We present Ouroboros Crypsinous, the first formally analysed privacy-preserving proof-ofstake (PoS) blockchain protocol. To model its security we give a thorough treatment of private ledgers in the universal composition (UC) setting that might be of independent interest. To prove our protocol secure against adaptive attacks, which are particularly critical in the PoS setting, we introduce a new coin evolution technique that relies on a SNARKs mechanism and key-private forward secure encryption. The latter primitive-and the associated constructioncan be of independent interest. We stress that existing approaches to private blockchains, such as the proof-of-work-based Zerocash are analyzed only against static corruptions. *
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.
Zero-knowledge succinct non-interactive arguments (zk-SNARKs) rely on knowledge assumptions for their security. Meanwhile, as the complexity and scale of cryptographic systems continues to grow, the composition of secure protocols is of vital importance. The current gold standards of composable security, the Universal Composability and Constructive Cryptography frameworks cannot capture knowledge assumptions, as their core proofs of composition prohibit white-box extraction. In this paper, we present a formal model allowing the composition of knowledge assumptions. Despite showing impossibility for the general case, we demonstrate the model's usefulness when limiting knowledge assumptions to few instances of protocols at a time. We finish by providing the first instance of a simultaneously succinct and composable zk-SNARK, by using existing results within our framework.
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 analyse, for the first time, a blockchain mechanism that produces a secure SRS with the characteristic that security is shown under comparable conditions to the blockchain protocol itself. Our mechanism makes use of the recent discovery of updateable structured 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 setup 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.
Privacy-oriented cryptocurrencies, like Zcash or Monero, provide fair transaction anonymity and confidentiality, but lack important features compared to fully public systems, like Ethereum. Specifically, supporting assets of multiple types and providing a mechanism to atomically exchange them, which is critical for e.g. decentralized finance (DeFi), is challenging in the private setting. By combining insights and security properties from Zcash and SwapCT (PETS 21, an atomic swap system for Monero), we present a simple zk-SNARKs based transaction scheme, called Zswap, which is carefully malleable to allow the merging of transactions, while preserving anonymity. Our protocol enables multiple assets and atomic exchanges by making use of sparse homomorphic commitments with aggregated open randomness, together with Zcash friendly simulation-extractable non-interactive zero-knowledge (NIZK) proofs. This results in a provably secure privacypreserving transaction protocol, with efficient swaps, and overall performance close to that of existing deployed private cryptocurrencies. It is similar to Zcash Sapling and benefits from existing code-bases and implementation expertise.
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