Implicit Zero-Knowledge Arguments and Applications to the Malicious Setting

We introduce \emph{implicit zero-knowledge} arguments (iZK) and simulation-sound variants thereof (SSiZK); these are lightweight alternatives to zero-knowledge arguments for enforcing semi-honest behavior. Our main technical contribution is a construction of efficient two-flow iZK and SSiZK protocols for a large class of languages under the (plain) DDH assumption in cyclic groups in the common reference string model. As an application of iZK, we improve upon the round-efficiency of existing protocols for securely computing inner product under the DDH assumption. This new protocol in turn provides privacy-preserving biometric authentication with lower latency

Private set intersection: A systematic literature review

Secure Multi-party Computation (SMPC) is a family of protocols which allow some parties to compute a function on their private inputs, obtaining the output at the end and nothing more. In this work, we focus on a particular SMPC problem named Private Set Intersection (PSI). The challenge in PSI is how two or more parties can compute the intersection of their private input sets, while the elements that are not in the intersection remain private. This problem has attracted the attention of many researchers because of its wide variety of applications, contributing to the proliferation of many different approaches. Despite that, current PSI protocols still require heavy cryptographic assumptions that may be unrealistic in some scenarios. In this paper, we perform a Systematic Literature Review of PSI solutions, with the objective of analyzing the main scenarios where PSI has been studied and giving the reader a general taxonomy of the problem together with a general understanding of the most common tools used to solve it. We also analyze the performance using different metrics, trying to determine if PSI is mature enough to be used in realistic scenarios, identifying the pros and cons of each protocol and the remaining open problems.This work has been partially supported by the projects: BIGPrivDATA (UMA20-FEDERJA-082) from the FEDER Andalucía 2014– 2020 Program and SecTwin 5.0 funded by the Ministry of Science and Innovation, Spain, and the European Union (Next Generation EU) (TED2021-129830B-I00). The first author has been funded by the Spanish Ministry of Education under the National F.P.U. Program (FPU19/01118). Funding for open access charge: Universidad de Málaga/CBU

Equivalences and Black-Box Separations of Matrix Diffie-Hellman Problems

The final publication is available at link.springer.comIn this paper we provide new algebraic tools to study the relationship between different Matrix Diffie-Hellman (MDDH) Problems, which are recently introduced as a natural generalization of the so-called Linear Problem. Namely, we provide an algebraic criterion to decide whether there exists a generic black-box reduction, and in many cases, when the answer is positive we also build an explicit reduction with the following properties: it only makes a single oracle call, it is tight and it makes use only of operations in the base group. It is well known that two MDDH problems described by matrices with a different number of rows are separated by an oracle computing certain multilinear map. Thus, we put the focus on MDDH problems of the same size. Then, we show that MDDH problems described with a different number of parameters are also separated (meaning that a successful reduction cannot decrease the amount of randomness used in the problem instance description). When comparing MDDH problems of the same size and number of parameters, we show that they are either equivalent or incomparable. This suggests that a complete classification into equivalence classes could be done in the future. In this paper we give some positive and negative partial results about equivalence, in particular solving the open problem of whether the Linear and the Cascade MDDH problems are reducible to each other. The results given in the paper are limited by some technical restrictions in the shape of the matrices and in the degree of the polynomials defining them. However, these restrictions are also present in most of the work dealing with MDDH Problems. Therefore, our results apply to all known instances of practical interest.Peer ReviewedPostprint (author's final draft

Implicit Zero-Knowledge Arguments and Applications to the Malicious Setting

We introduce \emph{implicit zero-knowledge} arguments (iZK) and simulation-sound variants thereof (SSiZK); these are lightweight alternatives to zero-knowledge arguments for enforcing semi-honest behavior. Our main technical contribution is a construction of efficient two-flow iZK and SSiZK protocols for a large class of languages under the (plain) DDH assumption in cyclic groups in the common reference string model. As an application of iZK, we improve upon the round-efficiency of existing protocols for securely computing inner product under the DDH assumption. This new protocol in turn provides privacy-preserving biometric authentication with lower latency

Advances in Functional Encryption

Functional encryption is a novel paradigm for public-key encryption that enables both fine-grained access control and selective computation on encrypted data, as is necessary to protect big, complex data in the cloud. In this thesis, I provide a brief introduction to functional encryption, and an overview of my contributions to the area