Yafa-108/146: Implementing ed25519-embedding Cocks-Pinch curves in arkworks-rs

This note describes two pairing-friendly curves that embed ed25519, of different bit security levels. Our search is not novel; it follows the standard recipe of the Cocks-Pinch method. We implemented these two curves on arkworks-rs. This note is intended to document how the parameters are being generated and how to implement these curves in arkworks-rs 0.4.0, for further reference. We name the two curves as Yafa-108 and Yafa-146: - Yafa-108 is estimated to offer 108-bit security, which we parameterized to match the 103-bit security of BN254 - Yafa-146 is estimated to offer 146-bit security, which we parameterized to match the 132-bit security of BLS12-446 or 123-bit security of BLS12-381 We use these curves as an example to demonstrate two things: - The elastic zero-knowledge proof, Gemini (EUROCRYPT \u2722), is more than being elastic, but it is more curve-agnostic and hardware-friendly. - The cost of nonnative field arithmetics can be drastic, and the needs of application-specific curves may be inherent. This result serves as evidence of the necessity of EIP-1962, and the insufficiency of EIP-2537

Metal: A Metadata-Hiding File-Sharing System

File-sharing systems like Dropbox offer insufficient privacy because a compromised server can see the file contents in the clear. Although encryption can hide such contents from the servers, metadata leakage remains significant. The goal of our work is to develop a file-sharing system that hides metadata---including user identities and file access patterns. Metal is the first file-sharing system that hides such metadata from malicious users and that has a latency of only a few seconds. The core of Metal consists of a new two-server multi-user oblivious RAM (ORAM) scheme, which is secure against malicious users, a metadata-hiding access control protocol, and a capability sharing protocol. Compared with the state-of-the-art malicious-user file-sharing scheme PIR-MCORAM (Maffei et al.\u2717), which does not hide user identities, Metal hides the user identities and is 500x faster (in terms of amortized latency) or 10^5x faster (in terms of worst-case latency)

Reducing Participation Costs via Incremental Verification for Ledger Systems

Ledger systems are applications run on peer-to-peer networks that provide strong integrity guarantees. However, these systems often have high participation costs. For a server to join this network, the bandwidth and computation costs grow linearly with the number of state transitions processed; for a client to interact with a ledger system, it must either maintain the entire ledger system state like a server or trust a server to correctly provide such information. In practice, these substantial costs centralize trust in the hands of the relatively few parties with the resources to maintain the entire ledger system state. The notion of *incrementally verifiable computation*, introduced by Valiant (TCC \u2708), has the potential to significantly reduce such participation costs. While prior works have studied incremental verification for basic payment systems, the study of incremental verification for a general class of ledger systems remains in its infancy. In this paper we initiate a systematic study of incremental verification for ledger systems, including its foundations, implementation, and empirical evaluation. We formulate a cryptographic primitive providing the functionality and security for this setting, and then demonstrate how it captures applications with privacy and user-defined computations. We build a system that enables incremental verification, for applications such as privacy-preserving payments, with universal (application-independent) setup. Finally, we show that incremental verification can reduce participation costs by orders of magnitude, for a bare-bones version of Bitcoin

MPCAuth: Multi-factor Authentication for Distributed-trust Systems

Systems with distributed trust have attracted growing research attention and seen increasing industry adoptions. In these systems, critical secrets are distributed across N servers, and computations are performed privately using secure multi-party computation (SMPC). Authentication for these distributed-trust systems faces two challenges. The first challenge is ease-of-use. Namely, how can an authentication protocol maintain its user experience without sacrificing security? To avoid a central point of attack, a client needs to authenticate to each server separately. However, this would require the client to authenticate N times for each authentication factor, which greatly hampers usability. The second challenge is privacy, as the client’s sensitive profiles are now exposed to all N servers under different trust domains, which creates N times the attack surface for the profile data. We present MPCAuth, a multi-factor authentication system for distributed-trust applications that address both challenges. Our system enables a client to authenticate to N servers independently with the work of only one authentication. In addition, our system is profile hiding, meaning that the client’s authentication profiles such as her email username, phone number, passwords, and biometric features are not revealed unless all servers are compromised. We propose secure and practical protocols for an array of widely adopted authentication factors, including email passcodes, SMS messages, U2F, security questions/passwords, and biometrics. Our system finds practical applications in the space of cryptocurrency custody and collaborative machine learning, and benefits future adoptions of distributed-trust applications

Titanium: A Metadata-Hiding File-Sharing System with Malicious Security

End-to-end encrypted file-sharing systems enable users to share files without revealing the file contents to the storage servers. However, the servers still learn metadata, including user identities and access patterns. Prior work tried to remove such leakage but relied on strong assumptions. Metal (NDSS \u2720) is not secure against malicious servers. MCORAM (ASIACRYPT \u2720) provides confidentiality against malicious servers, but not integrity. Titanium is a metadata-hiding file-sharing system that offers confidentiality and integrity against malicious users and servers. Compared with MCORAM, which offers confidentiality against malicious servers, Titanium also offers integrity. Experiments show that Titanium is 5x-200x faster or more than MCORAM

HOLMES: Efficient Distribution Testing for Secure Collaborative Learning

Using secure multiparty computation (MPC), organizations which own sensitive data (e.g., in healthcare, finance or law enforcement) can train machine learning models over their joint dataset without revealing their data to each other. At the same time, secure computation restricts operations on the joint dataset, which impedes computation to assess its quality. Without such an assessment, deploying a jointly trained model is potentially illegal. Regulations, such as the European Union\u27s General Data Protection Regulation (GDPR), require organizations to be legally responsible for the errors, bias, or discrimination caused by their machine learning models. Hence, testing data quality emerges as an indispensable step in secure collaborative learning. However, performing distribution testing is prohibitively expensive using current techniques, as shown in our experiments. We present HOLMES, a protocol for performing distribution testing efficiently. In our experiments, compared with three non-trivial baselines, HOLMES achieves a speedup of more than 10x for classical distribution tests and up to 10^4x for multidimensional tests. The core of HOLMES is a hybrid protocol that integrates MPC with zero-knowledge proofs and a new ZK-friendly and naturally oblivious sketching algorithm for multidimensional tests, both with significantly lower computational complexity and concrete execution costs

Cerebro: A Platform for Multi-Party Cryptographic Collaborative Learning

Many organizations need large amounts of high-quality data for their applications, and one way to acquire such data is to combine datasets from multiple parties. Since these organizations often own sensitive data that cannot be shared in the clear with others due to policy regulation and business competition, there is increased interest in utilizing secure multi-party computation (MPC). MPC allows multiple parties to jointly compute a function without revealing their inputs to each other. We present Cerebro, an end-to-end collaborative learning platform that enables parties to compute learning tasks without sharing plaintext data. By taking an end-to-end approach to the system design, Cerebro allows multiple parties with complex economic relationships to safely collaborate on machine learning computation through the use of release policies and auditing, while also enabling users to achieve good performance without manually navigating the complex performance tradeoffs between MPC protocols

An efficient verifiable state for zk-EVM and beyond from the Anemoi hash function

In our survey of the various zk-EVM constructions, it becomes apparent that verifiable storage of the EVM state starts to be one of the dominating costs. This is not surprising because a big differentiator of EVM from UTXO is exactly the ability to carry states and, most importantly, their transitions; i.e., EVM is a **state** machine. In other words, to build an efficient zk-EVM, one must first build an efficient verifiable state. The common approach, which has been used in production, is a Merkle forest to authenticate the memory that would be randomly accessed within zk-SNARK, and optimize the verification of such memory accesses. In this note, we describe a way to instantiate a Merkle tree with very few gates in TurboPlonk. We use customized gates in TurboPlonk to implement a SNARK-friendly hash function called Anemoi and its Jive mode of operation, by Clémence Bouvier, Pierre Briaud, Pyrros Chaidos, Léo Perrin, Robin Salen, Vesselin Velichkov, and Danny Willems. We demonstrate that with $16$ gates ($\approx1$ gate per round in a 14-round Amenoi hash), one can verify a 3-to-1 compression in a 3-ary Merkle tree. Before this, prior implementations would often require hundreds of gates. We anticipate this technique to benefit a large number of applications built off zk-SNARK. Our code can be found in $\mathtt{noah}$: https://github.com/FindoraNetwork/noa

The inspection model for zero-knowledge proofs and efficient Zerocash with secp256k1 keys

Proving discrete log equality for groups of the same order is addressed by Chaum and Pedersen\u27s seminal work. However, there has not been a lot of work in proving discrete log equality for groups of different orders. This paper presents an efficient solution, which leverages a technique we call delegated Schnorr. The discovery of this technique is guided by a design methodology that we call the inspection model, and we find it useful for protocol designs. We show two applications of this technique on the Findora blockchain: **Maxwell-Zerocash switching:** There are two privacy-preserving transfer protocols on the Findora blockchain, one follows the Maxwell construction and uses Pedersen commitments over Ristretto, one follows the Zerocash construction and uses Rescue over BLS12-381. We present an efficient protocol to convert assets between these two constructions while preserving the privacy. **Zerocash with secp256k1 keys:** Bitcoin, Ethereum, and many other chains do signatures on secp256k1. There is a strong need for ZK applications to not depend on special curves like Jubjub, but be compatible with secp256k1. Due to FFT unfriendliness of secp256k1, many proof systems (e.g., Groth16, Plonk, FRI) are infeasible. We present a solution using Bulletproofs over curve secq256k1 ( q ) and delegated Schnorr which connects Bulletproofs to TurboPlonk over BLS12-381. We conclude the paper with (im)possibility results about Zerocash with only access to a deterministic ECDSA signing oracle, which is the case when working with MetaMask. This result shows the limitations of the techniques in this paper. This paper is under a bug bounty program through a grant from Findora Foundation

Building Cryptographic Systems from Distributed Trust

Centralized systems are prone to data breaches, which may come from hackers and malicious or compromised employees inside the company. The scale and prevalence of such data breaches raise concerns from users, companies, and government agencies. In this dissertation, we study how to build systems that distribute centralized trust among many parties, such that the system remains secure as long as at least one of the parties is not compromised. We show how distributed trust can be used to secure systems for storage, machine learning, consensus, and authentication