feat: ed25519 digital signature scheme (#179)

* init: eddsa

* fix lint&spell

* improve code comment and add doc

* fix readme dsa, downgrade anim quality

* fix latex, add bench

* improve keygen algo

* improve doc

* fix doc

* fix doc tex, add sha512

* update spell dict

* mv imgs/gifs to assets, cleanup

* add mdbook and deploy on gh-pages

* fix fmt

* use write_all instead of write

* update readme,book.toml,add desc to create_mdbook

* finalize

* update book.toml

* add sk,pk to struct, generic sha

* remove unused feature

.codespell-ignore

@@ -2,3 +2,4 @@ ronkathon
 crate
 nd
 te
+SHS

.github/workflows/deploy.yml

@@ -0,0 +1,61 @@
+name: Deploy mdBook site to Pages
+
+on:
+  # Runs on pushes targeting the default branch
+  push:
+    branches: ["main"]
+
+  # Allows you to run this workflow manually from the Actions tab
+  workflow_dispatch:
+
+# Sets permissions of the GITHUB_TOKEN to allow deployment to GitHub Pages
+permissions:
+  contents: read
+  pages: write
+  id-token: write
+
+# Allow only one concurrent deployment, skipping runs queued between the run in-progress and latest queued.
+# However, do NOT cancel in-progress runs as we want to allow these production deployments to complete.
+concurrency:
+  group: "pages"
+  cancel-in-progress: false
+
+jobs:
+  # Build job
+  build:
+    runs-on: ubuntu-latest
+    env:
+      MDBOOK_VERSION: 0.4.43
+      MDBOOK_KATEX_VERSION: 0.9.2
+    steps:
+      - uses: actions/checkout@v4
+      - name: Install mdBook
+        run: |
+          curl --proto '=https' --tlsv1.2 https://sh.rustup.rs -sSf -y | sh
+          rustup update
+          cargo install --version ${MDBOOK_VERSION} mdbook
+          cargo install --version ${MDBOOK_KATEX_VERSION} mdbook-katex
+      - name: Setup Pages
+        id: pages
+        uses: actions/configure-pages@v5
+      - name: Build with mdBook
+        run: |
+          cargo run --bin create_mdbook
+          cp -r assets book/
+          mdbook build
+      - name: Upload artifact
+        uses: actions/upload-pages-artifact@v3
+        with:
+          path: ./docs
+
+  # Deployment job
+  deploy:
+    environment:
+      name: github-pages
+      url: ${{ steps.deployment.outputs.page_url }}
+    runs-on: ubuntu-latest
+    needs: build
+    steps:
+      - name: Deploy to GitHub Pages
+        id: deployment
+        uses: actions/deploy-pages@v4

.gitignore

@@ -33,3 +33,9 @@ dump
 
 # coverage files
 lcov.info
+
+# mdbook
+create_mdbook
+book
+mdbook
+docs

Cargo.toml

@@ -5,13 +5,16 @@ edition    ="2021"
 license    ="MIT OR Apache-2.0"
 name       ="ronkathon"
 repository ="https://github.com/pluto/ronkathon"
-version    = "0.1.1"
-exclude    =["CHANGELOG.md", "src/tree/ConstructMerkleTree.gif"]
+version    ="0.1.1"
+exclude    =["CHANGELOG.md", "assets/"]
 
 [dependencies]
-rand     ="0.8"
-itertools="0.14"
-hex      ="0.4"
+rand          ="0.8"
+itertools     ="0.14"
+hex           ="0.4"
+crypto-bigint ="0.6.0-rc.6"
+regex         ="1.11.1"
+num-traits    ="0.2.19"
 
 [dev-dependencies]
 rstest               ="0.24"
@@ -21,6 +24,7 @@ ark-ff               ={ version="0.5", features=["std"] }
 ark-crypto-primitives={ version="0.5", features=["sponge"] }
 des                  ="0.8"
 chacha20             ="0.9"
+hex-literal          ="0.4"
 
 [[bin]]
 name="hmac_sha256_bin"

README.md

@@ -34,9 +34,10 @@ to run example code.
 
 ## Primitives
 
-- [Finite Group](src/field/group.rs)
-- [Fields and Their Extensions](src/field/README.md)
-  - [Binary Fields](src/field/binary_towers/README.md)
+- **Fundamental Algebraic Structures**
+    - [Group](src/algebra/group/README.md)
+    - [Fields and Their Extensions](src/algebra/field/README.md)
+        - [Binary Fields](src/field/binary_towers/README.md)
 - [Curves and Their Pairings](src/curve/README.md)
 - [Polynomials](src/polynomial/mod.rs)
 - [KZG Commitments](src/kzg/README.md)
@@ -46,7 +47,9 @@ to run example code.
 
 ### Signatures
 
-- [Tiny ECDSA](src/ecdsa.rs)
+- [Digital Signature Algorithms](src/dsa/README.md)
+    - [Elliptic Curve Digital Signature Algorithm(ECDSA)](src/dsa/ecdsa.rs)
+    - [Edwards-Curve Digital Signature Algorithm(EdDSA)](src/dsa/eddsa/mod.rs)
 
 ### Encryption
 
@@ -68,10 +71,6 @@ to run example code.
 - [Sha256 Hash](src/hashes/README.md)
 - [Poseidon Hash](src/hashes/poseidon/README.md)
 
-## In Progress
-
-- [ ] Edwards curve Signatures (EdDSA)
-
 ## Resources
 
 We have found the following resources helpful in understanding the foundational mathematics behind this implementation. After going through these, you should be able to understand the codebase

SUMMARY.md

@@ -0,0 +1,22 @@
+- [Introduction](README.md)
+- [Algebra](src/algebra/README.md)
+    - [Field](src/algebra/field/README.md)
+        - [Binary Towers](src/algebra/field/binary_towers/README.md)
+    - [Group](src/algebra/group/README.md)
+- [Codes](src/codes/README.md)
+- [Compiler](src/compiler/README.md)
+- [Curve](src/curve/README.md)
+- [Digital Signature Algorithms](src/dsa/README.md)
+- [Encryption]()
+    - [Asymmetric]()
+        - [RSA](src/encryption/asymmetric/rsa/README.md)
+    - [Symmetric Encryption](src/encryption/symmetric/README.md)
+        - [AES](src/encryption/symmetric/aes/README.md)
+        - [ChaCha](src/encryption/symmetric/chacha/README.md)
+        - [DES](src/encryption/symmetric/des/README.md)
+        - [Modes](src/encryption/symmetric/modes/README.md)
+- [Hashes](src/hashes/README.md)
+    - [Poseidon](src/hashes/poseidon/README.md)
+- [HMAC](src/hmac/README.md)
+- [KZG](src/kzg/README.md)
+- [Merkle Trees](src/tree/README.md)

book.toml

@@ -0,0 +1,20 @@
+[book]
+authors = ["Contributors to Ronkathon"]
+language = "en"
+multilingual = false
+src = "book"
+title = "Ronkathon: Cryptography Educational Foundations"
+description = "Cryptography Educational Foundations"
+
+[build]
+build-dir = "docs"
+use-default-preprocessors = true
+create-missing = true
+
+[preprocessor.katex]
+after = ["links"]
+
+[output.html]
+default-theme = "dark"
+preferred-dark-theme = "coal"
+git-repository-url = "https://github.com/pluto/ronkathon"

examples/eddsa.rs

@@ -0,0 +1,10 @@
+/// Example of Ed25519 digital signature algorithm.
+use ronkathon::dsa::eddsa::Ed25519;
+
+fn main() {
+  let ed25519 = Ed25519::new(None);
+  let msg = b"Hello World";
+
+  let signature = ed25519.sign(msg);
+  assert!(ed25519.verify(msg, signature));
+}

src/algebra/field/binary_towers/README.md

@@ -1,6 +1,6 @@
 ## Binary Fields
 
-[Binary fields](https://en.wikipedia.org/wiki/GF%282%29) denoted as $GF(2)=Z/2Z$, i.e. quotient ring of integers modulo ring of 2 integers $\{0,1\}, are a special class of Finite Fields, with modulus = $2$. Main properties exhibited by Binary fields are:
+[Binary fields](https://en.wikipedia.org/wiki/GF%282%29) denoted as $GF(2)=Z/2Z$, i.e. quotient ring of integers modulo ring of 2 integers $\{0,1\}$, are a special class of Finite Fields, with modulus = $2$. Main properties exhibited by Binary fields are:
 - Addition corresponds to bitwise XOR
 - Multiplication corresponds to bitwise AND
 - since, $x+x=0\implies x=-x$, i.e. negation of a number is itself
@@ -50,4 +50,4 @@ A very nice property of binary fields is defining an element using it's subfield
 - Addition, Subtraction is just bitwise XOR
 - Negation is the element itself
 - Multiplication is done using a hybrid of Karatsuba multiplication
-- Inversion is $x^{(p-2)}$, using Fermat's little theorem
+- Inversion is $x^{(p-2)}$, using Fermat's little theorem

src/bin/create_mdbook.rs

@@ -0,0 +1,63 @@
+/// Read SUMMARY.md and copy `README.md` files given in it to `book` directory.
+/// Additionally, change the links to other `README.md` files to `index.md`, so that link
+/// points to correct file in the mdbook.
+use std::{
+  fs::{self, File},
+  io::{self, BufRead, BufReader, Write},
+  path::{Path, PathBuf},
+};
+
+use regex::Regex;
+
+const DEST: &str = "book";
+
+fn main() -> io::Result<()> {
+  let dest_path = Path::new(DEST);
+  if !dest_path.exists() {
+    fs::create_dir(dest_path)?;
+  }
+
+  let mut readmes = Vec::<PathBuf>::new();
+  let f = File::open("SUMMARY.md")?;
+  let reader = BufReader::new(f);
+
+  let re = Regex::new(r"\[.*\]\((.*)\)").unwrap();
+
+  for line in reader.lines() {
+    for (_, [link]) in re.captures_iter(&line?).map(|c| c.extract()) {
+      if !link.is_empty() {
+        readmes.push(PathBuf::from(link));
+      }
+    }
+  }
+
+  let readme_re = Regex::new(r"README.md").unwrap();
+
+  for src in &readmes {
+    println!("Working on: {}", src.display());
+
+    let dest = Path::new(DEST).join(src);
+    let dest_folder = dest.parent().unwrap();
+    if !dest_folder.exists() {
+      fs::create_dir_all(dest_folder)?;
+    }
+    let src_file = File::open(src)?;
+    let reader = BufReader::new(src_file);
+
+    let mut dest_file = File::create(&dest)?;
+
+    for line in reader.lines() {
+      let before = line.unwrap();
+      let after = readme_re.replace_all(&before, "index.md");
+      dest_file.write_all(after.as_bytes())?;
+      dest_file.write_all(b"\n")?;
+    }
+  }
+
+  println!("Copying SUMMARY.md to {DEST}/SUMMARY.md");
+  fs::copy("SUMMARY.md", "book/SUMMARY.md")?;
+
+  println!("Done!");
+
+  Ok(())
+}

src/dsa/README.md

@@ -0,0 +1,51 @@
+# Digital Signature Algorithms (DSA)
+
+### What are digital signatures?
+
+Like its name, **Digital Signatures** are digital analogs of physical signatures. For example, when you want to write a cheque you have to "sign" it for authentication purposes. But think about how you would do the same over the internet. 
+Here is where **Digital Signatures** come into the picture. 
+
+**Digital Signatures** have the following properties:
+1. **Authenticity**: Just like physical signatures, digital signatures provide a way to verify the identity of a signer.
+2. **Integrity**: Digital signatures provide a mechanism to detect unauthorized modification to a message.
+3. **Non-repudiation**: Digital signatures have a nice property that once a signer signs a message, they cannot deny having done so.
+
+### How does a digital signature scheme look like?
+
+Digital signature schemes consists of three algorithms $\text{Gen, Sign, Verify}$, such that:
+
+1. The key generation algorithm, $\text{Gen}$ which takes in the security parameter $n$ and outputs public key, $\text{pk}$ and private key, $\text{sk}$.
+2. The signing algorithm $\text{Sign}$ takes as input the keys and a message and outputs a signature.
+3. The verification algorithm $\text{Verify}$, takes as input the public key, a message, and a signature. 
+It outputs bit 1 if the signature is valid for the given message and public key, otherwise 0.
+
+### How is a digital signature scheme used?
+
+To explain how digital signature schemes are used, let's take the example of two people, Bobby and Alex.
+Bobby is the one whose signature is required, so Bobby will run the $\text{Gen(n)}$ algorithm to obtain, $\text{pk, sk}$. 
+Then, the public key, $\text{pk}$, is publicized as belonging to Bobby. This not only provides authentication but also ensures non-repudiation. This one of the critical parts of a secure digital signature scheme. 
+You can read more on this here: [Public key infrastructure](https://en.wikipedia.org/wiki/Public_key_infrastructure)
+
+![](../../assets/keygen.gif)
+
+Now when Alex sends a message(document, contract, etc.), $m$, for Bobby to sign, they compute the signature, $s$ as, $s\leftarrow\text{Sign(sk,m)}$ and sents $s$ to Alex or any other party who wants to take a look.
+Now, any party who wants to see if Bobby signed the document or not, applies the verification algorithm using the public key as $\text{Verify(pk,m,s)}$. Thus Alex or any other party can be sure of the authenicity of
+the signature as well as the integrity of the message.
+
+![](../../assets/sign_and_verify.gif)
+
+### When is a signature scheme said to be secure?
+
+A digital signature scheme is said to be secure if an adversary is unable to generate a forgery, that is, a message (not previously signed) and a valid signature for a fixed public key, in any case.
+
+### Examples of digital signature scheme
+
+1. Elliptic Curve Digital Signature Scheme(ECDSA)
+2. Edwards-Curve Digital Signature Scheme(EdDSA)
+
+## References
+
+1. "Introduction to Modern Cryptography" by Jonathan Katz and Yehuda Lindell
+2. [Digital Signatures](https://asecuritysite.com/signatures)
+
+

src/ecdsa.rs → src/dsa/ecdsa.rs

@@ -1,10 +1,8 @@
 //! ECDSA signature verification
 use std::hash::{DefaultHasher, Hasher};
 
-use algebra::field::FiniteField;
-use curve::CurveGroup;
-
 use super::*;
+use crate::{algebra::field::FiniteField, curve::CurveGroup};
 
 // PARAMETERS
 // *******************************************
@@ -118,9 +116,8 @@ fn hash_and_extract_bits<F: Field>(m: &[u8], bit_count: usize) -> F {
 
 #[cfg(test)]
 mod tests {
-  use algebra::{field::prime::PlutoScalarField, group::FiniteCyclicGroup, Finite};
-
   use super::*;
+  use crate::algebra::{field::prime::PlutoScalarField, group::FiniteCyclicGroup, Finite};
 
   #[test]
   fn test_sign_verify() {