One-Out-of-Many Proofs: Or How to Leak a Secret and Spend a Coin

We construct a 3-move public coin special honest verifier zero-knowledge proof, a so-called Sigma-protocol, for a list of commitments having at least one commitment that opens to 0. It is not required for the prover to know openings of the other commitments. The proof system is efficient, in particular in terms of communication requiring only the transmission of a logarithmic number of commitments. We use our proof system to instantiate both ring signatures and zerocoin, a novel mechanism for bitcoin privacy. We use our Sigma-protocol as a (linkable) ad-hoc group identification scheme where the users have public keys that are commitments and demonstrate knowledge of an opening for one of the commitments to unlinkably identify themselves (once) as belonging to the group. Applying the Fiat-Shamir transform on the group identification scheme gives rise to ring signatures, applying it to the linkable group identification scheme gives rise to zerocoin. Our ring signatures are very small compared to other ring signature schemes and we only assume the users’ secret keys to be the discrete logarithms of single group elements so the setup is quite realistic. Similarly, compared with the original zerocoin protocol we only rely on a weak cryptographic assumption and do not require a trusted setup. A third application of our Sigma protocol is an efficient proof of membership of a secret committed value belonging to a public list of values

miTLS: Verifying Protocol Implementations against Real-World Attacks

International audienceThe TLS Internet Standard, previously known as SSL, is the default protocol for encrypting communications between clients and servers on the Web. Hence, TLS routinely protects our sensitive emails, health records, and payment information against network-based eavesdropping and tampering. For the past 20 years, TLS security has been analyzed in various cryptographic and programming models to establish strong formal guarantees for various protocol configurations. However, TLS deployments are still often vulnerable to attacks and rely on security experts to fix the protocol implementations. The miTLS project intends to solve this apparent contradiction between published proofs and real-world attacks, which reveals a gap between TLS theory and practice. To this end, the authors developed a verified reference implementation and a cryptographic security proof that account for the protocol's low-level details. The resulting formal development sheds light on recent attacks, yields security guarantees for typical TLS usages, and informs the design of the protocol's next version

Mining for Privacy: How to Bootstrap a Snarky Blockchain

Non-interactive zero-knowledge proofs, and more specifically succinct non-interactive zero-knowledge arguments (zk-SNARKs), have been proven to be the “swiss army knife” of the blockchain and distributed ledger space, with a variety of applications in privacy, interoperability and scalability. Many commonly used SNARK systems rely on a structured reference string, the secure generation of which turns out to be their Achilles heel: If the randomness used for the generation is known, the soundness of the proof system can be broken with devastating consequences for the underlying blockchain system that utilises them. In this work we describe and analyze, for the first time, a blockchain mechanism that produces a secure SRS with the characteristic that security is shown for the exact same conditions under which the blockchain protocol is proven to be secure. Our mechanism makes use of the recent discovery of updateable structure reference strings to perform this secure generation in a fully distributed manner. In this way, the SRS emanates from the normal operation of the blockchain protocol itself without the need of additional security assumptions or off-chain computation and/or verification. We provide concrete guidelines for the parameterisation of this system which allows for the completion of a secure setup in a reasonable period of time. We also provide an incentive scheme that, when paired with the update mechanism, properly incentivises participants into contributing to secure reference string generation

Kachina - Foundations of Private Smart Contracts

Smart contracts present a uniform approach for deploying distributed computation and have become a popular means to develop security critical applications. A major barrier to adoption for many applications is the public nature of existing systems, such as Ethereum. Several systems satisfying various definitions of privacy and requiring various trust assumptions have been proposed; however, none achieved the universality and uniformity that Ethereum achieved for non-private contracts: One unified method to construct most contracts. We provide a unified security model for private smart contracts which is based on the Universal Composition (UC) model and propose a novel core protocol, Kachina, for deploying privacy-preserving smart contracts, which encompasses previous systems. We demonstrate the Kachina method of smart contract development, using it to construct a contract that implements privacy-preserving payments, along the lines of Zerocash, which is provably secure in the UC setting and facilitates concurrency

PEReDi: Privacy-Enhanced, Regulated and Distributed Central Bank Digital Currencies

Central Bank Digital Currencies (CBDCs) aspire to offer a digital replacement for physical cash and as such need to tackle two fundamental requirements that are in conflict. On the one hand, it is desired they are private so that a financial “panopticon” is avoided, while on the other, they should be regulation friendly in the sense of facilitating any threshold-limiting, tracing, and counterparty auditing functionality that is necessary to comply with regulations such as Know Your Customer (KYC), Anti Money Laundering (AML) and Combating Financing of Terrorism (CFT) as well as financial stability considerations. In this work, we put forth a new model for CBDCs and an efficient construction that, for the first time, fully addresses these issues simultaneously. Moreover, recognizing the importance of avoiding a single point of failure, our construction is distributed so that all its properties can withstand a suitably bounded minority of participating entities getting corrupted by an adversary. Achieving all the above properties efficiently is technically involved; among others, our construction uses suitable cryptographic tools to thwart manin-the-middle attacks, it showcases a novel traceability mechanism with significant performance gains compared to previously known techniques and, perhaps surprisingly, shows how to obviate Byzantine agreement or broadcast from the optimistic execution path of a payment, something that results in an essentially optimal communication pattern and communication overhead when the sender and receiver are honest. Going beyond “simple” payments, we also discuss how our scheme can facilitate one-off large transfers complying with Know Your Transaction (KYT) disclosure requirements. Our CBDC concept is expressed and realized in the Universal Composition (UC) framework providing in this way a modular and secure way to embed it within a larger financial ecosystem

A Domain Transformation for Structure-Preserving Signatures on Group Elements

We present a generic transformation that allows us to use a large class of pairing-based signatures to construct schemes for signing group elements in a structure preserving way. As a result of our transformation we obtain a new efficient signature scheme for signing a vector of group elements that is based only on the well established decisional linear assumption (DLIN). Moreover, the public keys and signatures of our scheme consist of group elements only, and a signature is verified by evaluating a set of pairing-product equations. In combination with the Groth-Sahai proof system, such a signature scheme is an ideal building block for many privacy-enhancing protocols. To do this, we start by proposing a new stateful signature scheme for signing vectors of exponents that is F-unforgeable under weak chosen message attacks. This signature scheme is of independent interest as it is compatible with Groth-Sahai proofs and secure under a computational assumption implied by DLIN. Then we give a general transformation for signing group elements based on signatures (for signing exponents) with efficient non-interactive zero-knowledge proofs. This transform also removes any dependence on state in the signature used to sign exponents. Finally, we obtain our result by instantiating this transformation with the above signature scheme and Groth-Sahai proofs