1. Core Principles of Digital Signatures

Digital signatures rely on Asymmetric Cryptography (Public Key Infrastructure or PKI).

Key Benefits (What it Guarantees)

• Authentication: Proves the identity of the signatory (sender). Since only the sender possesses the private key, the signature must originate from them.
• Integrity: Guarantees that the signed message or document has not been altered since it was signed.
• Non-Repudiation: Prevents the sender from successfully denying they sent the message, as their private key was used to create the unique signature.

Cryptographic Components

• Private Key: Used by the sender (signer) to create the digital signature. It must be kept secret.
• Public Key: Used by the receiver to verify the digital signature. It is openly shared.
• Hash Function (e.g., SHA-256): A mathematical algorithm that generates a fixed-length string (the "hash" or "message digest") from any input message. This hash is unique to the content.

2. How a Digital Signature is Created and Verified

A. Creation (Signing the Document)

1. 1
   Hash Generation: The original document/message is run through a hash function, creating a unique, short Message Digest ($H$).
2. 2
   Signature Creation: The Message Digest ($H$) is encrypted using the sender's Private Key. The result is the **Digital Signature** ($S$).
3. 3
   Transmission: The original document, along with the newly created Digital Signature ($S$), is sent to the receiver.

B. Verification (Validating the Signature)

1. 4
   Signature Decryption: The receiver uses the sender's Public Key to decrypt the received Digital Signature ($S$), which yields the original Message Digest ($H_{sent}$).
2. 5
   Local Hash Generation: The receiver runs the received original document through the *exact same* hash function to create a new local hash ($H_{local}$).
3. 6
   Comparison: The receiver compares the decrypted digest ($H_{sent}$) with the locally generated digest ($H_{local}$).

   • If $H_{sent} = H_{local}$: The signature is valid (integrity and authenticity confirmed).
   • If $H_{sent} \neq H_{local}$: The message was either tampered with, or the wrong private key was used to sign it (signature is invalid).