Digital Signatures
Asymmetric encryption and hashing are used to create digital signatures. A digital signature is information encrypted with creator's private key. Information so encrypted can only be decrypted using the corresponding public key. Therefore, successful decryption with an entity's public key proves that the message could only have been created by using the corresponding private key. By definition, that private key is know only to its owner. Consequently, only the entity owning the pair of public and private keys could have created that message.