Single Secret Leader Election protocols (SSLE, for short) allow a group of users to select a random leader so that the latter remains secret until she decides to reveal herself. Thanks to this feature, SSLE can be used to build an election mechanism for proof-of-stake based blockchains. In particular, a recent work by Azouvi and Cappelletti (ACM AFT 2021) shows that in comparison to probabilistic leader election methods, SSLE-based proof-of-stake blockchains have significant security gains, both with respect to grinding attacks and with respect to the private attack. Yet, as of today, very few concrete constructions of SSLE are known. In particular, all existing protocols are only secure in a model where the adversary is supposed to corrupt participants before the protocol starts -- an assumption that clashes with the highly dynamic nature of decentralized blockchain protocols. In this paper we make progress in the study of SSLE by proposing new efficient constructions that achieve stronger security guarantees than previous work. In particular, we propose the first SSLE protocol that achieves adaptive security. Our scheme is proven secure in the universal composability model and achieves efficiency comparable to previous, less secure, realizations in the state of the art.

A double-authentication preventing signature (DAPS) scheme is a digital signature scheme equipped with a self-enforcement mechanism. Messages consist of an address and a payload component, and a signer is penalized if she signs two messages with the same addresses but different payloads. The penalty is the disclosure of the signer’s signing key. Most of the existing DAPS schemes are proved secure in the random oracle model (ROM), while the efficient ones in the standard model only support address spaces of polynomial size. We present DAPS schemes that are efficient, secure in the standard model under standard assumptions and support large address spaces. Our main construction builds on vector commitments (VC) and double-trapdoor chameleon hash functions (DCH). We also provide a DAPS realization from Groth–Sahai (GS) proofs that builds on a generic construction by Derler et al., which they instantiate in the ROM. The GS-based construction, while less efficient than our main one, shows that a general yet efficient instantiation of DAPS in the standard model is possible. An interesting feature of our main construction is that it can be easily modified to guarantee security even in the most challenging setting where no trusted setup is provided. To the best of our knowledge, ours seems to be the first construction achieving this in the standard model.

Presents the introductory editorial for this issue of the publication.

We show a technique to transform a linearly-homomorphic encryption into a scheme capable of evaluating degree-2 computations on ciphertexts. Our transformation is surprisingly simple and requires only one very mild property on the underlying linearly-homomorphic scheme: the message space must be a public ring in which it is possible to sample elements uniformly at random. This allows us to instantiate our transformation with virtually all existing number-theoretic linearly-homomorphic schemes, such as Goldwasser-Micali, Paillier, or ElGamal. Our resulting schemes achieve circuit privacy and are compact when considering a subclass of degree-2 polynomials where the number of additions of degree-2 terms is bounded by a constant.

Zero knowledge sets (ZKS), introduced by Micali, Rabin, and Kilian in 2003, allow a prover to commit to a secret set$S$in a way such that it can later prove, non interactively, statements of the form$x\in S$(or$x\notin S$), without revealing any further information (on top of what explicitly revealed by the inclusion/exclusion statements above) on$S$, not even its size. Later, Chaseabstracted away the Micali, Rabin, and Kilian's construction by introducing an elegant new variant of commitments that they called (trapdoor) mercurial commitments. Using this primitive, it was shown how to construct zero knowledge sets from a variety of assumptions (both general and number theoretic). This paper introduces the notion of trapdoor$q$-mercurial commitments (${\ssr qTMC}$s), a notion of mercurial commitment that allows the sender to commit to an ordered sequence of exactly$q$messages, rather than to a single one. Following the previous work, it is shown how to construct ZKS from${\ssr qTMC}$s and collision resistant hash functions. Then, it is presented an efficient realization of${\ssr qTMC}$s that is secure under the so called Strong Diffie Hellman (SDH) assumption, a number theoretic conjecture recently introduced by Boneh and Boyen. Using such scheme as basic building block, it is obtained a construction of ZKS that allows for proofs that are much shorter with respect to the best previously known implementations. In particular, for an appropriate choice of the parameters, our proofs are up to 33% shorter for the case of proofs of membership, and up to 73% shorter for the case of proofs of nonmembership. Experimental tests confirm practical time performances.

Onion routing protocols allow users to establish anonymous channels to preserve their privacy over a public network. Several protocols implementing this primitive have been proposed in recent years, and TOR, a real-life implementation, provides an onion routing service to thousands of users over the internet.

We re-examine Paillier's cryptosystem, and show that by choosing a particular discrete log base g, and by introducing an alternative decryption procedure, we can extend the scheme to allow an arbitrary exponent e instead of N. The use of low exponents substantially increases the efficiency of the scheme. The semantic security is now based on a new decisional assumption, namely the hardness of deciding whether an element is a "small" e-th residue modulo N2.We also show how to use Paillier's original cryptosystem to build a trapdoor commitment scheme. This new scheme is information-theoretically private, and computationally binding (this property holds under the assumption that the RSA function with exponent N is hard to invert). A novel property of this new commitment scheme is that most of the work can be done offline before knowing the message one wants to commit to. Once the message is known only two multiplications are required. This is the first trapdoor commitment scheme with this online-offline efficiency property which is also length-preserving.