# Digital Signatures Protocol
To explain how digital signatures work, let’s imagine two parties:
* **Alice** (the signer)
* **Bob** (the verifier)
The process follows three main steps: **Key Generation, Signing, and Verification**.
***
### Step 1 – Generating a Key Pair
Alice begins by creating an **asymmetric key pair**:
* A **private key (k****pr****)** – kept secret, used for signing.
* A **public key (k****pub****)** – shared openly, used for verification.
**Key properties:**
1. The keys are **mathematically related**. Bob can verify a signature created with kpr using kpub.
2. It is **easy** to derive kpub from kpr, but **computationally infeasible** to derive kpr from kpub.
3. Keeping kₚᵣ secret ensures **authentication** and **non-repudiation**.
4. Public keys can be published in **registries** (e.g., websites) to link them with an identity.
***
### Step 2 – Signing
When Alice wants to sign a document:
* Inputs: the **message (x)** and Alice’s **private key (kₚᵣ)**.
* The signing algorithm outputs the **digital signature (y)**.
**Notes:**
* A “message” can be text, bytes, or hex.
* In practice, the message is first processed with a **hash function**. This produces a fixed-length digest, making signing more efficient and secure.
* Some digital signature schemes automatically include hashing in the signing process.
***
### Step 3 – Verification
When Bob receives Alice’s message and signature:
* Inputs: **message (x)**, **signature (y)**, and Alice’s **public key (k****pub****)**.
* The verification algorithm checks the signature’s validity.
* Output:
* **True (1)** if valid
* **False (0)** if invalid
***
### End-to-End Protocol
1. Alice generates kₚᵣ and kₚᵤb.
2. She shares **k****pub** with Bob (via a registry or direct communication).
3. Alice signs the **message (x)** with **k****pr**, producing signature **(y)**.
4. She sends **x** and **y** to Bob.
5. Bob verifies them using **k****pub**.
6. The algorithm returns **True/False**.
***
### What Happens Behind the Scenes
The specific details of key generation, signing, and verification depend on the cryptographic scheme used, such as:
* **RSA**
* **ECDSA**
These define the mathematics behind how kpr and kₚᵤᵦ are created and applied.
***
### Key Takeaway
The **Digital Signatures Protocol** enables Alice to prove authorship of a message with her **private key (k****pr****)**, while Bob—or anyone with access to her **public key (k****pub****.)**—can verify it, ensuring trust without ever exposing the private key.
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