Biblio

We present Ouroboros Crypsinous, the first formally analyzed privacy-preserving proof-of-stake blockchain protocol. To model its security we give a thorough treatment of private ledgers in the (G)UC setting that might be of independent interest. To prove our protocol secure against adaptive attacks, we introduce a new coin evolution technique relying on SNARKs and key-private forward secure encryption. The latter primitive-and the associated construction-can be of independent interest. We stress that existing approaches to private blockchain, such as the proof-of-work-based Zerocash are analyzed only against static corruptions.

We present a group signature scheme, based on the hardness of lattice problems, whose outputs are more than an order of magnitude smaller than the currently most efficient schemes in the literature. Since lattice-based schemes are also usually non-trivial to efficiently implement, we additionally provide the first experimental implementation of lattice-based group signatures demonstrating that our construction is indeed practical – all operations take less than half a second on a standard laptop. A key component of our construction is a new zero-knowledge proof system for proving that a committed value belongs to a particular set of small size. The sets for which our proofs are applicable are exactly those that contain elements that remain stable under Galois automorphisms of the underlying cyclotomic number field of our lattice-based protocol. We believe that these proofs will find applications in other settings as well. The motivation of the new zero-knowledge proof in our construction is to allow the efficient use of the selectively-secure signature scheme (i.e. a signature scheme in which the adversary declares the forgery message before seeing the public key) of Agrawal et al. (Eurocrypt 2010) in constructions of lattice-based group signatures and other privacy protocols. For selectively-secure schemes to be meaningfully converted to standard signature schemes, it is crucial that the size of the message space is not too large. Using our zero-knowledge proofs, we can strategically pick small sets for which we can provide efficient zero-knowledge proofs of membership.

Zero-knowledge SNARKs (zk-SNARKs) are non-interactive proof systems with short and efficiently verifiable proofs. They elegantly resolve the juxtaposition of individual privacy and public trust, by providing an efficient way of demonstrating knowledge of secret information without actually revealing it. To this day, zk-SNARKs are being used for delegating computation, electronic cryptocurrencies, and anonymous credentials. However, all current SNARKs implementations rely on pre-quantum assumptions and, for this reason, are not expected to withstand cryptanalitic efforts over the next few decades. In this work, we introduce the first designated-verifier zk-SNARK based on lattice assumptions, which are believed to be post-quantum secure. We provide a generalization in the spirit of Gennaro et al. (Eurocrypt'13) to the SNARK of Danezis et al. (Asiacrypt'14) that is based on Square Span Programs (SSPs) and relies on weaker computational assumptions. We focus on designated-verifier proofs and propose a protocol in which a proof consists of just 5 LWE encodings. We provide a concrete choice of parameters as well as extensive benchmarks on a C implementation, showing that our construction is practically instantiable.

Certification of keys and attributes is in practice typically realized by a hierarchy of issuers. Revealing the full chain of issuers for certificate verification, however, can be a privacy issue since it can leak sensitive information about the issuer's organizational structure or about the certificate owner. Delegatable anonymous credentials solve this problem and allow one to hide the full delegation (issuance) chain, providing privacy during both delegation and presentation of certificates. However, the existing delegatable credentials schemes are not efficient enough for practical use. In this paper, we present the first hierarchical (or delegatable) anonymous credential system that is practical. To this end, we provide a surprisingly simple ideal functionality for delegatable credentials and present a generic construction that we prove secure in the UC model. We then give a concrete instantiation using a recent pairing-based signature scheme by Groth and describe a number of optimizations and efficiency improvements that can be made when implementing our concrete scheme. The latter might be of independent interest for other pairing-based schemes as well. Finally, we report on an implementation of our scheme in the context of transaction authentication for blockchain, and provide concrete performance figures.

We propose a new class of post-quantum digital signature schemes that: (a) derive their security entirely from the security of symmetric-key primitives, believed to be quantum-secure, and (b) have extremely small keypairs, and, (c) are highly parameterizable. In our signature constructions, the public key is an image y=f(x) of a one-way function f and secret key x. A signature is a non-interactive zero-knowledge proof of x, that incorporates a message to be signed. For this proof, we leverage recent progress of Giacomelli et al. (USENIX'16) in constructing an efficient Σ-protocol for statements over general circuits. We improve this Σ-protocol to reduce proof sizes by a factor of two, at no additional computational cost. While this is of independent interest as it yields more compact proofs for any circuit, it also decreases our signature sizes. We consider two possibilities to make the proof non-interactive: the Fiat-Shamir transform and Unruh's transform (EUROCRYPT'12, '15,'16). The former has smaller signatures, while the latter has a security analysis in the quantum-accessible random oracle model. By customizing Unruh's transform to our application, the overhead is reduced to 1.6x when compared to the Fiat-Shamir transform, which does not have a rigorous post-quantum security analysis. We implement and benchmark both approaches and explore the possible choice of f, taking advantage of the recent trend to strive for practical symmetric ciphers with a particularly low number of multiplications and end up using Low MC (EUROCRYPT'15).