feat: ed25519 digital signature scheme

.codespell-ignore

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

Cargo.toml

@@ -5,13 +5,14 @@ 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"
 
 [dev-dependencies]
 rstest               ="0.24"
@@ -21,6 +22,7 @@ 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"

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() {