Homomorphic Secret Sharing for Low Degree Polynomials

Homomorphic secret sharing (HSS) allows $n$ clients to secret-share data to $m$ servers, who can then homomorphically evaluate public functions over the shares. A natural application is outsourced computation over private data. In this work, we present the first plain-model homomorphic secret sharing scheme that supports the evaluation of polynomials with degree higher than 2. Our construction relies on any degree-$k$ (multi-key) homomorphic encryption scheme and can evaluate degree-$\left( (k+1)m -1 \right)$ polynomials, for any polynomial number of inputs $n$ and any sub-logarithmic (in the security parameter) number of servers $m$. At the heart of our work is a series of combinatorial arguments on how a polynomial can be split into several low-degree polynomials over the shares of the inputs, which we believe is of independent interest

Tightly Secure Inner Product Functional Encryption: Multi-Input and Function-Hiding Constructions

Tightly secure cryptographic schemes have been extensively studied in the fields of chosen-ciphertext secure public-key encryption (CCA-secure PKE), identity-based encryption (IBE), signatures and more. We extend tightly secure cryptography to inner product functional encryption (IPFE) and present the first tightly secure schemes related to IPFE. We first construct a new IPFE scheme that is tightly secure in the multi-user and multi-challenge setting. In other words, the security of our scheme does not degrade even if an adversary obtains many ciphertexts generated by many users. Our scheme is constructible on a pairing-free group and secure under the matrix decisional Diffie-Hellman (MDDH) assumption, which is the generalization of the decisional Diffie-Hellman (DDH) assumption. Applying the known conversions by Lin (CRYPTO 2017) and Abdalla et al. (CRYPTO 2018) to our scheme, we can obtain the first tightly secure function-hiding IPFE scheme and multi-input IPFE (MIPFE) scheme respectively. Our second main contribution is the proposal of a new generic conversion from function-hiding IPFE to function-hiding MIPFE, which was left as an open problem by Abdalla et al. (CRYPTO 2018). We can obtain the first tightly secure function-hiding MIPFE scheme by applying our conversion to the tightly secure function-hiding IPFE scheme described above. Finally, the security reductions of all our schemes are fully tight, which means that the security of our schemes is reduced to the MDDH assumption with a constant security loss

Inner-Product Functional Encryption with Fine-Grained Access Control

We construct new functional encryption schemes that combine the access control functionality of attribute-based encryption with the possibility of performing linear operations on the encrypted data. While such a primitive could be easily realized from fully fledged functional encryption schemes, what makes our result interesting is the fact that our schemes simultaneously achieve all the following properties. They are public-key, efficient and can be proved secure under standard and well established assumptions (such as LWE or pairings). Furthermore, security is guaranteed in the setting where adversaries are allowed to get functional keys that decrypt the challenge ciphertext. Our first results are two functional encryption schemes for the family of functions that allow users to embed policies (expressed by monotone span programs) in the encrypted data, so that one can generate functional keys to compute weighted sums on the latter. Both schemes are pairing-based and quite generic: they combine the ALS functional encryption scheme for inner products from Crypto 2016 with any attribute-based encryption schemes relying on the dual-system encryption methodology. As an additional bonus, they yield simple and elegant multi-input extensions essentially for free, thereby broadening the set of applications for such schemes. Multi-input is a particularly desirable feature in our setting, since it gives a finer access control over the encrypted data, by allowing users to associate different access policies to different parts of the encrypted data. Our second result builds identity-based functional encryption for inner products from lattices. This is achieved by carefully combining existing IBE schemes from lattices with adapted, LWE-based, variants of ALS. We point out to intrinsic technical bottlenecks to obtain richer forms of access control from lattices. From a conceptual point of view, all our results can be seen as further evidence that more expressive forms of functional encryption can be realized under standard assumptions and with little computational overhead

Efficient Designated-Verifier Non-Interactive Zero-Knowledge Proofs of Knowledge

We propose a framework for constructing efficient designated-verifier non-interactive zero-knowledge proofs (DVNIZK) for a wide class of algebraic languages over abelian groups, under standard assumptions. The proofs obtained via our framework are proofs of knowledge, enjoy statistical, and unbounded soundness (the soundness holds even when the prover receives arbitrary feedbacks on previous proofs). Previously, no efficient DVNIZK system satisfying any of those three properties was known. Our framework allows proving arbitrary relations between cryptographic primitives such as Pedersen commitments, ElGamal encryptions, or Paillier encryptions, in an efficient way. For the latter, we further exhibit the first non-interactive zero-knowledge proof system in the standard model that is more efficient than proofs obtained via the Fiat-Shamir transform, with still-meaningful security guarantees and under standard assumptions. Our framework has numerous applications, in particular for the design of efficient privacy-preserving non-interactive authentication

Towards Predicting Ad Effectiveness via an Eye Tracking Study

This paper presents the pilot study of a project for which the main aim is to implement an evaluation methodology service for the identification of the best locations on Cypriot web space based on eye tracking studies. Advertising budget, social demographics and web usage are some of the factors that are being considered. During this pilot study, a description in existing patterns of advertisement placement on websites is first presented. Then we present the methodologies of two pilot studies where user data are collected with the use of eye tracking technologies in order to understand how users look at Web advertising and how effective each location is as well as Marketers’ questionnaire. Stimuli were three Cypriot websites with advertisements of various types and three locations: ads being static and animated, types being skyscraper and display ads and location varied around the page. Eye-tracking data are compared to ad choices of marketing managers in Cyprus who rated the ad position and it’s attention value. Results demonstrate the correlation between user attention, advert types and the value as rated by marketers. This pilot study revealed conclusions that could form the basis towards predicting ad effectiveness of webpages with the use of ad number, location, size, and type

Linearly Homomorphic Encryption from DDH

We design a linearly homomorphic encryption scheme whose security relies on the hardness of the decisional Diffie-Hellman problem. Our approach requires some special features of the underlying group. In particular, its order is unknown and it contains a subgroup in which the discrete logarithm problem is tractable. Therefore, our instantiation holds in the class group of a non maximal order of an imaginary quadratic field. Its algebraic structure makes it possible to obtain such a linearly homomorphic scheme whose message space is the whole set of integers modulo a prime p and which supports an unbounded number of additions modulo p from the ciphertexts. A notable difference with previous works is that, for the first time, the security does not depend on the hardness of the factorization of integers. As a consequence, under some conditions, the prime p can be scaled to fit the application needs.Initiative d'excellence de l'Université de BordeauxLattices: algorithms and cryptograph

Bandwidth-Efficient Threshold EC-DSA

Threshold Signatures allow n parties to share the power of issuing digital signatures so that any coalition of size at least t+1 can sign, whereas groups of t or less players cannot. Over the last few years many schemes addressed the question of realizing efficient threshold variants for the specific case of EC-DSA signatures. In this paper we present new solutions to the problem that aim at reducing the overall bandwidth consumption. Our main contribution is a new variant of the Gennaro and Goldfeder protocol from ACM CCS 2018 that avoids all the required range proofs, while retaining provable security against malicious adversaries in the dishonest majority setting. Our experiments show that-for all levels of security-our signing protocol reduces the bandwidth consumption of best previously known secure protocols for factors varying between 4.4 and 9, while key generation is consistently two times less expensive. Furthermore compared to these same protocols, our signature generation is faster for 192-bits of security and beyond.AppLicAtions de la MalléaBIlité en Cryptographi

Blind Functional Encryption

International audienceFunctional encryption (FE) gives the power to retain control of sensitive information and is particularly suitable in several practical real-world use cases. Using this primitive, anyone having a specific functional decryption key (derived from some master secret key) could only obtain the evaluation of an authorized function f over a message m, given its encryption. For many scenarios, the data owner is always different from the functionality owner, such that a classical implementation of functional encryption naturally implies an interactive key generation protocol between an entity owning the function f and another one managing the master secret key. We focus on this particular phase and consider the case where the function needs to be secret.In this paper, we introduce the new notion of blind functional encryption in which, during an interactive key generation protocol, the master secret key owner does not learn anything about the function f. Our new notion can be seen as a generalisation of the existing concepts of blind IBE/ABE. After a deep study of this new property and its relation with other security notions, we show how to obtain a generic blind FE from any non-blind FE, using homomorphic encryption and zero-knowledge proofs of knowledge. We finally illustrate such construction by giving an efficient instantiation in the case of the inner product functionality

Two-Party ECDSA from Hash Proof Systems and Efficient Instantiations

ECDSA is a widely adopted digital signature standard. Unfortunately, efficient distributed variants of this primitive are notoriously hard to achieve and known solutions often require expensive zero knowledge proofs to deal with malicious adversaries. For the two party case, Lindell [Lin17] recently managed to get an efficient solution which, to achieve simulation-based security, relies on an interactive, non standard, assumption on Paillier’s cryptosystem. In this paper we generalize Lindell’s solution using hash proof systems. The main advantage of our generic method is that it results in a simulation-based security proof without resorting to non-standard interactive assumptions. Moving to concrete constructions, we show how to instantiate our framework using class groups of imaginary quadratic fields. Our implementations show that the practical impact of dropping such interactive assumptions is minimal. Indeed, while for 128-bit security our scheme is marginally slower than Lindell’s, for 256-bit security it turns out to be better both in key generation and signing time. Moreover, in terms of communication cost, our implementation significantly reduces both the number of rounds and the transmitted bits without exception.AppLicAtions de la MalléaBIlité en Cryptographi