In cryptography, a digital signature or digital signature scheme is a type of cryptography used to simulate the security properties of a signature in digital, rather than written form. Digital signature schemes normally give two algorithms; one for signing which involves the user's secret or private key, and one for verifying signatures which involves the user's public key. The output of the signature process is called the 'digital signature'.

Digital signatures, like written signatures, are used to provide authentication of the associated input, usually called a 'message'. Messages may be anything, from electronic mail to a contract, or even a message sent in a more complicated cryptographic protocol. Digital signatures are used to create public key infrastructure (PKI ) schemes in which a user's public key (whether for public-key encryption, digital signatures, or any other purpose) is tied to a user by a digital identity certificate issued by a certificate authority. PKI schemes attempt to unbreakable bind user information (name, address, phone number, etc.) to a public key, so that public keys can be used as a form of identification.

Public key cryptography, also known as asymmetric cryptography, is a form of cryptography in which a user has a pair of cryptographic keys - a public key and a private key. The private key is kept secret, while the public key may be widely distributed. The keys are related mathematically, but the private key cannot be practically derived from the public key. A message encrypted with the public key can be decrypted only with the corresponding private key.

The two main branches of public key cryptography are:

Public Key Encryption — a message encrypted with a user's public key cannot be decrypted by anyone except the user possessing the corresponding private key. This is used to ensure confidentiality.

Digital Signatures — a message signed with a user's private key can be verified by anyone who has access to the user's public key, thereby proving that the user signed it and that the message has not been tampered with. This is used to ensure authenticity.

An analogy for public-key encryption is that of a locked mailbox with a mail slot. The mail slot is exposed and accessible to the public; its location (the street address) is in essence the public key. Anyone knowing the street address can go to the door and drop a written message through the slot; however, only the person who possesses the key can open the mailbox and read the message.

An analogy for digital signatures is the sealing of an envelope with a personal wax seal. The message can be opened by anyone, but the presence of the seal authenticates the sender.

A Postal Analogy

An analogy which can be used to understand the advantages of an asymmetric system is to imagine two people, Alice and Bob, sending a secret message through the public mail. In this example, Alice has the secret message and wants to send it to Bob, after which Bob sends a secret reply.

With a symmetric key system, Alice first puts the secret message in a box, and then locks the box using a padlock to which she has a key. She then sends the box to Bob through regular mail. When Bob receives the box, he uses an identical copy of Alice's key (which he has somehow obtained previously, maybe by a face-to-face meeting) to open the box, and reads the message. Bob can then use the same padlock to send his secret reply.

In an asymmetric key system, Bob and Alice have separate padlocks. First, Alice asks Bob to send his open padlock to her through regular mail, keeping his key to himself. When Alice receives it she uses it to lock a box containing her message, and sends the locked box to Bob. Bob can then unlock the box with his key and read the message from Alice. To reply, Bob must similarly get Alice's open padlock to lock the box before sending it back to her.

The critical advantage in an asymmetric key system is that Bob and Alice never need to send a copy of their keys to each other. This prevents a third party (perhaps, in the example, a corrupt postal worker) from copying a key while it is in transit, allowing said third party to spy on all future messages sent between Alice and Bob, so in the public key scenario, Alice and Bob need not trust the postal service as much. In addition, if Bob were to be careless and allow someone else to copy his key, Alice's messages to Bob would be compromised, but Alice's messages to other people would remain secret, since the other people would be providing different padlocks for Alice to use.

Some content within this topic is licensed under the GNU Free Documentation Licence. It uses material from the Wikipedia articles Digital Signature and Asymmetric Key Algorithm.