==== Digital Signature Using Hash Functions ====

A hash function acts like a **digital fingerprint** for a document. The function ensures that the hash code is varied enough for any given document. But how does digital signing work with this process?

Steps:

1. **Compute the hash**: Calculate \( y = H(x) \) for a document \( x \). This creates a unique "fingerprint" of the document.

2. **Encrypt the hash**: Use the **private key** to encrypt the hash \( y \).

3. **Attach the result**: The encrypted hash is attached to the document as the **signature**.

=== Consequences ===

  * The signed document remains readable.
  * The signature can be stored separately from the document, for example, at a notary or in a database.

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During **network communication**, the following data is transmitted:

1. The **original document**.

2. The **hash of the document**, encrypted with the sender's private key.

3. The sender’s **public key**.

=== How to Verify the Integrity of the Signature ===

1. **Calculate the hash** of the received document.

2. **Decrypt the encrypted hash** using the sender’s public key.

3. Compare the two hash codes. If they match, the document's integrity is intact.

This process ensures that the document has not been tampered with and that the signature is valid.