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BUAACTF 2024 Writeup
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简况 得分 8345,总榜第一 攻克数量 35/44 一血 *10,二血 *10,三血 *1 分方向 Misc 10/10,一血 *6,二血 *2 Crypto 8/8,一血 *2,二血 *2,三血 *1 Pwn 5/9 Web 2/6 Reverse 9/10,一血 *1,二血 *6 Blockchain 1/1,一血 *1 感觉又学了好多新玩意( [Web] leaked sec
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Chapter 14 基于离散对数的多项式承诺
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基本定义 这章的核心内容是建立泛用性较强的多项式承诺系统,并介绍若干基于此的协议。 采用常见的多项式承诺的相关记号,考虑对向量 u∈Fnu\in \mathbb{F}^nu∈Fn 构造承诺,之后对任意向量 y∈Fny\in \mathbb{F}^ny∈Fn 生成 ⟨u,v⟩\lang u,v\rang⟨u,v⟩ 的承诺。 若将多项式 q=∑uiXiq=\sum u_iX^iq=∑uiXi 的系数
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<a href="2024/02/13/ProofsArgsAndZK/05-fiatshamir/" target="_self">
Chapter 5 Fiat-Shamir 转化
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在交互式证明系统或论证系统中,V\mathcal{V}V 的掷币结果可向 P\mathcal{P}P 公开,这种协议称为公开掷币(public-coin)协议。不失一般性地,在这种协议中,可以约定 V\mathcal{V}V 向 P\mathcal{P}P 发送的所有信息均为掷币结果。这是因为 V\mathcal{V}V 的算法是确定性的,P\mathcal{P}P 可以自行计算 V\mathca
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<a href="2024/02/12/ProofsArgsAndZK/04c-gkr/" target="_self">
Chapter 4C GKR 协议
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基本定义 GKR 协议是具有较好泛用性的协议。GKR 协议能证明满足一定限制的算术电路 C\mathcal{C}C 的输出。 对于 C={Cn∣n∈N}\mathcal{C}=\{\mathcal{C}_n\mid n\in \mathbb{N}\}C={Cn∣n∈N} 的要求: C\mathcal{C}C 是 log-space uniform 的,这指的是存在一个运行在对数空间内的图灵机
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<a href="2024/02/08/ProofsArgsAndZK/04b-matmulip/" target="_self">
Chapter 4B 矩阵乘法 IP 的应用
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再探三元环计数 对于无向简单图 GGG 的邻接矩阵 A\bm{A}A,GGG 中三元环的数量可表示为 16∑ij(A2)ijAij\cfrac{1}{6}\sum_{ij}(\bm{A}^2)_{ij}\bm{A}_{ij} 61ij∑(A2)ijAij 考虑证明计算结果 6Δ=∑ij(A2)ijAij6\Delta = \sum_{ij}(\bm{A}^2)_{ij}\bm{A}_{ij
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<a href="2024/02/06/ProofsArgsAndZK/04a-sumcheck/" target="_self">
Chapter 4A Sum-Check 协议
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Sum-Check 协议 考虑有限域 F\mathbb{F}F 上的 vvv 元多项式 ggg,其关于每个未定元 xix_ixi 的次数 degig\deg_i gdegig 均满足 degig≤d\deg_i g\le ddegig≤d。Sum-Check 协议的总目标是证明: H≔∑b1∈{0,1}∑b2∈{0,1}⋯∑bv∈{0,1}g(b1,…,bv)H\coloneqq\sum
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<a href="2024/02/06/ProofsArgsAndZK/03-prelim/" target="_self">
Chapter 3 定义与背景知识
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交互式证明 对于映射 f:{0,1}n→Rf:\{0, 1\}^n\to \mathcal{R}f:{0,1}n→R,一个 kkk-消息的交互式证明系统(IP)包含: 一个随机化的 Verifier 算法 V\mathcal{V}V 一个确定性的 Prover 算法 P\mathcal{P}P 交互流程: 公共输入 x∈{0,1}nx\in \{0, 1\}^nx∈{0,1}n P\math
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<a href="2024/02/05/ProofsArgsAndZK/02-randomness/" target="_self">
Chapter 2 随机的力量:数据水印与插值
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Reed-Solomon 水印 Alice / Bob 有串 a,ba, ba,b,希望证明 a=ba=ba=b。确定性策略的通信量下界是 n=∣a∣n=|a|n=∣a∣。 策略 考虑构造随机性策略,从一族哈希函数 H\mathcal{H}H 中选取一个 hhh,我们希望对于 x≠yx\neq yx=y,有: Prh∈H[h(x)=h(y)]≤ε\Pr_{h\in \mathcal{H}}[h
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Zig-zag Perm 的 EGF
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Zig-zag Perm 考虑两项之间的关系分别是增、减、增、减……的 111 到 nnn 的排列,比如 4 8 6 7 5 9 1 3 2。只考虑长度为奇数的排列。数量的前几项是 1,2,16,272,79361,2,16,272,79361,2,16,272,7936。 书说它的 EGF 直接就是 tanz\tan ztanz,太神了,待我看看怎么推的 考虑最大值所在的位置,感觉它好像只能在
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BUAACTF 2023 Writeup
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嗯,分专题地一个个搞总感觉太专业了,我一个业余选手还是按时间顺序以写游记的心态来写吧( 简况 总排名 2/45 赛道排名 1/22 得分 6931 攻克数量 26/41 一血 *5,二血 *3,三血 *4 分方向 Misc 4/8,二血 *1,三血 *1 Crypto 8/8,一血 *3,二血 *1,三血 *2 Pwn 2/7,三血 *1 Web 4/9,一血 *1 Reverse 8/9
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