## Introduction to Public Keys

A public key is an encrypted code that is used to encode and decode messages in public key cryptography. Public key cryptography, also known as asymmetric cryptography, uses a pair of keys – a public key and a private key – to encrypt and decrypt data.

The public key can be freely shared with anyone, while the private key must be kept secret by its owner. Together, the two keys are used to secure communications and authenticate identities in public key infrastructure (PKI) systems.

Public keys play a crucial role in popular cryptographic systems like PGP, SSL/TLS, and cryptocurrencies. They enable key security properties like confidentiality, integrity, authentication, and non-repudiation in modern computing.

## What is a Public Key?

A public key is a type of code made up of a long string of numbers and letters. The key is mathematically generated using cryptographic algorithms.

While the public key can be openly shared, the algorithms also generate a corresponding private key that must be kept secret. The public and private keys are mathematically linked and designed so that data encrypted with one key can only be decrypted by its pair.

In public key cryptography, the public key is used to:

- Encrypt messages so that only the holder of the private key can decrypt them.
- Verify digital signatures created with the corresponding private key.

Meanwhile, the private key is used to:

- Decrypt messages that were encrypted with the public key.
- Digitally sign messages and data to prove the sender’s identity.

Neither key can perform both functions by itself. The public key cannot be used to decrypt messages or create signatures, while the private key cannot encrypt messages intended for the owner of the public key pair.

This asymmetry is the foundation for public key cryptography’s security benefits. The system enables secure communication between parties who have never exchanged secret keys, unlike symmetric key cryptography.

## How Public Key Cryptography Works

Public key cryptography depends on complex mathematical functions rather than a single shared secret key. Here’s a high level overview of how it works:

**Key Generation:**A key pair is mathematically generated – a public key and private key linked together.**Distribution:**The public key is distributed freely while the private key is kept secret.**Encryption:**To encrypt a message for the owner of the key pair, the sender uses the public key.**Decryption:**The private key is used by the key pair owner to decrypt the message encrypted with the public key.**Signing:**To digitally sign data, the private key is used to create the signature.**Verification:**To verify the signature, the public key is used to validate it was created with the corresponding private key.

The most widely used public key algorithms are RSA and ECC (elliptic curve cryptography). Different cryptographic hash functions are also used in the process.

Public key encryption converts plain text messages into ciphertext that can only be decrypted by the intended recipient’s private key. This ensures confidentiality and privacy.

Digital signatures enable authentication and integrity while preventing repudiation. The ability to validate signatures with the public key verifies the identity of the signer without the need to exchange secrets.

## The Role of Public Keys in Cryptography

Public key cryptography was revolutionary when introduced in the 1970s. Prior to this, all encryption relied on symmetric cryptography which uses a single shared key.

Public key systems removed the complex key distribution problem faced in symmetric cryptography by making one key public while keeping the other private.

Some of the key advantages and security services enabled by public keys include:

### Confidentiality

Messages encrypted with the public key can only be decrypted by the intended recipient who holds the corresponding private key. This ensures privacy and confidentiality.

### Authentication

Digital signatures created with the private key can be verified with the public key, authenticating the identity of the signer.

### Non-repudiation

By verifying digital signatures with public keys, the sender cannot deny sending the message (non-repudiation).

### Key Exchange

Public keys can be used to securely exchange symmetric encryption keys for encrypting large data.

### Integrity

Any changes to encrypted messages will be detected when attempting to decrypt them with the private key.

This unique asymmetry of public keys solved complex problems related to key distribution, authentication, and non-repudiation which were previously unsolvable.

Public key cryptography enabled major advances in computing and communications security including:

- Secure email (PGP)
- Website security (HTTPS/SSL/TLS)
- User authentication (SSH, OAuth)
- Cryptocurrencies (blockchain)
- Code signing and software security

Today, public key cryptography is a critical foundation for security on the internet and modern computing systems.

## Real-World Applications of Public Keys

Public key cryptography is extensively used in both enterprise and consumer applications today. Anywhere secure communications, transactions, or identity verification is required, you will find public key systems in use.

Some of the most common public key applications include:

### Secure Websites (HTTPS/SSL/TLS)

The HTTPS protocol used to secure websites relies on SSL/TLS certificates which contain the website’s public key. This enables encrypted communication and verifies the site’s identity.

### Email Encryption (PGP, S/MIME)

Public key encryption is used to encrypt email messages and digitally sign them to ensure confidentiality, integrity, and authentication.

### Cryptocurrencies

Public keys enable users to securely interact with blockchain-based cryptocurrency networks like Bitcoin, validating transactions and proving identity.

### User Authentication (SSH, OAuth)

Public keys authenticate users in SSH connections. OAuth uses public/private key pairs to authorize apps and services without exposing passwords.

### Domain Validation Certificates

DV SSL certificates contain public keys to verify ownership of domains by those requesting certificates.

### Code Signing Certificates

Code signing uses public key certificates to authenticate developers and validate that code has not been altered.

### Document Signing

Public key signatures are legally valid electronic signatures used by individuals and businesses to sign documents and contracts.

These are just a few examples. Public key cryptography also secures VPNs, messaging apps, connected devices and much more. The public keys provide the core cryptographic operations that enable security across countless applications.

## How Are Public Keys Generated?

Public keys are generated mathematically using cryptographic algorithms. While the specifics vary by algorithm, here are the general steps:

### 1. Generate a Private Key

The algorithm randomly generates a unique private key, which is a long string of numbers. This key must be kept securely by its owner.

### 2. Derive a Public Key

Using the private key, a mathematical function derives the corresponding public key. The two keys are mathematically linked.

### 3. Additional Parameters

Extra parameters may be required depending on the algorithm such as prime numbers.

### 4. Output the Key Pair

The end result is a key pair containing the linked public and private keys. The public key can be freely shared for use in cryptographic operations.

The most common algorithms used to generate public keys today are RSA and Elliptic Curve Cryptography (ECC):

**RSA Algorithm**

Based on the difficulty of factoring large prime numbers. RSA keys are generally 1024-4096 bits long.

**Elliptic Curve Cryptography (ECC)**

Relies on the algebraic properties of elliptic curves over finite fields. ECC keys are much smaller than RSA keys for the same strength. A 256-bit ECC key provides equivalent security to a 3072-bit RSA key.

Once generated, public keys are distributed in standard formats like X.509 certificates or PGP public keys for use in public key systems.

## Public Key Formats

Public keys are distributed within standard formats that include additional details like owner identity, digital signatures, and metadata. This enables public keys to be openly shared and securely used.

Some common public key formats include:

### X.509 Certificates

The X.509 standard defines the most common format for public keys. X.509 certificates contain identifying information for both people and devices along with the public key. Certificates are digitally signed to protect against tampering.

X.509 certificates secure websites, code signing, SSL/TLS, email, and more.

### OpenPGP Keys

The OpenPGP standard is used for PGP encryption. It defines an open format and protocols for sharing public keys necessary for PGP.

### SSH Keys

SSH public key authentication uses the OpenSSH format to share public keys. These keys are used to authenticate SSH connections.

### Cryptocurrency Keys

Unique standardized formats are defined for public keys used in major cryptocurrencies like Bitcoin, Ethereum, and others.

## Conclusion

Public keys are an essential element of public key cryptography that enables secure communication and transactions in the digital world. They provide a secure method of encryption and verification that solves key problems like confidentiality, authentication, and non-repudiation.

A public key is one half of a key pair that can be openly shared. Data encrypted with the public key can only be decrypted by its corresponding private key. Digital signatures created with the private key can be verified using the public key.

Public key cryptography has enabled major advances in security from encrypted web connections and emails to cryptocurrencies and connected device security. Public keys also secure numerous enterprise systems and business processes.

Understanding what public keys are, how they work, and their role in cryptography gives you valuable insight into modern digital security. Public key infrastructure and applications built on proven cryptographic algorithms will only continue grow in importance.

## Frequently Asked Questions

### What is the main purpose of a public key?

The main purposes of public keys are to encrypt messages intended for the owner of the paired private key and to verify digital signatures created with the private key.

### What are the differences between a public key and private key?

The public key can be freely shared while the private key must be kept secret. The public key cannot decrypt or sign messages – only the private key can. The private key cannot encrypt messages or verify signatures.

### What are some common public key algorithms?

RSA and ECC (Elliptic Curve Cryptography) are the most widely used algorithms used to generate public/private key pairs today.

### What are some applications that use public key cryptography?

Common public key applications include HTTPS/SSL/TLS (websites), email encryption (PGP), cryptocurrencies, SSH authentication, and code signing certificates.

### What is a X.509 certificate?

X.509 is a standard format for public keys used in TLS/SSL certificates, code signing certificates, and other applications. X.509 certificates include identity information and the public key.

### Can a public key be used to decrypt data encrypted with it?

No, only the corresponding private key can decrypt data that was encrypted using the public key. The public key cannot decrypt messages.

### What is public key infrastructure (PKI)?

PKI (Public Key Infrastructure) refers to the standards, policies, hardware, and procedures required to create, manage, distribute, use, store, and revoke digital certificates and manage public key encryption.