Square Span Programs with Applications to Succinct NIZK Arguments

We use SSPs to construct succinct non-interactive zero-knowledge arguments of knowledge. For performance, our proof system is defined over Type III bilinear groups; proofs consist of just 4 group elements, verified in just 6 pairings. Concretely, using the Pinocchio libraries, we estimate that proofs will consist of 160 bytes verified in less than 6 ms

Snarky Signatures: Minimal Signatures of Knowledge from Simulation-Extractable SNARKs

We construct a pairing based simulation-extractable SNARK (SE-SNARK) that consists of only 3 group elements and has highly efficient verification. By formally linking SE-SNARKs to signatures of knowledge, we then obtain a succinct signature of knowledge consisting of only 3 group elements. SE-SNARKs enable a prover to give a proof that they know a witness to an instance in a manner which is: (1) succinct - proofs are short and verifier computation is small; (2) zero-knowledge - proofs do not reveal the witness; (3) simulation-extractable - it is only possible to prove instances to which you know a witness, even when you have already seen a number of simulated proofs. We also prove that any pairing based signature of knowledge or SE-NIZK argument must have at least 3 group elements and 2 verification equations. Since our constructions match these lower bounds, we have the smallest size signature of knowledge and the smallest size SE-SNARK possible

Lattice-Based zk-SNARKs from Square Span Programs

Zero-knowledge SNARKs (zk-SNARKs) are non-interactive proof systems with short (i.e., independent of the size of the witness) 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 widely deployed all over the planet and are used to keep alive a system worth billion of euros, namely the cryptocurrency Zcash. However, all current SNARKs implementations rely on so-called pre-quantum assumptions and, for this reason, are not expected to withstand cryptanalitic efforts over the next few decades. In this work, we introduce a new zk-SNARK that can be instantiated from lattice-based assumptions, and which is thus 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 (SSP) 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, showing that our construction is practically instantiable

Lattice-Based zk-SNARKs from Square Span Programs

International audienceZero-knowledge SNARKs (zk-SNARKs) are non-interactive proof systems with short (i.e., independent of the size of the witness) 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 widely deployed all over the planet and are used to keep alive a system worth billion of euros, namely the cryptocurrency Zcash. However, all current SNARKs implementations rely on so-called pre-quantum assumptions and, for this reason, are not expected to withstand cryptanalitic efforts over the next few decades. In this work, we introduce a new zk-SNARK that can be instantiated from lattice-based assumptions, and which is thus 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 (SSP) 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, showing that our construction is practically instantiable

Побудова загальної моделі STARK–доведень для підтвердження коректності отриманих результатів

Метою даною роботи є аналiз iснуючих пiдходiв до доведень без розголошення, зокрема, STARK-доведень, та побудова загальної моделi iнтерактивного та неiнтерактивного STARK-доведення. Об’єктом дослiдження. Об’єктом дослiдження є процес захисту персональних даних при виконаннi автентифiкацiї та авторизацiї. Предметом дослiдження є STARK-протоколи та побудова загальної моделi та алгоритму STARK-протоколу. Були розглянутi рiзнi приклади застосування STARK-доведень, був побудований загальний вигляд STARK-протоколу, його алгоритм, проаналiзованi умови, коли можна створити STARK-доведення, та була оцiнений час його роботи та довжина доведення.The aim of this work is to analyze existing approaches to evidence without disclosure, in particular, STARK-evidence, and to build a general model of interactive and non-interactive STARK-proof. The object of study. The object of research is the process of personal data protection during authentication and authorization. The subject of the research is STARK-protocols and construction of the general model and algorithm of STARK-protocol. Various examples of the use of STARK proofs were considered, a general view of the STARK protocol, its algorithm, the conditions under which STARK proofs can be created were analyzed, and the time of its operation and the length of proofing were estimated

Practical Zero-Knowledge Arguments from Structured Reference Strings

Zero-knowledge proofs have become an important tool for addressing privacy and scalability concerns in cryptographic protocols. For zero-knowledge proofs used in blockchain applications, it is desirable to have small proof sizes and fast verification. Yet by design, existing constructions with these properties such as zk-SNARKs also have a secret trapdoor embedded in a relation dependent structured reference string (SRS). Knowledge of this trapdoor suffices to break the security of these proofs. The SRSs required by zero-knowledge proofs are usually constructed with multiparty computation protocols, but the resulting parameters are specific to each individual circuit. In this thesis, we propose a model for constructing zero-knowledge arguments (i.e. zero-knowledge proofs with computational soundness) in which the generation of the SRS is directly considered in the security analysis. In our model the same SRS can be used across multiple applications. Further, the model is updatable i.e. users can update the universal SRS and the SRS is considered secure provided at least one of these users is honest. We propose two zero-knowledge arguments with updatable and universal SRSs, as well as a third which is neither updatable nor universal, but which through similar techniques achieves simulation extractability. The proposed arguments are practical, with proof sizes never more than a constant number of group elements. Verification for two of our constructions consist of a small number of pairing operations. For our other construction, which has the desirable property of a linear sized updatable and universal SRS, we describe efficient batching techniques so that verification is fast in the amortised setting