Hua Lu, Jack Peterson
Verifiable secret sharing (VSS) is designed to allow parties to collaborate to keep secrets. We describe here a method of fabricating false secret shares that appear to other parties to be legitimate, which can prevent assembly of the decryption key. This vulnerability affects VSS schemes using verification commitments bounded to a finite field.
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This note provides an introduction to the PPATS Commitment Consistent Encryption (CCE) scheme proposed by Cuvelier, Pereira and Peters and its use in the design of end-to-end verifiable elections with a perfectly private audit trail. These elections can be verified using audit data that will never leak any information about the vote, even if all the private keys of the elections are compromised, or if the cryptographic assumptions are broken.
Threshold secret sharing schemes do not prevent any malicious behavior of the dealer or shareholders and so we need verifiable secret sharing, to detect and identify the cheaters, to achieve fair reconstruction of a secret. The problem of verifiable secret sharing is to verify the shares distributed by the dealer. A novel approach for verifiable secret sharing is presented in this paper where both the dealer and shareholders are not assumed to be honest. In this paper, we extend the term verifiable secret sharing to verify the shares, distributed by a dealer as well as shares submitted by shar…
In the $\left( {t,n} \right)$ threshold quantum secret sharing scheme, it is difficult to ensure that internal participants are honest. In this paper, a verifiable $\left( {t,n} \right)$ threshold quantum secret sharing scheme is designed combined with classical secret sharing scheme. First of all, the distributor uses the asymmetric binary polynomials to generate the shares and sends them to each participant. Secondly, the distributor sends the initial quantum state with the secret to the first participant, and each participant performs unitary operation that using the mutually unbiased bases…
To detect frauds from some internal participants or external attackers, some verifiable threshold quantum secret sharing schemes have been proposed. In this paper, we present a new verifiable threshold structure based on a single qubit using bivariate polynomial. First, Alice chooses an asymmetric bivariate polynomial and sends a pair of values from this polynomial to each participant. Then Alice and participants implement in sequence unitary transformation on the $d$-dimensional quantum state based on unbiased bases, where those unitary transformations are contacted by this polynomial. Finall…
In this work we present hbAVSS, the Honey Badger of Asynchronous Verifiable Secret Sharing (AVSS) protocols - an AVSS protocol that guarantees linear amortized communication overhead even in the worst case. The best prior work can achieve linear overhead only at a suboptimal resilience level (t < n/4) or by relying on optimism (falling back to quadratic overhead in case of network asynchrony or Byzantine faults). Our protocol therefore closes this gap, showing that linear communication overhead is possible without these compromises. The main idea behind our protocol is what we call the encrypt…
This paper introduces a new way to incorporate verifiable secret sharing (VSS) schemes into Byzantine Fault Tolerance (BFT) protocols. This technique extends the threshold guarantee of classical Byzantine Fault Tolerant algorithms to include privacy as well. This provides applications with a powerful primitive: a threshold trusted third party, which simplifies many difficult problems such as a fair exchange. In order to incorporate VSS into BFT, we introduced sAVSS, a framework that transforms any VSS scheme into an asynchronous VSS scheme with constant overhead. By incorporating Kate et al.'s…
In his paper Stadler develops techniques for improving the security of existing secret sharing protocols by allowing to check whether the secret shares given out by the dealer are valid. In particular, the secret sharing is executed over abelian groups. In this paper we develop similar methods over non-abelian groups.
Verifiable Weighted Secret Sharing
针对现有加权秘密共享（WSS）无法抵御恶意分发者的问题，本文提出首个兼容基于CRT的WSS的高效可验证方案，利用Bulletproofs和隐私保护技术实现高效验证，在Ethereum上通信复杂度较现有设计提升达100倍。
Secret sharing allows split/distributed control over the secret (e.g. master key). Verifiable secret sharing (VSS) is the secret sharing extended by verification capacity. Usually verification comes at the price. We propose "free lunch", the approach that allows to overcome this inconvenience.
Proof in a Bottle: Long-Lived Verifiable Secret Sharing via Pre-Quantum Commitment and Immutable Ledger Binding
研究传统可验证秘密共享技术易受量子攻击的问题，提出瓶中证明（PiB）方法，通过解耦可验证性与长期绑定，利用Pedersen承诺和不可变账本哈希，保护诚实交易免受量子对手攻击。
We address the problem of efficiently verifying a commitment in a two-party computation. This addresses the scenario where a party P1 commits to a value $x$ to be used in a subsequent secure computation with another party P2 that wants to receive assurance that P1 did not cheat, i.e. that $x$ was indeed the value inputted into the secure computation. Our constructions operate in the publicly verifiable covert (PVC) security model, which is a relaxation of the malicious model of MPC appropriate in settings where P1 faces a reputational harm if caught cheating. We introduce the notion of PVC com…
A verifiable multi-secret sharing (VMSS) scheme enables the dealer to share multiple secrets, and the deception of both participants and the dealer can be detected. After analyzing the security of VMSS schemes proposed by Mashhadi and Dehkordi in 2015, we illustrate that they cannot detect some deception of the dealer. By using nonhomogeneous linear recursion and LFSR public key cryptosystem, we introduce two new VMSS schemes. Our schemes can not only overcome the drawback mentioned above, but also have shorter private/public key length at the same safety level. Besides, our schemes have dynam…
BioZero: Privacy-Preserving and Publicly Verifiable On-Chain Biometric Authentication via Homomorphic Commitments and Zero-Knowledge Proofs
BioZero通过同态承诺和零知识证明实现去中心化身份系统中隐私保护的生物识别认证，支持链上公开验证，降低网络调整总认证延迟并提升证明效率。
Preserving data confidentiality in clouds is a key issue. Secret Sharing, a cryptographic primitive for the distribution of a secret among a group of $n$ participants designed so that only subsets of shareholders of cardinality $0 < t \leq n$ are allowed to reconstruct the secret by pooling their shares, can help mitigating and minimizing the problem. A desirable feature of Secret Sharing schemes is cheater detection, i.e. the ability to detect one or more malicious shareholders trying to reconstruct the secret by obtaining legal shares from the other shareholders while providing them with fak…
Publicly Verifiable Private Information Retrieval Protocols Based on Function Secret Sharing
本研究提出两种多服务器环境下的公开可验证PIR构造及三种实例化，在点查询中实现低通信成本与强可验证性，在谓词查询中通信复杂度不随数据库规模增长，适用于大规模私有查询。
EByFTVeS: Efficient Byzantine Fault Tolerant-based Verifiable Secret-sharing in Distributed Privacy-preserving Machine Learning
本文提出EByFTVeS方案，通过自适应份额延迟提供策略和定制模型污染攻击，提升分布式隐私保护机器学习中可验证秘密共享的效率和一致性。
We propose an adaptive threshold multi secret sharing scheme based solely on cryptographically secure hash functions. We show that the proposed scheme is also: perfect, ideal, verifiable, and proactive. Moreover the proposed scheme has a low computational complexity comparing to the most common schemes operating over finite fields.
Commitments are equivalent to statistically-verifiable one-way state generators
本文证明 O(n/log n) 份统计可验证单向态生成器等价于量子承诺，并给出受经典 OWF 到 PRG 构造启发但更简单的新构造。
We describe new unconditionally secure bit commitment schemes whose security is based on Minkowski causality and the monogamy of quantum entanglement. We first describe an ideal scheme that is purely deterministic, in the sense that neither party needs to generate any secret randomness at any stage. We also describe a variant that allows the committer to proceed deterministically, requires only local randomness generation from the receiver, and allows the commitment to be verified in the neighbourhood of the unveiling point. We show that these schemes still offer near-perfect security in the p…
In the paper we apply graph vertex coloring for verification of secret shares. We start from showing how to convert any graph into the number and vice versa. Next, theoretical result concerning properties of n-colorable graphs is stated and proven. From this result we derive graph coloring check-digit scheme. Feasibility of proposed scheme increases with the size of the number, which digits are checked and overall probability of errors. The check-digit scheme is used to build shares verification method that does not require cooperation of the third party. It allows implementing verification st…
Secret sharing was proposed primarily in 1979 to solve the problem of key distribution. In recent decades, researchers have proposed many improvement schemes. Among all these schemes, the verifiable multi-secret sharing (VMSS) schemes are studied sufficiently, which share multiple secrets simultaneously and perceive malicious dealer as well as participants. By pointing out that the schemes presented by Dehkordi and Mashhadi in 2008 cannot detect some vicious behaviors of the dealer, we propose two new VMSS schemes by adding validity check in the verification phase to overcome this drawback. Ou…
Verifiable Secret-Sharing (VSS) is a fundamental primitive in secure distributed computing. It is used as a building block in several distributed computing tasks, such as Byzantine agreement and secure multi-party computation. In this article, we consider VSS schemes with perfect security, tolerating computationally unbounded adversaries. We comprehensively survey the existing perfectly-secure VSS schemes in three different communication settings, namely synchronous, asynchronous and hybrid setting and provide full details of the existing schemes in these settings. The aim of this survey is to…
Homomorphic secret sharing (HSS) allows multiple input clients to secret-share their data among multiple servers such that each server is able to locally compute a function on its shares to obtain a partial result and all partial results enable the reconstruction of the function's value on the outsourced data by an output client. The existing HSS schemes for {\em high-degree} polynomials either {\em require a large number of servers} or {\em lack verifiability}, which is essential for ensuring the correctness of the outsourced computations. In this paper, we propose a two-server verifiable HSS…
Holding Secrets Accountable: Auditing Privacy-Preserving Machine Learning
本文提出用于审计隐私保护机器学习的MPC框架Arc，其核心协议能高效验证MPC输入，性能比现有方法快达10^4倍且简洁达10^6倍。
Secret sharing schemes create an effective method to safeguard a secret by dividing it among several participants. By using hash functions and the herding hashes technique, we first set up a (t+1, n) threshold scheme which is perfect and ideal, and then extend it to schemes for any general access structure. The schemes can be further set up as proactive or verifiable if necessary. The setup and recovery of the secret is efficient due to the fast calculation of the hash function. The proposed scheme is flexible because of the use of existing hash functions.
Secret sharing allows distributing a secret among several parties such that only authorized subsets, specified by an access structure, can reconstruct the secret. Sehrawat and Desmedt (COCOON 2020) introduced hidden access structures, that remain secret until some authorized subset of parties collaborate. However, their scheme assumes semi-honest parties and supports only restricted access structures. We address these shortcomings by constructing an access structure hiding verifiable secret sharing scheme that supports all monotone access structures. It is the first secret sharing scheme to su…
Publicly Verifiable Secret Sharing: Generic Constructions and Lattice-Based Instantiations in the Standard Model
针对现有PVSS协议依赖随机预言机模型或量子脆弱假设的问题，提出标准模型下基于LWE假设的通用构造，实现首个后量子PVSS并保证合理渐近效率。
ByzSecAgg: A Byzantine-Resistant Secure Aggregation Scheme for Federated Learning Based on Coded Computing and Vector Commitment
本文提出ByzSecAgg方案，通过ramp秘密共享、编码计算和向量承诺实现联邦学习中抗拜占庭攻击且保护隐私的高效安全聚合，通信负载显著优于基线方案BREA。
MerkleSpeech: Public-Key Verifiable, Chunk-Localised Speech Provenance via Perceptual Fingerprints and Merkle Commitments
MerkleSpeech通过感知指纹和梅尔克承诺实现公钥可验证的语音来源证明，提供两个层级的保证，以应对语音处理中的各种转换和干扰。
Despite exciting progress on cryptography, secure and efficient query processing over outsourced data remains an open challenge. We develop a communication-efficient and information-theoretically secure system, entitled Obscure for aggregation queries with conjunctive or disjunctive predicates, using secret-sharing. Obscure is strongly secure (i.e., secure regardless of the computational-capabilities of an adversary) and prevents the network, as well as, the (adversarial) servers to learn the user's queries, results, or the database. In addition, Obscure provides additional security features, …
Publicly verifiable delegative democracy with secret voting power
本研究提出一种基于Merkle树的承诺方案，在保护公民隐私的前提下实现投票权转移与可逆委托的公开验证，明确了委托、转移、撤销及投票各环节的操作规则。
In recent years, the confidentiality of smart contracts has become a fundamental requirement for practical applications. While many efforts have been made to develop architectural capabilities for enforcing confidential smart contracts, a few works arise to extend confidential smart contracts to Multi-Party Computation (MPC), i.e., multiple parties jointly evaluate a transaction off-chain and commit the outputs on-chain without revealing their secret inputs/outputs to each other. However, existing solutions lack public verifiability and require O(n) transactions to enable negotiation or resist…
This paper proposes Prism, a secret sharing based approach to compute private set operations (i.e., intersection and union), as well as aggregates over outsourced databases belonging to multiple owners. Prism enables data owners to pre-load the data onto non-colluding servers and exploits the additive and multiplicative properties of secret-shares to compute the above-listed operations in (at most) two rounds of communication between the servers (storing the secret-shares) and the querier, resulting in a very efficient implementation. Also, Prism does not require communication among the server…
The problem of obtaining secret commitments from multiple parties and revealing them after a certain time is useful for sealed-bid auctions, games, and other applications. Existing solutions, dating back to Rivest, Shamir and Wagner, either do not scale or rely on synchrony for the commitment phase and trust of $t/n$ parties. We formalize the problem of implementing such commitments with a probabilistic delay and without the aforementioned assumptions as Multi-Party Timed Commitments (MPTC) and present a solution -- the Time-Capsule protocol. Like previous approaches, Time Capsule forms a puzz…
Pivot: Proactive and Verifiable Threshold Oblivious Pseudorandom Functions From Isogeny Group Actions
本文提出基于同构群作用的主动可验证阈值不经意伪随机函数PIVOT，解决现有同构阈值OPRF易受移动攻击的问题，支持密钥份额刷新等功能，保障长期安全并实现分布式私有查找服务。
It is well-known that the linear secret-sharing scheme (LSSS) can be constructed from linear error-correcting codes (Brickell [1], R.J. McEliece and D.V.Sarwate [2],Cramer, el.,[3]). The theory of linear codes from algebraic-geometric curves (algebraic-geometric (AG) codes or geometric Goppa code) has been well-developed since the work of V.Goppa and Tsfasman, Vladut, and Zink(see [17], [18] and [19]). In this paper the linear secret-sharing scheme from algebraic-geometric codes, which are non-threshold scheme for curves of genus greater than 0, are presented . We analysis the minimal access s…
Non-malleable secret sharing was recently proposed by Goyal and Kumar in independent tampering and joint tampering models for threshold secret sharing (STOC18) and secret sharing with general access structure (CRYPTO18). The idea of making secret sharing non-malleable received great attention and by now has generated many papers exploring new frontiers in this topic, such as multiple-time tampering and adding leakage resiliency to the one-shot tampering model. Non-compartmentalized tampering model was first studied by Agrawal et.al (CRYPTO15) for non-malleability against permutation composed w…
Secret sharing was firstly proposed in 1979 by Shamir and Blakley respectively. To avoid deficiencies of original schemes, researchers presented improvement schemes, among which the multi-secret sharing scheme (MSS) is significant. There are three categories of MSSs, however, we focus on multi-stage secret sharing scheme (MSSS) recovering secrets with any order in this work. By observing inhomogeneous linear recursions (ILRs) in the literature, we conclude a general formula and divide ILRs into two types according to different variables in them. Utilizing these two kinds of ILRs, we propose fo…
Blind quantum computation protocols allow a user with limited quantum technology to delegate an intractable computation to a quantum server while keeping the computation perfectly secret. Whereas in some protocols a user can verify that calculated outcomes are correct, a third party cannot do this, which allows a dishonest user or owner to benefit illegally. I propose a new blind quantum computation protocol with a new property called public verifiability, which enables any third party to assure that a party does not benefit from attempted deception.
Verifiable Data Sharing Scheme for Dynamic Multi-Owner Setting
针对动态多所有者文件共享中依赖第三方及签名流程复杂的问题，提出可验证数据共享方案VDS-DM，结合线性秘密共享与聚合技术实现无第三方签名更新与独立验证，实验证明其可行且节省开销。
VeriSBOM: Secure and Verifiable SBOM Sharing Via Zero-Knowledge Proofs
VeriSBOM通过零知识证明实现安全且可验证的SBOM共享，保护知识产权并确保合规性。
In this paper, we present a very important primitive called Information Checking Protocol (ICP) which plays an important role in constructing statistical Verifiable Secret Sharing (VSS) and Weak Secret Sharing (WSS) protocols. Informally, ICP is a tool for authenticating messages in the presence of computationally unbounded corrupted parties. Here we extend the basic bare-bone definition of ICP, introduced by Rabin et al. and then present an ICP that attains the best communication complexity and round complexity among all the existing ICPs in the literature. We also show that our ICP satisfies…
Seal, Then Sample: Sampled Layerwise Proofs for Verifiable LLM Inference from GPT-2 to 70B
提出分层采样证明（SLP）协议，通过承诺边界激活并仅证明验证者选定的块子集，实现从 GPT-2 到 70B 模型的可验证 LLM 推理，显著降低证明成本与时间。
It is a standard result in the theory of quantum error-correcting codes that no code of length n can fix more than n/4 arbitrary errors, regardless of the dimension of the coding and encoded Hilbert spaces. However, this bound only applies to codes which recover the message exactly. Naively, one might expect that correcting errors to very high fidelity would only allow small violations of this bound. This intuition is incorrect: in this paper we describe quantum error-correcting codes capable of correcting up to (n-1)/2 arbitrary errors with fidelity exponentially close to 1, at the price of i…
UC-Secure Star DKG for Non-Exportable Key Shares with VSS-Free Enforcement
本文提出一种UC安全的星形DKG方案，适用于多设备阈值钱包，实现1+1-out-of-n的星形访问结构，通过结合KeyBox保密性、USV验证和Fischlin-based UC可提取NIZK论证，在gRO-CRP模型下实现 transcript驱动的改进。
A Publicly Verifiable Secret Sharing (PVSS) scheme allows anyone to verify the validity of the shares computed and distributed by a dealer. The idea of PVSS was introduced by Stadler in [18] where he presented a PVSS scheme based on Discrete Logarithm. Later, several PVSS schemes were proposed. In [2], Behnad and Eghlidos present an interesting PVSS scheme with explicit membership and disputation processes. In this paper, we present a new PVSS having the advantage of being simpler while offering the same features.
Learning from data owned by several parties, as in federated learning, raises challenges regarding the privacy guarantees provided to participants and the correctness of the computation in the presence of malicious parties. We tackle these challenges in the context of distributed averaging, an essential building block of federated learning algorithms. Our first contribution is a scalable protocol in which participants exchange correlated Gaussian noise along the edges of a network graph, complemented by independent noise added by each party. We analyze the differential privacy guarantees of ou…
Trustless Audits without Revealing Data or Models
针对模型与数据保密和算法审计之间的冲突，本文提出 ZkAudit 协议，用密码学承诺与零知识证明在不泄露权重和数据的情况下验证训练及审计函数执行。
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