Biblio

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.

"Our Laws are not generally known; they are kept secret by the small group of nobles who rule us. We are convinced that these ancient laws are scrupulously administered; nevertheless it is an extremely painful thing to be ruled by laws that one does not know."–Franz Kafka, Parables and Paradoxes. Post 9/11, journalists, scholars and activists have pointed out that it secret laws - a body of law whose details and sometime mere existence is classified as top secret - were on the rise in all three branches of the US government due to growing national security concerns. Amid heated current debates on governmental wishes for exceptional access to encrypted digital data, one of the key issues is: which mechanisms can be put in place to ensure that government agencies follow agreed-upon rules in a manner which does not compromise national security objectives? This promises to be especially challenging when the rules, according to which access to encrypted data is granted, may themselves be secret. In this work we show how the use of cryptographic protocols, and in particular, the idea of zero knowledge proofs can ensure accountability and transperancy of the government in this extraordinary, seemingly deadlocked, setting. We propose an efficient record-keeping infrastructure with versatile publicly verifiable audits that preserve (information-theoretic) privacy of record contents as well as of the rules by which the records are attested to abide. Our protocol is based on existing blockchain and cryptographic tools including commitments and zero-knowledge SNARKs, and satisfies the properties of indelibility (i.e., no back-dating), perfect data privacy, public auditability of secret data with secret laws, accountable deletion, and succinctness. We also propose a variant scheme where entities can be required to pay fees based on record contents (e.g., for violating regulations) while still preserving privacy. Our scheme can be directly instantiated on the Ethereum blockchain (and a simplified version with weaker guarantees can be instantiated with Bitcoin).