Notes for chapter 1 (#1)

1. Notes for chapter 1
2. Impl the IP case

.github/workflows/gh-page.yml

@@ -0,0 +1,35 @@
+# CI jobs to be run upon the code lands to the main branch or GitHub Action test branches.
+
+name: ci-post-land
+
+on:
+  push:
+    branches: [main, gha-test-*]
+
+jobs:
+  generate-documentation:
+    name: Generate the Book using mdBook and deploy it to gh-page(deploy-gh-page)
+    runs-on: ubuntu-20.04
+    concurrency:
+      group: ${{ github.workflow }}-${{ github.ref }}
+    steps:
+      - uses: actions/checkout@v3
+        with:
+          ref: main
+
+      - name: Setup mdBook
+        uses: peaceiris/actions-mdbook@v1
+        with:
+          mdbook-version: '0.4.10'
+          # mdbook-version: 'latest'
+
+      - name: install mdbook-katex
+        run: "cargo install mdbook-katex"
+
+      - run: mdbook build book
+
+      - name: Deploy
+        uses: peaceiris/actions-gh-pages@v3
+        with:
+          github_token: ${{ secrets.GITHUB_TOKEN }}
+          publish_dir: ./book/book/

.gitignore

@@ -12,3 +12,6 @@ Cargo.lock
 
 # MSVC Windows builds of rustc generate these, which store debugging information
 *.pdb
+
+.idea
+.vscode

1-ip/Cargo.toml

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+[package]
+name = "ip"
+version = "0.1.0"
+edition = "2021"
+description = "The interactive proofs case(1.2.1) in chapter 1"
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+rand = "0.8.5"
+rand_core = { version = "0.6.4", default-features = false, features = ["std"] }

1-ip/src/lib.rs

@@ -0,0 +1,86 @@
+/// The interactive proofs case(1.2.1) in chapter 1
+mod prover;
+mod utils;
+mod verify;
+
+use rand_core::{OsRng, RngCore};
+use std::iter;
+use std::iter::{once, Sum};
+
+use crate::prover::Prover;
+use crate::utils::{calculate_hash, ComputeType};
+use crate::verify::Verify;
+
+pub(crate) struct Data {
+    name: String,
+    index: u64,
+    data: Vec<u64>,
+}
+
+// Completeness of the IP means that if the cloud correctly runs the program on the data and follows
+// the prescribed protocol, then the user will be convinced to accept the answer as valid.
+#[test]
+fn completeness() {
+    println!("storage data");
+
+    // init business and clouder provider
+    let mut business = Prover::default();
+    let mut cloud_provider = Verify::default();
+
+    // send & receive data
+    let data = business.send();
+    cloud_provider.receive(data.clone());
+    println!("received data\n");
+
+    // challenge and response about data
+    let challenge = OsRng.next_u64() % 100;
+    calculate_hash(&data);
+    assert_eq!(
+        business.summary + challenge,
+        cloud_provider.summary(challenge)
+    );
+    println!("verified equal");
+
+    fn sum(datas: &Vec<u64>) -> u64 {
+        datas.iter().sum()
+    }
+
+    assert_eq!(sum(&data), cloud_provider.compute(sum));
+    println!("completeness");
+}
+
+// Soundness of the IP means that if the cloud returns the wrong output, then the user will reject the answer
+// as invalid with high probability no matter how hard the cloud works to trick the user into accepting the answer as valid.
+#[test]
+fn soundness() {
+    println!("storage datas");
+
+    // init business and clouder provider
+    let mut business = Prover::default();
+    let mut cloud_provider = Verify::default();
+
+    // send & receive data
+    let raw_data = business.send();
+
+    let mut data = raw_data.clone();
+    println!("Add the mess info");
+    data.push(OsRng.next_u64());
+    cloud_provider.receive(data.clone());
+    println!("received datas\n");
+
+    // challenge and response about data
+    let challenge = OsRng.next_u64() % 100;
+    calculate_hash(&data);
+    assert_ne!(
+        business.summary + challenge,
+        cloud_provider.summary(challenge)
+    );
+    println!("verified non equal");
+
+    fn sum(datas: &Vec<u64>) -> u64 {
+        datas.iter().sum()
+    }
+
+    assert_ne!(sum(&raw_data), cloud_provider.compute(sum));
+    println!("Soundness");
+}

1-ip/src/prover.rs

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+use crate::utils::calculate_hash;
+use rand_core::{OsRng, RngCore};
+
+#[derive(Default)]
+pub struct Prover {
+    // hash key of data
+    pub(crate) summary: u64,
+}
+
+impl Prover {
+    pub(crate) fn send(&mut self) -> Vec<u64> {
+        // generate data
+        let data = Self::generate_data();
+        println!("data.size:{:?}", data.len());
+        // obtain key by hash the data
+        self.summary = calculate_hash(&data);
+        // send data
+        data
+    }
+
+    fn generate_data() -> Vec<u64> {
+        let mut rng = OsRng;
+        let size = 5 + rng.next_u32() % 15;
+        (0..size).map(|_| rng.next_u32() as u64).collect::<Vec<_>>()
+    }
+}

1-ip/src/utils.rs

@@ -0,0 +1,13 @@
+use std::collections::hash_map::DefaultHasher;
+use std::hash::{Hash, Hasher};
+
+/// calculate the hash of the data
+pub fn calculate_hash<T: Hash>(t: &T) -> u64 {
+    let mut s = DefaultHasher::new();
+    t.hash(&mut s);
+    s.finish()
+}
+
+pub enum ComputeType {
+    Sum,
+}

1-ip/src/verify.rs

@@ -0,0 +1,20 @@
+use crate::utils::{calculate_hash, ComputeType};
+
+#[derive(Default)]
+pub struct Verify {
+    data: Vec<u64>,
+}
+
+impl Verify {
+    pub(crate) fn receive(&mut self, data: Vec<u64>) {
+        self.data = data;
+    }
+
+    pub(crate) fn summary(&self, challenge: u64) -> u64 {
+        calculate_hash(&self.data) + challenge
+    }
+
+    pub(crate) fn compute(&self, f: fn(&Vec<u64>) -> u64) -> u64 {
+        f(&self.data)
+    }
+}

Cargo.toml

@@ -0,0 +1,4 @@
+[workspace]
+members = [
+    "1-ip",
+]

book/.gitignore

@@ -0,0 +1,2 @@
+/book
+/target

book/README.md

@@ -0,0 +1,14 @@
+
+## Run it locally
+
+* prepare
+```rust
+cargo install mdbook 
+cargo install mdbook-katex 
+cargo install mdbook-plantuml
+```
+
+* run
+```rust
+mdbook serve -o
+```

book/book.toml

@@ -0,0 +1,40 @@
+[book]
+title = "zk book notes"
+description = ""
+authors = ["ChengYueJia"]
+language = "en"
+multilingual = false
+src = "src"
+
+
+[output.html]
+mathjax-support = true
+curly-quotes = true
+no-section-label = true
+git-repository-url = "https://github.com/ChengYueJia/zkbook-notes"
+git-repository-icon = "fa-github"
+
+[output.html.print]
+page-break = true
+
+[output.html.playground]
+editable = true
+line-numbers = true
+
+[output.html.search]
+limit-results = 20
+use-boolean-and = true
+boost-title = 2
+boost-hierarchy = 2
+boost-paragraph = 1
+expand = true
+heading-split-level = 2
+
+[output.html.fold]
+enable = true
+level = 3
+
+# output pdf
+#[output.pdf]
+
+

book/macros.txt

@@ -0,0 +1,65 @@
+\sample:{\overset{?}{\ \gets \ }}
+\GG:{\mathbb{G}}
+\FF:{\mathbb{F}}
+\language:{\mathcal{L}}
+\relation:{\mathcal{R}}
+\witness:{\text{w}}
+\statement:{\text{x}}
+
+\chalfold:{\alpha}
+\chaleval:{\zeta}
+\chalu:{u}
+\chalv:{v}
+
+\openx:{x}
+\openy:{y}
+\comm:{C}
+
+\accCom:{U}
+\accChal:{\chalfold}
+
+\genOpen:{H}
+
+\hpoly:{h}
+
+\relAcc:{\relation_{\mathsf{Acc},\vec{G}}}
+\relPCS:{\relation_{\mathsf{PCD},#1}}
+\relIPA:{\relation_{\mathsf{IPA},#1}}
+
+
+\langPCS:{\language_{\mathsf{PCD},#1}}
+
+\rounds:{k}
+\degree:{d}
+
+\and:{\small \mathsf{AND}}
+\xor:{\small \mathsf{XOR}}
+\inv:{\small \mathsf{INV}}
+
+\sC:{\small \mathsf{C}}
+\sI:{\small \mathsf{I}}
+\sH:{\small \mathsf{H}}
+\sX:{\small \mathsf{X}}
+\sY:{\small \mathsf{Y}}
+
+\S:{\small S}
+\G:{\small G}
+\R:{\small R}
+\T:{\small T}
+
+
+\bF:{\small \mathbb{F}}
+\bG:{\small \mathbb{G}}
+
+
+\lsb:{\small \mathsf{LSB}}
+\sha:{\small\mathsf{SHA}256}
+\aes:{\small \mathsf{AES}}
+\gc:{\small \mathcal{GC}}
+\bit:{\{0,1\}}
+\zero:{\color{red}{0}}
+\one:{\color{blue}{1}}
+\enc:{\small \mathsf{Enc}}
+\gid:{\mathsf{gid}}
+\counter:{\mathsf{counter}}
+\prg:{\small \mathsf{PRG}}