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Shirzad et al. proposed a black-box transformation from any PCS to relaxed modular PCS in their paper, applied to integer SNARKs, achieving the first fully succinct proof scheme for integer constraint systems.Shirzad等人在论文中提出了一种从任意PCS构建松弛模块化PCS的黑盒转换方法，并应用于整数SNARK，实现了首个完全简洁的整数约束系统证明方案。
Key Points:要点：
- •Proposed black-box transformation from any PCS to relaxed modular PCS, extending existing techniques提出从任意PCS构建松弛模块化PCS的黑盒转换方法，扩展了现有技术
- •Instantiated with tensor-code PCS for O(log(N+B)) proof size and verification time, transparent and post-quantum secure基于张量码PCS实例化，实现O(log(N+B))证明大小和验证时间，透明且后量子安全
- •Applied in Garetta et al. framework to achieve first fully succinct SNARK for integer customizable constraint systems在Garetta等人框架下应用，获得首个完全简洁的整数自定义约束系统SNARK
- •Prover time O(BlogN + NlogNlogB), verifier time and proof size O(log(N+B))证明者时间O(BlogN + NlogNlogB)，验证者时间和证明大小O(log(N+B))
- •Used commitment-switching technique for integer polynomials and new batched integer commitment scheme采用整数多项式承诺切换技术和新的批处理整数承诺方案
- •Improved arguments for integer addition, multiplication, NTT correctness, and Diophantine relations改进整数加法、乘法、数论变换正确性及丢番图关系的论证
Hollander et al. proposed SPRINT, a polynomial IOP-based isogeny proof of knowledge system in their paper, achieving significant performance improvements with DeepFold PCS and constructing a new signature scheme based on the isogeny path problem.Hollander等人在论文中提出了SPRINT，一种基于多项式IOP的同源知识证明系统，结合DeepFold承诺方案显著提升了同源证明的性能，并构建了基于同源路径问题的新签名方案。
Key Points:要点：
- •SPRINT encodes radical 2-isogeny formulas into multivariate polynomials, combined with DeepFold PCS for efficient proofs.SPRINT将2-同源公式编码为多元多项式系统，结合DeepFold PCS实现高效证明
- •For NIST security level I, proving and verification take only milliseconds with ~80kB proof sizes.在NIST安全级别I下，证明和验证仅需几毫秒，证明大小约80kB
- •Achieves 1.1-8x prover speedup, 4.4-24x verifier speedup, and 1.2-2.3x smaller proofs vs. prior works.相比现有方案，证明速度提升1.1-8倍，验证速度提升4.4-24倍，证明大小减少1.2-2.3倍
- •Studies weak simulation extractability (wSE), enabling modular signature construction.研究了证明系统的弱模拟可提取性，为模块化签名构建提供基础
- •Builds new signature family based solely on the isogeny path problem using SPRINT and wSE.基于SPRINT和wSE结果，构建了仅依赖同源路径问题的新签名方案家族
- •Prototype performance matches optimized SQIsign NIST spec, relies on weaker assumptions with flexible framework.原型实现性能与高度优化的SQIsign NIST规范相当，依赖更弱假设且框架灵活
Benno et al. proposed Jolt Atlas, a zkML framework based on the Jolt proving system, enabling efficient verifiable inference via lookup arguments and ONNX format, supporting streaming proofs in memory-constrained environments.Benno等人在论文中提出了Jolt Atlas，一种基于Jolt证明系统的zkML框架，通过查找参数和ONNX格式实现高效可验证推理，支持内存受限环境下的流式证明。
Key Points:要点：
- •Jolt Atlas extends the Jolt proving system to ONNX tensor operations, simplifying memory consistency verification.Jolt Atlas扩展Jolt证明系统，直接应用于ONNX张量操作，简化内存一致性验证
- •Uses lookup arguments with Sumcheck protocol, well-suited for non-linear functions in modern ML.采用查找参数和Sumcheck协议，特别适合处理现代ML中的非线性函数
- •Optimizes lookup table size via neural teleportation while preserving model accuracy.通过神经传送等技术优化查找表大小，同时保持模型精度
- •Supports streaming proofs in memory-constrained environments, runnable on-device without specialized hardware.支持内存受限环境下的流式证明，无需专用硬件即可在设备上运行
- •Achieves zero-knowledge through BlindFold technique for enhanced privacy.利用BlindFold技术实现零知识属性，增强隐私保护
- •Demonstrates practical proving times for classification, embedding, automated reasoning, and small language models.在分类、嵌入、自动推理和小型语言模型上展示实际证明时间
Wang and Zhang proposed UltraFold, the first distributed BaseFold PCS supporting general polynomials, scaling to any number of workers while maintaining succinct proof size.Wang和Zhang在论文中提出了UltraFold，首个支持通用多项式、可扩展至任意数量工作节点且保持证明简洁性的分布式BaseFold多项式承诺方案。
Key Points:要点：
- •Transparent, code-based PCS like BaseFold are suitable for large-scale ZKPs but limited by single-machine capacity.BaseFold等透明、基于代码的PCS适合大规模ZKP，但单机处理能力有限
- •Existing distributed approaches have limitations: specific polynomial structures, proof size growth with workers, poor scalability.现有分布式方案存在限制：仅支持特定结构多项式、证明大小随工作节点增加、扩展性不足
- •UltraFold uses interleaved Merkle leaf layout for efficient distributed commitment/opening with one all-to-all exchange.UltraFold通过交错Merkle叶布局实现高效分布式承诺和打开，仅需一次部分编码值的全交换
- •Packed Merkle trees reduce hashing overhead, lowering prover time and proof size.采用打包Merkle树减少开销，降低证明者时间和证明大小
- •Evaluation: 256 single-core workers handle 134M-coefficient polynomial in <2s, proof size 216KB.实验显示，256个单核工作节点可在2秒内处理1.34亿系数多项式，证明大小216KB
- •Scheme avoids trusted setup, relies on standard hash assumptions, offers post-quantum security.方案避免可信设置，基于标准哈希假设，提供后量子安全性
Javier Ron and Martin Monperrus propose a zkVM-based approach for software provenance verification in their paper, generating compiled outputs and proofs to ensure secure and verifiable compilation.Javier Ron和Martin Monperrus在论文中提出了一种基于zkVM的软件来源验证方法，通过在zkVM中执行编译器，生成编译输出和证明，确保编译过程的安全性和可验证性。
Key Points:要点：
- •Traditional reproducible builds require matching toolchains and environments, making implementation difficult.传统可复现构建技术依赖工具链和环境匹配，实施困难
- •zkVM compilation executes compilers within zkVMs to produce outputs and cryptographic proofs.zkVM编译方法通过在zkVM中执行编译器，生成编译输出和密码学证明
- •Proofs verify compilation was performed on claimed source code with claimed compiler.证明能验证编译是否在声明的源代码和编译器上执行
- •Proof-of-concept implemented using RISC Zero zkVM and ChibiCC C compiler.使用RISC Zero zkVM和ChibiCC C编译器实现概念验证
- •Evaluated on 200 synthetic programs and real-world software like OpenSSL and libsodium.在200个合成程序及OpenSSL、libsodium等真实软件上评估
- •Successfully blocks adversarial tests including compiler substitution, source tampering, output manipulation, and replay attacks.成功阻止编译器替换、源代码篡改、输出操纵和重放攻击等对抗性测试
Merz and García propose new algebraic attacks on Poseidon2(b) in their paper, exploiting weak matrices and operation modes to significantly improve attack efficiency.Merz和García在论文中提出了针对Poseidon2(b)的新型代数攻击，利用线性层矩阵结构和操作模式弱点，显著提升了攻击效率。
Key Points:要点：
- •Attack exploits specific structure of linear layer matrices in Poseidon2(b), improving round-skipping for CICO problem攻击利用Poseidon2(b)线性层矩阵的特定结构弱点，改进了CICO问题的轮次跳过攻击
- •Direct modeling of algebraic preimage attacks in compression and sponge modes outperforms solving corresponding CICO problem在压缩和海绵模式下直接建模代数原像攻击，攻击效果优于对应CICO问题求解
- •First example where algebraic collision attack outperforms algebraic preimage attack首次展示了代数碰撞攻击优于代数原像攻击的实例
- •Improves over state-of-the-art algebraic collision attacks by factor of 2^106 for some parameters (e.g., 128-bit)对某些推荐参数（如128位）的攻击效率比现有最佳代数碰撞攻击提升2^106倍
- •Primitive still meets claimed security level due to algebraic security margin由于代数安全余量，该攻击未导致原语低于宣称的安全级别
- •Discusses mitigation measures without affecting Poseidon2(b) efficiency论文讨论了不影响Poseidon2(b)效率的缓解措施
Qu et al. proposed Lightning, a coding-based PCS in their paper, using the Lightning code family to significantly improve prover efficiency at the cost of increased proof size.Qu等人在论文中提出了Lightning，一种基于编码的PCS，通过新线性码族Lightning code显著提升证明者效率，以证明大小增加为代价。
Key Points:要点：
- •Lightning is a coding-based PCS for applications like zkSNARKsLightning是一种基于编码的PCS，适用于zkSNARK等应用
- •Key contribution: Lightning code family, instantiable from any base code with constant relative distance核心贡献是Lightning code，可从任何具有恒定相对距离的基码实例化
- •Reduces encoding cost vs. base code by trading off relative distanceLightning code通过牺牲相对距离显著降低编码成本
- •Integrated into Ligero and Brakedown frameworks; experiments show up to 2.7x reduction in prover commitment time集成到Ligero和Brakedown框架，实验显示证明者承诺时间减少达2.7倍
- •Cost: 2.4x increase in proof size, offering a trade-off mechanism代价是证明大小增加2.4倍，提供其与效率的权衡机制
- •Field-agnostic design supports flexible use方案具有域无关性，支持灵活应用
@icerdesign and @ChinnellHeish developed an anonymous prediction market using threshold encryption and ZK proofs to prevent copy-trading and front-running. Featuring browser-native P2P DKG and batch settlement, it won 1st Place in the Mantle Hackathon ZK Track.@icerdesign 和 @ChinnellHeish 开发的匿名预测市场项目，利用阈值加密和ZK证明实现加密投注，防止跟单和抢先交易，包括浏览器原生P2P DKG和批量结算等功能，获得Mantle黑客松ZK赛道第一名。
Key Points:要点：
- •Won 1st Place in the Mantle Hackathon ZK Track获得Mantle黑客松ZK赛道第一名
- •Addresses prediction market transparency by encrypting bets to hide positions and prevent copy-trading and front-running.解决区块链预测市场透明度问题，通过加密隐藏投注位置，防止跟单和抢先交易
- •Uses threshold encryption and ZK proofs to keep betting directions private until settlement.采用阈值加密和ZK证明，确保投注方向在结算前完全保密
- •Implements browser-native P2P DKG without centralized servers for enhanced decentralization and security.实现浏览器原生P2P DKG，无需中心化服务器
- •Employs ephemeral keys to simplify decryption, supporting asynchronous workflows for robustness.使用临时密钥简化解密流程，支持异步解密
- •Reduces gas costs via batch ZK proof settlement, improving efficiency.通过批量ZK证明结算，减少Gas成本，提升效率
Celi et al. analyzed security and privacy issues in zkLogin in their paper, noting it relies on non-cryptographic assumptions like JWT parsing and trust policies, and identified three vulnerability classes.Celi等人在论文中分析了zkLogin系统的安全性和隐私问题，指出其不仅依赖ZKP，还涉及JWT解析、信任策略等非加密假设，并识别了三类漏洞。
Key Points:要点：
- •zkLogin security relies not just on ZKP, but also on JWT parsing and trust policies.zkLogin安全性不能仅简化为底层ZKP，还依赖非加密假设如JWT解析和信任策略
- •Key vulnerabilities: permissive JWT parsing, missing context binding, and centralization risks.漏洞包括：允许畸形JWT的声明提取、短期认证转长期授权时缺乏上下文绑定、集中化和隐私风险
- •Non-cryptographic flaws may lead to impersonation and identity leaks.非加密漏洞可能导致跨应用冒充和用户身份属性泄露
- •System inherits and may amplify web authentication weaknesses.系统继承了Web认证生态的脆弱性，在某些情况下还放大了风险
- •Recommendations: clarify protocol properties, diversify issuers and proving infra.建议加强协议级属性规范和执行，减少对少数发行者和外包证明基础设施的依赖
- •Both cryptographic and non-cryptographic factors are vital for ZKA security.研究强调ZKA系统需全面考虑加密和非加密因素以确保安全
@LayerZero_Core released Zero, a decentralized multi-core world computer using ZK proofs to decouple execution from verification, enabling a heterogeneous architecture with lightweight validators and aiming for 2 million TPS per Zone.@LayerZero_Core 发布了Zero，这是一种去中心化的多核世界计算机，利用ZK证明将执行与验证解耦，实现异构架构，支持轻量级验证器，目标达到每Zone 200万TPS。
Key Points:要点：
- •Claimed to have proven one month of Ethereum blocks in 30s据称在30秒内完成了一个月的以太坊区块验证
- •Zero decouples execution from verification via ZK proofs, eliminating redundant replay.Zero利用ZK证明解耦执行与验证，避免所有验证器重复执行交易
- •Heterogeneous architecture: lightweight validators + high-performance producers using Jolt prover.异构架构：轻量验证器+高性能生产者，使用Jolt证明器
- •Targets 2M TPS per Zone, addressing state storage and parallel compute bottlenecks.目标每Zone 200万TPS，解决状态存储与并行计算瓶颈
- •Atomicity Zones enable horizontally scalable concurrent execution.Atomicity Zones提供水平可扩展的并发执行环境
- •Aims to replace centralized cloud with decentralized infrastructure.旨在提供去中心化基础设施，替代集中式云提供商
Wang et al. proposed the zkAgent system in their paper, enabling verifiable agent execution via one-shot complete LLM inference proofs, significantly improving efficiency and supporting end-to-end verification.Wang等人在论文中提出了zkAgent系统，通过一次性完整LLM推理证明实现可验证的智能体执行，显著提升证明效率并支持端到端验证。
Key Points:要点：
- •First system for verifiable agent execution with full LLM inference and tool interactionszkAgent是首个支持完整LLM推理和工具交互验证的智能体系统
- •One-shot inference proof replaces token-by-token generation for scalable proving一次性推理证明替代逐令牌生成，实现高效可扩展证明
- •294× proving speedup vs zkGPT (1.05s/token vs 309s/token)证明时间比zkGPT快294倍（1.05秒/令牌 vs 309秒/令牌）
- •9690× verification speedup (0.45s vs 4361s)验证时间减少9690倍（0.45秒 vs 4361秒）
- •End-to-end agent proofs in 240s, verification in ~0.5s端到端智能体执行证明仅需240秒，验证约0.5秒
- •42MB proof size enables practical real-world deployment42MB证明大小使可验证智能体执行具备实际部署可行性
Khovratovich et al. proposed a novel hybrid compression method in their paper, enabling the use of two different hash functions in SNARK proofs to optimize both on-chain gas usage and prover time.Khovratovich等人在论文中提出了一种名为混合压缩的新方法，允许在SNARK证明中使用两种不同的哈希函数，以同时优化链上验证的gas消耗和证明生成时间。
Key Points:要点：
- •Long statements in Groth16 are costly; hashing helps but is expensive in contracts or circuitsGroth16中长 statement 成本高，哈希解决方案在合约或电路中开销大
- •Hybrid compression uses two hashes: one circuit-optimized, one for on-chain verification混合压缩方法使用两种哈希：一种优化电路，一种优化链上验证
- •Defined joint UHF hardness and proved it in random oracle model定义联合UHF硬度安全属性，在随机预言机模型中证明合理性
- •Benchmarks show near-optimal gas and prover time基准测试显示gas消耗和证明时间均接近最优
- •8KB statement: 10s prover time, 270K gas vs 290s (SHA-256) or 5M gas (Poseidon)8KB statement 仅需10秒证明和270K gas，优于SHA-256的290秒或Poseidon的5M gas
- •Two-party protocol for cross-hash input equality with efficient communication开发两方协议，高效检查使用不同哈希函数时的输入相等性
Bak et al. analyzed reduced instances of Poseidon and Poseidon2 hash functions in their paper, using a new resultant-based algebraic attack to successfully break multiple challenge instances and claim Ethereum Foundation bounties.Bak等人在论文中分析了Poseidon和Poseidon2哈希函数的简化实例，使用基于结果式（resultant）的新代数攻击方法成功破解多个挑战实例，并获得了以太坊基金会的赏金。
Key Points:要点：
- •Ethereum Foundation issued bounty challenges for Poseidon and Poseidon2 hash functions in Nov 2024以太坊基金会于2024年11月发布针对Poseidon和Poseidon2哈希函数的赏金挑战
- •Team successfully broke multiple reduced instances of Poseidon2-31m, Poseidon2-31k and Poseidon-256研究团队成功破解Poseidon2-31m、Poseidon2-31k和Poseidon-256的多个简化实例
- •Used new resultant-based algebraic attack for Poseidon2 instances对Poseidon2实例使用了基于结果式的新代数攻击方法
- •Used known univariate root finding for Poseidon-256 instances对Poseidon-256实例使用了已知的单变量求根方法
- •All solutions except first Poseidon-256 instance confirmed eligible for bounties除第一个Poseidon-256实例外，其他破解方案均被确认符合赏金条件
- •Research reveals potential security risks in reduced configurations of Poseidon hash functions该研究揭示了Poseidon系列哈希函数在简化配置下的潜在安全风险
Kobeissi analyzes formally verified cryptographic libraries like libcrux and hpke-rs in the paper, highlighting verification boundary issues that allowed multiple security vulnerabilities.Kobeissi在论文中分析了Cryspen的libcrux和hpke-rs等宣称形式化验证的密码库，指出其存在验证边界问题，导致多个安全漏洞被忽略。
Key Points:要点：
- •Formal verification is often marketed as highest assurance but has boundary issues.形式化验证常被宣传为最高安全保证，但实际存在验证边界问题
- •Case study finds five vulnerabilities in Cryspen's libcrux and hpke-rs libraries.案例研究揭示Cryspen的libcrux和hpke-rs库存在五个漏洞
- •Vulnerabilities include SHA-3 output failure, missing X25519 validation, nonce reuse.漏洞包括SHA-3输出失败、X25519验证缺失、nonce重用等
- •Formal verification targets specific properties; needs complementary engineering practices.形式化验证仅针对特定属性，需结合传统工程实践
- •Gap between marketing claims and engineering reality poses systemic risk.营销声称的完整验证与工程现实间的差距构成系统性风险
- •Recommend precise communication of verification scope to avoid security theater.建议精确沟通验证范围，避免形式化验证沦为安全剧场
Nguyen et al. proposed Hachi, a lattice-based multilinear polynomial commitment scheme in their paper, achieving square-root verification time and compact proofs (~55KB) by integrating Greyhound with ring-switching.Nguyen等人在论文中提出了Hachi，一种基于格的多线性多项式承诺方案，通过结合Greyhound与环切换技术，实现了验证时间的平方根复杂度提升和约55KB的紧凑证明。
Key Points:要点：
- •Hachi offers poly(ℓ,λ) proof size and Õ(√2^ℓλ) verifier time for ℓ-variate polynomials under Module-SISHachi基于Module-SIS假设，为ℓ变量多项式提供poly(ℓ,λ)大小的证明和Õ(√2^ℓλ)验证时间
- •Achieves Õ(λ) asymptotic improvement over Greyhound, with 12.5x practical speedup相比当前最优方案Greyhound，验证时间渐进改进Õ(λ)，实际加速达12.5倍
- •Uses sumcheck protocol but addresses bottlenecks in lattice-based constructions采用sumcheck协议优化验证，但标准sumcheck在格构造中存在效率瓶颈
- •Novel integration of Greyhound with ring-switching eliminates R_q multiplications for verifier创新结合Greyhound与环切换技术，使验证器无需在R_q上进行乘法运算
- •Generic reduction converts extension field proofs to cyclotomic ring statements引入通用归约，将扩展域F_{q^k}上的多项式求值证明转换为分圆环R_q上的等价陈述
- •Technique applicable to lattice-based SNARKs for faster verification该技术可独立应用于构建基于格的SNARK，特别适用于实现更快验证
Block et al. proposed a field-agnostic SNARK based on expand-accumulate codes in their paper, addressing the limitation of existing schemes that rely on specific finite fields, with proof generation time as low as 0.23 seconds, two orders of magnitude faster than non-field-agnostic SNARKs.Block等人在论文中提出了一种基于扩展累积码的域无关SNARK，解决了现有方案依赖特定有限域的问题，证明生成时间仅需0.23秒，比非域无关方案快两个数量级。
Key Points:要点：
- •Proposed a field-agnostic SNARK based on expand-accumulate codes, independent of specific finite fields提出基于扩展累积码的域无关SNARK，不依赖特定有限域
- •Key technical contribution: proved these codes have constant rate and relative distance, solving an open problem主要技术贡献：证明这些码具有恒定速率和相对距离，解决先前开放问题
- •Prover time O(M log M), proof size O(√M), with significant concrete efficiency improvements证明者时间为O(M log M)，证明大小为O(√M)，具体效率显著提升
- •ECDSA verification on secp256k1 requires only 0.23s proof generation, 100x faster than non-field-agnostic SNARKsECDSA验证在secp256k1曲线上证明生成仅需0.23秒，比非域无关方案快100倍
- •Compared to Brakedown, proof size reduced by 1.9-2.8x with only 1.2x overhead in prover time相比Brakedown，证明大小减少1.9-2.8倍，证明者时间仅增加1.2倍开销
- •Features transparent setup and plausible post-quantum security, suitable for various practical applications具有透明设置和潜在的后量子安全性，适用于多种实际应用场景
Fu et al. proposed the zkCraft framework in their paper, combining deterministic localization with proof search to detect semantic inconsistencies in ZK circuits, using LLM-guided mutation templates to improve edge-case coverage and reduce solver interaction costs.Fu等人在论文中提出了zkCraft框架，结合确定性定位与证明搜索来检测ZK电路语义不一致，利用LLM引导突变模板提升边缘案例覆盖，减少求解器交互成本。
Key Points:要点：
- •ZK circuits are tricky due to tight witness-constraint coupling, causing subtle bugs.ZK电路因见证计算与约束紧密耦合而难以正确实现，易产生语义不一致
- •zkCraft uses R1CS-aware localization and proof search to catch under/over-constrained issues.zkCraft框架结合确定性R1CS感知定位与证明承载搜索，检测欠约束和过约束故障
- •Row-Vortex polynomials encode edits; Violation IOP replaces repeated solver checks with a proof.将候选约束编辑编码为Row-Vortex多项式，用Violation IOP替代重复求解器查询，提供简洁证明
- •LLM-guided mutations target edge cases, keeping algebraic verification auditable.确定性LLM驱动突变模板偏向探索边缘案例，同时保持可审计的代数验证
- •Tested on Circom, zkCraft finds diverse bugs, lowers false positives and solver costs.在真实Circom代码评估中，证明承载定位检测多种故障，假阳性低，减少求解器交互成本
- •Links formal verification with automated debugging for scalable ZK circuit development.该方法连接形式验证与自动调试，为稳健ZK电路开发提供可扩展路径
@AntoineFONDEUR open-sourced stark-v, a general-purpose zkVM built on Stwo that generates STARK proofs for RISC-V program execution, enabling rapid constraint development.@AntoineFONDEUR 开源了stark-v，这是一个基于Stwo构建的通用zkVM，为RISC-V程序执行生成STARK证明，支持快速约束开发。
Key Points:要点：
- •stark-v is an RV32IM zkVM that generates STARK proofs for RISC-V program execution.stark-v 是一个RV32IM zkVM，为RISC-V程序执行生成STARK证明。
- •Uses declarative macros to generate Stwo AIR components for rapid constraint development.使用声明式宏生成Stwo AIR组件，加速新约束的开发过程。
- •Defines fixed memory layout for program code, input/output, and stack in guest programs.提供内存布局定义，支持固定地址范围的程序代码、输入输出和堆栈。
- •Includes benchmarks measuring proof throughput (kHz) and explores parallelization strategies.包含基准测试，测量证明吞吐量（kHz），并探索并行化策略。
- •Project is a work in progress and not yet ready for production use.项目仍在开发中，暂不建议用于生产环境。
- •Architecture inspired by OpenVM, supports allocators like jemalloc and mimalloc.架构灵感来源于OpenVM，支持多种分配器如jemalloc、mimalloc。