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An emerging direction for authenticating people is the adoption of biometric authentication systems. Biometric credentials are becoming increasingly popular as a means of authenticating people due to the wide range of advantages that they provide with respect to classical authentication methods (e.g., password-based authentication). The most characteristic feature of this authentication method is the naturally strong bond between a user and her biometric credentials. This very same advantageous property, however, raises serious security and privacy concerns in case the biometric trait gets compromised. In this article, we present the most challenging issues that need to be taken into consideration when designing secure and privacypreserving biometric authentication protocols. More precisely, we describe the main threats against privacy-preserving biometric authentication systems and give directions on possible countermeasures in order to design secure and privacy-preserving biometric authentication protocols.

Homomorphic authenticators (HAs) enable a client to authenticate a large collection of data elements m1,. .. , mt and outsource them, along with the corresponding authenticators, to an untrusted server. At any later point, the server can generate a short authenticator σ f,y vouching for the correctness of the output y of a function f computed on the outsourced data, i.e., y = f (m1,. .. , mt). Recently researchers have focused on HAs as a solution, with minimal communication and interaction, to the problem of delegating computation on outsourced data. The notion of HAs studied so far, however, only supports executions (and proofs of correctness) of computations over data authenticated by a single user. Motivated by realistic scenarios (ubiquitous computing, sensor networks, etc.) in which large datasets include data provided by multiple users, we study the concept of multi-key homomorphic authenticators. In a nutshell, multi-key HAs are like HAs with the extra feature of allowing the holder of public evaluation keys to compute on data authenticated under different secret keys. In this paper, we introduce and formally define multi-key HAs. Secondly, we propose a construction of a multi-key homomorphic signature based on standard lattices and supporting the evaluation of circuits of bounded polynomial depth. Thirdly, we provide a construction of multi-key homomorphic MACs based only on pseudorandom functions and supporting the evaluation of low-degree arithmetic circuits. Albeit being less expressive and only secretly verifiable, the latter construction presents interesting efficiency properties.

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