Digital signature

A digital signature is a special mark for computer files.

It is like a name written on paper. It shows who sent a message. It also shows the message was not changed.

To make one, a person uses a secret key. This key stays private. They use it to sign a message. Then, others use a public key to check it.

This helps banks and schools stay safe. It can even help send software updates. It is a smart way to stop fakes. Digital signatures keep our digital world working well.

A digital signature is a way to prove a message is real. It works like a handwritten name on paper.

But a digital signature is much safer. It is tied to the message itself. This makes it very hard to fake.

There are three main parts to this system. First, a computer makes two keys. One is a private key. This key stays secret. The other is a public key. Anyone can see the public key.

Next, the sender uses their private key to sign a message. This creates a signature. Finally, the receiver uses the public key to check the signature. If the check passes, the message is safe. This means the sender is known. It also means no one changed the message.

People use this for many things. Banks use it to check money transfers. Schools use it for student records. Even the government uses it for laws. It also helps when computers get software updates. This makes sure the update is not bad software. It keeps our digital world working well.

A digital signature is a mathematical way to prove a message is real. It acts much like a handwritten signature on a piece of paper. However, digital signatures are much more secure than ink on paper. A handwritten signature can be copied or forged onto a new document. A digital signature is mathematically tied to the specific content of the message. This means it is nearly impossible for anyone to fake a signature on a different message.

These tools help people trust digital documents and messages.

To make this work, a system uses three different computer steps. First, a key generation algorithm creates two different keys. One is a private key that stays secret, and the other is a public key that anyone can see. Next, a signing algorithm uses the secret private key and a message to create a signature. Finally, a verifying algorithm uses the public key and the message to check the signature.

If the math matches, the signature is accepted as true. This ensures the message is both real and unchanged.

People have been working on these ideas for a long time. In 1976, Whitfield Diffie and Martin Hellman first described the idea of digital signature schemes. Shortly after, Ronald Rivest, Adi Shamir, and Len Adleman invented the RSA algorithm. This was an important step for creating early digital signatures. In 1988, Shafi Goldwasser, Silvio Micali, and Ronald Rivest defined how to make these systems secure.

Later, the Lotus Notes 1.0 software became the first widely marketed package to use these signatures in 1989.

There are many ways these signatures are used in our daily lives. Banks use them to make sure money transfers are safe and authentic. They need to know that a request to change an account balance is real. Universities like Stanford and the University of Chicago use them for student transcripts. Even the United States Government Printing Office uses them for laws and congressional bills.

Computers also use them to check software updates. This helps stop bad software, or malware, from being installed on a device.

Digital signatures help solve many hard jobs in the digital world. They provide authentication, which proves who sent a message. They also provide integrity, which shows that no one changed the data. In many cases, they provide non-repudiation, meaning a sender cannot deny they sent the message.

However, they do have some limits. For example, they cannot stop a "replay attack." This is when someone records a valid signed message and tries to use it again. Even with these limits, they are vital for our digital lives.

A digital signature is a mathematical scheme used to verify the authenticity of digital messages or documents. It provides a way for a recipient to feel confident that a message actually came from a known sender. While it is similar to a handwritten signature on paper, it is much more secure. A physical signature can be copied onto a different piece of paper through forgery. In contrast, a digital signature is mathematically bound to the specific content of the message. This makes it computationally infeasible for anyone to forge a valid signature on a different message.

To function, a digital signature scheme relies on three distinct mathematical algorithms. The first is a key generation algorithm. This algorithm selects a private key at random from a set of possible keys. It then outputs both that private key and a corresponding public key. The second step is the signing algorithm. This process takes a message and the private key to produce a unique signature. The final step is the signature verifying algorithm. This algorithm uses the message, the public key, and the signature to either accept or reject the claim of authenticity.

For a digital signature to be considered successful, it must meet two main requirements: correctness and security. Correctness means that signatures produced by the signing algorithm must pass the verification algorithm when using the correct public key. Security, often referred to as existential unforgeability under chosen-message attack (EUF-CMA), is also vital. This means it should be nearly impossible for an attacker to generate a valid signature for a party without knowing that party's private key. Even if an attacker can see many valid signatures, they should not be able to create a new one for a new message.

The history of this technology began in 1976. During that year, Whitfield Diffie and Martin Hellman first described the concept of a digital signature scheme. They conjectured that these schemes could exist using functions known as trapdoor one-way permutations. Soon after, Ronald Rivest, Adi Shamir, and Len Adleman invented the RSA algorithm. While "plain" RSA signatures were only a proof-of-concept and not fully secure, they were a major milestone. In 1988, Shafi Goldwasser, Silvio Micali, and Ronald Rivest rigorously defined the security requirements for these schemes. The first widely marketed software to use digital signatures was Lotus Notes 1.0, which was released in 1989 using the RSA algorithm.

In modern practice, many systems do not sign a whole document directly. Instead, they use a method called "hash-then-sign." First, the message is run through a hash function to create a short digest. This digest is then padded to a larger width and signed with a private key. There are several practical reasons for this approach. Using a hash is much more efficient because hashing is generally faster than signing. It also ensures compatibility, as a hash can convert any message into the specific format required by the signature scheme. Finally, it protects integrity by ensuring the receiver can recognize if all parts of a message are present and in the correct order.

Digital signatures are used in many important ways today. They provide authentication, which proves the identity of the sender. This is critical for banks that must verify instructions to change account balances. They also provide integrity, which ensures that no one has modified the message during transit. For example, a software author might sign a patch to ensure computers do not install malicious software, or malware. Furthermore, they provide non-repudiation, which means a sender cannot later deny that they sent the message. Organizations like the United States Government Printing Office use them for laws, and universities like Stanford use them for student transcripts.

Despite their strength, digital signatures have certain limitations. They do not prevent a "replay attack." In a replay attack, a person records a valid signed message and maliciously reuses it later. For instance, a signed request to transfer money could be reused to drain an account if the system lacks unique transaction IDs. Additionally, signatures can sometimes be "malleable," meaning one valid signature might be transformed into another valid signature without knowing the private key. Finally, while a public key can verify a signature, a signature cannot be used to verify that a public key is authentic.