Digital signature: cryptographic security mechanism

Digital signature is a cryptographic solution used to ensure the authenticity and integrity of digital data. It can be viewed as a more complex and secure version of a traditional handwritten signature. Simply put, a digital signature is a code added to documents to prove that the data has not been altered in transit. The signature functions as a unique digital certificate for each specific message.

The nature of signatures and cryptographic background

A digital signature differs significantly from a handwritten signature on paper. While handwritten signatures tend to look similar across documents, a digital signature is unique to each message. Applying the concept of signatures in a digital environment solves a complex problem: how to verify that the sender of the data is indeed who they claim to be, and that the message has not been altered during transmission.

Although the history of cryptography dates back to antiquity, digital signature schemes became a reality in the 1970s. This was made possible through the development of public key cryptography (PKC). Since then, signatures have become increasingly important in the fields of cyber signatures and data authentication.

Hash functions: building blocks

Hashing is one of the fundamental building blocks of a digital signature system. The hashing process transforms data of any length into a fixed-length output. This is done using specialized algorithms called hash functions.

The output generated by a hash function is called a hash value or message digest. Combining cryptographic hash functions allows the creation of a unique digital “fingerprint.” This means that even a small change in the input data produces a completely different output. Therefore, cryptographic hash functions are widely used to verify the authenticity of digital data. In the context of signatures, this is important because it ensures that even the slightest modification to a document invalidates the signature.

Public key cryptography: the two-key system

Public key cryptography (PKC) is a cryptographic system that uses a pair of keys: a public key and a private key. These two keys are mathematically related, and their relationship enables secure encryption and signing of data.

PKC is significantly more secure than older symmetric encryption methods. Traditional systems used the same key for encrypting and decrypting data. PKC, on the other hand, allows data to be encrypted with a public key and decrypted with the corresponding private key. This asymmetry forms the basis of security.

PKC schemes are also used for generating digital signatures. Essentially, the message is hashed and then signed with the sender’s private key. The recipient can then verify the validity of the signature using the sender’s public key. An important nuance here is that digital signatures are not always encrypted. For example, Bitcoin blockchain uses PKC and signatures, but no encryption occurs. Bitcoin employs the so-called elliptic curve digital signature algorithm (ECDSA).

How digital signatures actually work: three critical stages

In cryptocurrencies and other applications, a digital signature system typically consists of three main steps: hashing, signing, and verification. These steps are closely interconnected and form a trustworthy whole.

Data hashing

The first step is hashing the message or digital data. This creates a hash value—message digest—using a hash function. Although messages can vary greatly, all their hash values have the same fixed length. This is a key property of hash functions.

Technically, data hashing is not mandatory for signing—private keys can be used on unhashed messages. However, in cryptocurrencies, data is always hashed because fixed-length message digests simplify the process and increase efficiency.

Signing and encryption process

After hashing the data, the sender must sign the message. This is where public key cryptography becomes active. Various digital signature algorithms exist, but the core principle remains the same: the hashed message is encrypted with the private key. The recipient can then verify the signature’s validity using the sender’s public key.

A critical point: if the private key is not involved in creating the signature, the recipient cannot use the corresponding public key to verify it. The sender generates both the public and private keys but only transmits the public key to the recipient. This asymmetry is fundamental to security.

An important feature: digital signatures are directly linked to the content of each message. Unlike handwritten signatures, each digitally signed message has a different signature.

Signature verification process: Alice and Bob example

Let’s consider a specific scenario to illustrate the entire process up to verification. Imagine Alice sends a message to Bob. She hashes it, then combines the hash value with her private key to create a digital signature. This signature acts as a unique digital certificate for that particular message.

When the message reaches Bob, he can verify the signature’s validity using Alice’s public key. This way, Bob can be confident that the signer was Alice, since only she has the private key corresponding to that public key (assuming the private key has not been leaked).

For Alice, it is vital to keep her private key secret. If someone else gains access to Alice’s private key, they can impersonate her and create her digital signatures. In the context of Bitcoin, this means someone could use Alice’s private key to transfer her coins without permission. This makes the security of the private key the core of the system.

Practical applications and importance of digital signatures

Digital signatures are used to achieve three main objectives:

Data integrity

Bob can verify that Alice’s message has not been altered in transit. Any modification to the message results in a completely different signature, revealing manipulation.

Authenticity

As long as Alice’s private key remains secure, Bob can use her public key to confirm that the digital signatures were created by Alice, not someone else. This authenticates the source of the message.

Non-repudiation

Once a signature is created, Alice cannot deny having signed the message, unless her private key has been compromised. This establishes legal accountability.

Industry applications of digital signatures

Digital signatures can be added to various digital documents and certificates, leading to widespread applications such as:

• Information technology: strengthening security of internet communication systems and secure data exchanges.
• Finance: digital signatures in audits, expense reports, loan agreements, and financial documentation.
• Legal sector: digital signing of business contracts, legal agreements, and government documents.
• Healthcare: digital signatures prevent forgery of prescriptions and medical records.
• Blockchain and cryptocurrencies: digital signatures ensure that only authorized owners can sign transactions for transferring funds.

System limitations and challenges

The main challenges of digital signature schemes relate to three critical aspects:

Algorithm quality

The quality of algorithms used in signature systems is crucial. This includes selecting reliable hash functions and cryptosystems. Weak algorithms undermine the security foundation.

Implementation and deployment

Even if the algorithm is strong, poor implementation can leave the entire signature system vulnerable. Practical deployment is essential for security.

Private key security

If the private key is leaked or compromised, the authenticity and non-repudiation requirements are not met. For cryptocurrency users, losing the private key can lead to severe financial loss.

Electronic vs. digital signatures: what’s the difference?

In simple terms, a digital signature is a subset of electronic signatures. A digital signature is any method of signing electronic documents and messages that uses cryptography. Therefore, all digital signatures are electronic signatures, but not all electronic signatures are digital.

The main difference lies in the authentication method. Digital signatures employ cryptographic systems—hash functions, public key cryptography, and encryption techniques. Electronic signatures may use other authentication methods.

Summary

Hash functions and public key cryptography form the foundation of digital signature systems, which are widely used today across various fields. Proper implementation of digital signatures can significantly enhance security, guarantee data integrity, and facilitate authentication of digital data. In blockchain and cryptocurrencies, signatures are used to sign and authorize transactions. Bitcoin and other cryptocurrencies rely heavily on the security of digital signatures, ensuring that only rightful owners with proper private keys can spend coins.

Although signature systems have been in use for many years, their development potential remains high. Much of today’s bureaucracy still relies on paper-based processes, but the adoption of digital signature technology is increasing as systems move toward digitalization. The future of digital signatures appears to be a progressive integration into all digital formats, bringing better security and efficiency.