International Association
for Cryptologic Research

Suppose a prover, in possession of a large body of valuable evidence, wants to quickly convince a verifier by presenting only a small portion of the evidence. We define an Approximate Lower Bound Argument, or ALBA, which allows the prover to do just that: to succinctly prove knowledge of a large number of elements satisfying a predicate (or, more generally, elements of a sufficient total weight when a predicate is generalized to a weight function). The argument is approximate because there is a small gap between what the prover actually knows and what the verifier is convinced the prover knows. This gap enables very efficient schemes. We present noninteractive constructions of ALBA in the random oracle and Uniform Random String models and show that our proof sizes are nearly optimal. We also show how our constructions can be made particularly communication-efficient when the evidence is distributed among multiple provers working together, which is of practical importance when ALBA is applied to a decentralized setting. We demonstrate two very different applications of ALBAs: for large-scale decentralized signatures and for achieving universal composability in general-purpose succinct proof systems (SNARKs).

Advanced cryptographic protocols such as Zero-knowledge (ZK) proofs of knowledge, widely used in cryptocurrency applications such as Zcash, Monero, Filecoin, Tezos, Topos, demand new cryptographic hash functions that are efficient not only over the binary field $\F_2$, but also over large fields of prime characteristic $\F_p$. This need has been acknowledged by the wider community and new so-called Arithmetization-Oriented (AO) hash functions have been proposed, e.g. MiMC-Hash, Rescue, Poseidon, ReinforcedConcrete and Griffin to name a few. In this paper we propose Anemoi: a new family of ZK-friendly permutations, that can be used to construct efficient hash functions and compression functions. The main features of these algorithms are that 1) they are designed to be efficient within multiple proof systems (e.g. Groth16, Plonk, etc.), 2) they contain dedicated functions optimised for specific applications (namely Merkle tree hashing and general purpose hashing), 3) they have highly competitive performance e.g. about a factor of 2 improvement over Poseidon and Rescue in terms of R1CS constraints, a 21%-35% Plonk constraint reduction over a highly optimized Poseidon implementation, as well as competitive native performance, running between two and three times faster than Rescue, depending on the field size. On the theoretical side, Anemoi pushes further the frontier in understanding the design principles that are truly entailed by arithmetization-orientation. In particular, we identify and exploit a previously unknown relationship between CCZ-equivalence and arithmetization-orientation. In addition, we propose two new standalone components that can be easily reused in new designs. One is a new S-box called Flystel, based on the well-studied butterfly structure, and the second is Jive -- a new mode of operation, inspired by the ``Latin dance'' symmetric algorithms (Salsa, ChaCha and derivatives). Our design is a conservative one: it uses a very classical Substitution-Permutation Network structure, and our detailed analysis of algebraic attacks highlights can be of independent interest.

Group signatures allow members of a group to anonymously sign on behalf of the group. Membership is administered by a designated group manager. The group manager can also reveal the identity of a signer if and when needed to enforce accountability and deter abuse. For group signatures to be applicable in practice, they need to support fully dynamic groups, i.e., users may join and leave at any time. Existing security definitions for fully dynamic group signatures are informal, have shortcomings, and are mutually incompatible. We fill the gap by providing a formal rigorous security model for fully dynamic group signatures. Our model is general and is not tailored toward a specific design paradigm and can therefore, as we show, be used to argue about the security of different existing constructions following different design paradigms. Our definitions are stringent and when possible incorporate protection against maliciously chosen keys. We consider both the case where the group management and tracing signatures are administered by the same authority, i.e., a single group manager, and also the case where those roles are administered by two separate authorities, i.e., a group manager and an opening authority. We also show that a specialization of our model captures existing models for static and partially dynamic schemes. In the process, we identify a subtle gap in the security achieved by group signatures using revocation lists. We show that in such schemes new members achieve a slightly weaker notion of traceability. The flexibility of our security model allows to capture such relaxation of traceability.

Email communication is amongst the most prominent online activities, and as such, can put sensitive information at risk. It is thus of high importance that internet email applications are designed in a privacy-aware manner and analyzed under a rigorous threat model. The Snowden revelations (2013) suggest that such a model should feature a global adversary, in light of the observational tools available. Furthermore, the fact that protecting metadata can be of equal importance as protecting the communication context implies that end-to-end encryption may be necessary, but it is not sufficient.With this in mind, we utilize the Universal Composability framework [Canetti, 2001] to introduce an expressive cryptographic model for email “ecosystems” that can formally and precisely capture various well-known privacy notions (unobservability, anonymity, unlinkability, etc.), by parameterizing the amount of leakage an ideal-world adversary (simulator) obtains from the email functionality.Equipped with our framework, we present and analyze the security of two email constructions that follow different directions in terms of the efficiency vs. privacy tradeoff. The first one achieves optimal security (only the online/offline mode of the users is leaked), but it is mainly of theoretical interest; the second one is based on parallel mixing [Golle and Juels, 2004] and is more practical, while it achieves anonymity with respect to users that have similar amount of sending and receiving activity.