Hash function: First, a hash function is applied to the digital data or document. A hash function is a mathematical algorithm that takes an input of any length and produces a fixed-length output called a hash value or digest. This hash value is a unique representation of the input data, and even the slightest change in the input data will result in a completely different hash value.Signing with the private key: The signer's private key is then used to encrypt the hash value, creating the digital signature. The private key is a secret key known only to the signer, and it is used to create the digital signature.Verification with the public key: To verify the digital signature, the recipient uses the signer's public key (which corresponds to the private key used for signing) to decrypt the digital signature. The recipient also calculates the hash value of the received data or document using the same hash function used by the signer.Comparison: The recipient compares the decrypted hash value (obtained from the digital signature using the public key) with the hash value calculated from the received data or document. If the two hash values match, it means that the data or document has not been altered since it was signed, and the digital signature is valid and has been created by the owner of the private key (the signer).Digital signatures provide several benefits, including:Authentication: Digital signatures verify the identity of the signer, ensuring that the data or document originated from a specific person or entity.Integrity: Digital signatures ensure that the data or document has not been altered or tampered with since it was signed.Non-repudiation: Digital signatures provide evidence that the signer cannot deny having signed the data or document, as it requires the signer's private key to create the signature.