A digital signature is essentially the hash of the signed document, encrypted by the private key of the signer. The genuineness of the document can be verified by generating the hash of the document received, decrypting the signature using the public key of the sender, and comparing the hash contained in the signature to the one generated from the received document. If the two hashes are identical, the document received is the same as the one sent by the sender, and has not been modified on the way.