This work describes a fast fully homomorphic encryption scheme over the torus (TFHE), that revisits, generalizes and improves the fully homomorphic encryption (FHE) based on GSW and its ring variants. The simplest FHE schemes consist in bootstrapped binary gates. In this gate bootstrapping mode, we show that the scheme FHEW of [29] can be expressed only in terms of external product between a GSW and a LWE ciphertext. As a consequence of this result and of other optimizations, we decrease the running time of their bootstrapping from 690ms to 13ms single core, using 16MB bootstrapping key instead of 1GB, and preserving the security parameter. In leveled homomorphic mode, we propose two methods to manipulate packed data, in order to decrease the ciphertext expansion and to optimize the evaluation of look-up tables and arbitrary functions in RingGSW based homomorphic schemes. We also extend the automata logic, introduced in [31], to the efficient leveled evaluation of weighted automata, and present a new homomorphic counter called TBSR, that supports all the elementary operations that occur in a multiplication. These improvements speed-up the evaluation of most arithmetic functions in a packed leveled mode, with a noise overhead that remains additive. We finally present a new circuit bootstrapping that converts LWE ciphertexts into low-noise RingGSW ciphertexts in just 137ms, which makes the leveled mode of TFHE composable, and which is fast enough to speed-up arithmetic functions, compared to the gate bootstrapping approach. Finally, we provide an alternative practical analysis of LWE based schemes, which directly relates the security parameter to the error rate This work was done while I. Chillotti was a PhD student in the Laboratoire de Mathématiques de Versailles, UVSQ (Versailles, France) and while M. Georgieva worked in Gemalto (Meudon, France). of LWE and the entropy of the LWE secret key, and we propose concrete parameter sets and timing comparison for all our constructions.

No abstract

Most electronic voting schemes aim at providing verifiability: voters should trust the result without having to rely on some authorities. Actually, even a prominent voting system like Helios cannot fully achieve verifiability since a dishonest bulletin board may add ballots. This problem is called ballot stuffing. In this paper we give a definition of verifiability in the computational model to account for a malicious bulletin board that may add ballots. Next, we provide a generic construction that transforms a voting scheme that is verifiable against an honest bulletin board and an honest registration authority (weak verifiability) into a verifiable voting scheme under the weaker trust assumption that the registration authority and the bulletin board are not simultaneously dishonest (strong verifiability). This construction simply adds a registration authority that sends private credentials to the voters, and publishes the corresponding public credentials. We further provide simple and natural criteria that imply weak verifiability. As an application of these criteria, we formally prove the latest variant of Helios by Bernhard, Pereira and Warinschi weakly verifiable. By applying our generic construction we obtain a Helios-like scheme that has ballot privacy and strong verifiability (and thus prevents ballot stuffing). The resulting voting scheme, Helios-C, retains the simplicity of Helios and has been implemented and tested.

This work deals with the security challenges in authentication protocols employing volatile biometric features, where the authentication is indeed a comparison between a fresh biometric template and that enrolled during the enrollment phase. We propose a security model for biometric-based authentication protocols by assuming that the biometric features to be public. Extra attention is paid to the privacy issues related to the sensitive relationship between a biometric feature and the relevant identity. Relying on the Goldwasser-Micali encryption scheme, we introduce a protocol for biometric-based authentication and prove its security in our security model.

No abstract

No abstract

International audienceIn lattice cryptography, worst-case to average-case reductions rely on two problems: Ajtai’s SIS and Regev’s LWE, which both refer to a very small class of random lattices related to the group G=Znq. We generalize worst-case to average-case reductions to all integer lattices of sufficiently large determinant, by allowing G to be any (sufficiently large) finite abelian group. Our main tool is a novel generalization of lattice reduction, which we call structural lattice reduction: given a finite abelian group G and a lattice L, it finds a short basis of some lattice L¯ such that L⊆L¯ and L¯/L≃G. Our group generalizations of SIS and LWE allow us to abstract lattice cryptography, yet preserve worst-case assumptions: as an illustration, we provide a somewhat conceptually simpler generalization of the Alperin-Sheriff-Peikert variant of the Gentry-Sahai-Waters homomorphic scheme. We introduce homomorphic mux gates, which allows us to homomorphically evaluate any boolean function with a noise overhead proportional to the square root of its number of variables, and bootstrap the full scheme using only a linear noise overhead

Real-world elections often require threshold cryptosystems so that any t out of trustees can proceed to tallying. This is needed to protect the confidentiality of the voters' votes against curious authorities (at least t + 1 trustees must collude to learn individual votes) as well as to increase the robustness of the election (in case some trustees become unavailable, t + 1 trustees suffice to compute the election result). We describe a fully distributed (with no dealer) threshold cryptosystem suitable for the Helios voting system (in particular, suitable to partial decryption), and prove it secure under the Decisional Diffie-Hellman assumption. Secondly, we propose a fully distributed variant of Helios, that allows for arbitrary threshold parameters , t, together with a proof of ballot privacy when used for referendums. Our modification of Helios can be seen as revision of the seminal multi-authority election system from Cramer, Gennaro and Schoenmakers, upon which the original Helios system is based. As such, our work implies, to our knowledge, the first formal proof of ballot privacy for the scheme by Cramer et al. Thirdly, we provide the first open-source implementation of Helios with a fully distributed key generation setup.