWE) assumption. Technically, we build two new passively secure protocols, which build upon recent advances in homomorphic secret sharing from (R)LWE (Boyle et al. in: EUROCRYPT 2019, Part II (2019) 3–33 Springer), with optimizations tailored to the setting of OLE. We upgrade these to active security using efficient amortized zero-knowledge techniques for lattice relations (Baum et al. in: CRYPTO 2018, Part II (2018) 669–699 Springer), and design new variants of zero-knowledge arguments that are necessary for some of our constructions. Our protocols offer several advantages over existing constructions. Firstly, they have the lowest communication complexity amongst previous, practical protocols from RLWE and other assumptions; secondly, they are conceptually very simple, and have just one round of interaction for the case of OLE where b is randomly chosen. We demonstrate this with an implementation of one of our passively secure protocols, which can perform more than 1 million OLEs per second over the ring Z m , for a 120-bit modulus m, on standard hardware.

Multimedia contents are inherently sensitive signals that must be protected when processed in untrusted environments. The field of Secure Signal Processing addresses this challenge by developing methods which enable operating with sensitive signals in a privacy-conscious way. Recently, we introduced a hard lattice problem called m-RLWE (multivariate Ring Learning with Errors) which gives support to efficient encrypted processing of multidimensional signals. Afterwards, Bootland et al. presented an attack to m-RLWE that reduces the security of the underlying scheme from a lattice with dimension \prod_in_i to \max\n_i\ _i . Our work introduces a new pre-/post-coding block that addresses this attack and achieves the efficient results of our initial approach while basing its security directly on RLWE with dimension \prod_in_i, hence preserving the security and efficiency originally claimed. Additionally, this work provides a detailed comparison between a conventional use of RLWE, m-RLWE and our new pre-/post-coding procedure, which we denote "packed''-RLWE. Finally, we discuss a set of encrypted signal processing applications which clearly benefit from the proposed framework, either alone or in a combination of baseline RLWE, m-RLWE and "packed''-RLWE.

Recent advances in Next Generation Sequencing have increased the availability of genomic data for more accurate analyses, like testing for the genetic susceptibility to a disease. Current laboratories' facilities cannot cope with this data growth, and genomic processing needs to be outsourced, comprising serious privacy risks. This work proposes an encrypted genomic susceptibility test protocol based on lattice homomorphic cryptosystems, and introduces optimizations like data packing and transformed processing to achieve considerable gains in performance, bandwidth and storage needs.

Multimedia contents are inherently sensitive signals that must be protected whenever they are outsourced to an untrusted environment. This problem becomes a challenge when the untrusted environment must perform some processing on the sensitive signals; a paradigmatic example is Cloud-based signal processing services. Approaches based on Secure Signal Processing (SSP) address this challenge by proposing novel mechanisms for signal processing in the encrypted domain and interactive secure protocols to achieve the goal of protecting signals without disclosing the sensitive information they convey. This paper presents a novel and comprehensive set of approaches and primitives to efficiently process signals in an encrypted form, by using Number Theoretic Transforms (NTTs) in innovative ways. This usage of NTTs paired with appropriate signal pre-and post-coding enables a whole range of easily composable signal processing operations comprising, among others, filtering, generalized convolutions, matrix-based processing or error correcting codes. Our main focus is on unattended processing, in which no interaction from the client is needed; for implementation purposes, efficient lattice-based somewhat homomorphic cryptosystems are used. We exemplify these approaches and evaluate their performance and accuracy, proving that the proposed framework opens up a wide variety of new applications for secured outsourced-processing of multimedia contents.

Images are inherently sensitive signals that require privacy-preserving solutions when processed in an untrusted environment, but their efficient encrypted processing is particularly challenging due to their structure and size. This work introduces a new cryptographic hard problem called m-RLWE (multivariate Ring Learning with Errors) extending RLWE. It gives support to lattice cryptosystems that allow for encrypted processing of multidimensional signals. We show an example cryptosystem and prove that it outperforms its RLWE counterpart in terms of security against basis-reduction attacks, efficiency and cipher expansion for encrypted image processing.