Cryptography refers to a suite of techniques that protect information like messages, payments, and social media posts as they move across vulnerable networks like the internet. The goal is to transform readable data (plaintext) into an encrypted form (ciphertext) that hides its meaning and prevents unauthorized access.

There are three fundamental types of cryptography that each work differently to accomplish the vital task of securing data:

- Symmetric encryption
- Hash functions
- Asymmetric (public key) encryption

By understanding what distinguishes each method, you‘ll gain valuable insight into how cryptography operates behind the scenes to safeguard your digital information and identity. This guides dives into the details so you can grasp the critical role mathematics and advanced algorithms play in enabling secure communications and trustworthy systems across industries and the internet.

## Symmetric Cryptography: Simplicity and Speed

Symmetric algorithms utilize a single secret key shared between communicating parties to encrypt and decrypt data. Since the same key secures information in transit and at rest, properly managing and protecting its secrecy is imperative.

Benefits of symmetric cryptography include:

- Speed and computational efficiency from using one key
- Conceptual simplicity
- Wide range of trusted algorithms

Let‘s explore how symmetric encryption works to protect confidential data along with examples of common algorithms and their usage in essential security systems we rely on daily.

### How Symmetric Encryption Works

Symmetric schemes apply the same key to scramble plaintext into ciphertext at the originating end, then reverse the process at the receiving end to restore the original data. This single key must remain confidential to ensure security.

For example, if you wanted to securely transmit your tax ID number over email, encryption would work as follows:

- Your email client software takes your plaintext tax ID number and encryption key as input
- A symmetric algorithm (like AES or Blowfish) mathematically transforms the plaintext into ciphertext gibberish
- The ciphertext gets sent over email across the internet
- At the destination, your receiving email system decrypts the ciphertext back into the readable tax ID number using the same encryption key

As long as the key remains secret, your secure tunnel for transmitting confidential data persists between endpoints.

### Common Symmetric Algorithms

Symmetric ciphers utilize various mathematical techniques to repeatedly transform plaintext data in a convoluted manner such that it becomes computationally infeasible to recover the original information without the key.

Popular symmetric encryption algorithms include:

Algorithm | Key Lengths | Description |
---|---|---|

AES | 128, 192, 256 bits | Advanced Encryption Standard (AES) is fast, secure, and widely used across many applications and systems today |

Blowfish, Twofish | 64 bits | Flexible and optimized symmetric ciphers designed for speed |

3DES | 48 bits | Enhances outdated DES cipher by applying the algorithm three times with three keys |

RC4/ARC4 | 40 – 2,048 bits | Fast stream cipher but has weaknesses enabling attacks so it has fallen out of favor |

Each algorithm makes tradeoffs around encryption strength, performance, complexity, and flexibility to support different goals.

### Use Cases of Symmetric Cryptography

Robust and ubiquitous symmetric encryption protects sensitive information across many digital systems:

- Secure internet protocols like TLS, SSH, PGP, and IPsec apply these techniques to encrypt web and application data in transit
- Messaging apps like WhatsApp and Signal use these ciphers to safeguard conversations
- Disk encryption software like VeraCrypt secures devices and volumes by scrambling data at rest
- Password manager apps encrypt your entire vault of credentials and passwords
- Cryptocurrencies depend on this cryptography to secure decentralized blockchain ledgers and digital wallet transactions

When properly implemented and keyed, symmetric cryptography delivers high performance, simplicity, flexibility, and security to the communication channels and data storage solutions we depend on daily.

## Cryptographic Hash Functions: Digital Fingerprints

Unlike encryption meant to intentionally conceal information, cryptographic hash functions produce fixed-length message digests that act like unique digital fingerprints identifying data.

Key attributes make hash functions invaluable:

- Determinism: Identical inputs always produce the same hash digest
- Quick computation even for larger data sets
- Extreme sensitivity to input changes
- One-way operation makes digest reversal nearly impossible
- High cryptographic security strength

Understanding how hash algorithms generate these distinctive digests sheds light on their usefulness in verifying data authenticity and integrity across many modern technologies.

### How Hash Functions Operate

A hash function accepts an input message of any size like documents or binary data and runs it through multiple rounds of manipulation to generate a fixed small digest.

For example, an input message gets broken into 512-bit chunks and put through multiple compression functions that randomly combine, divide, shift, and flip the binary bits to diffuse changes across the entire eventual hash output. Additional algorithms manipulate and randomize the data to produce a fixed-length output like 256 bits for SHA-256.

Even the slightest change to the input message results in a wildly different hash digest value. This extreme sensitivity means hashes uniquely identify the input data, acting as its fingerprint.

### Common Cryptographic Hash Algorithms

Many hash functions exist that make various tradeoffs between security level, processing speed, digest size, and more:

Algorithm | Digest Size | Overview |
---|---|---|

MD5 | 128 bits | Produces a 128-bit hash but researchers have broken its collision resistance allowing attacker manipulation |

SHA-1 | 160 bits | Outputs a 160-bit hash, but weaknesses means it should get avoided today |

SHA-256 | 256 bits | Member of the SHA-2 algorithm family and widely adopted for its optimized security |

SHA-3 | Various sizes | Next generation standard that will evolve along with cryptography advances to stay resilient to attacks |

BLAKE2 | Any size | Optimized for software applications and supports variable hash digest sizes |

### Use Cases of Hash Functions

By generating unique fixed-length digests quickly, hash functions enable vital services:

**File verification**: Hash digests detect unauthorized file changes by detecting mismatches between digests produced before and after transmission**Password storage**: Storing password hashes rather than plaintext improves login security**Blockchain**: Cryptocurrency transactions get hashed into an immutable ledger as the backbone of decentralization**Deduplication**: Matches inputs to identical hash digests rather than storing full duplicate copies**Digital signatures**: Contains hashed content to allow tamper evidence

Overall, cryptographic hash functions serve as fundamental building blocks underpinning security across information technology.

## Asymmetric Public Key Cryptography

Unlike symmetric schemes applying the same key, asymmetric cryptography utilizes a mathematically connected pair of public and private keys. The private key remains confidential while the public key disseminates openly.

This revolutionary technique arrived in 1976 when Whitfield Diffie and Martin Hellman introduced the groundbreaking idea. Benefits include:

- Enhanced security since private keys stay private
- Resilient public key distribution
- Authentication via hard-to-forge digital signatures

Let‘s explore how this process works.

### Public Key Encryption in Action

A high-level asymmetric encryption flow looks like:

- Bob and Alice‘s devices each generate a matched set of private and public keys using key generation algorithms
- Alice and Bob exchange their public keys but carefully guard their private keys
- To encrypt to Alice, Bob uses Alice‘s public key. Only Alice‘s private key decrypts.
- To reply, Alice uses Bob‘s public key. Only Bob‘s private key can decrypt.

This facilitates secure two-way communication without transmitting secret keys that could get compromised. Even if adversaries eavesdrop on the channel and capture ciphertexts, only Alice and Bob retain the capability to decrypt each message intended for them.

Additionally, public keys get linked to identities through certificates signed by certificate authorities (CAs), enabling authentication.

### Common Public Key Algorithms

Practical asymmetric encryption emerged through algorithms mathematically connecting key pairs. Each has benefits and downsides regarding proof of security, speed, and computational resource demands.

Prominent public key algorithms include:

**RSA:**First implementation, deriving strength from factoring large prime numbers**ECC:**Uses elliptic curve math, offering efficiency gains over RSA**Diffie-Hellman**: Enables private key exchange over unsecure channels**DSA**: Digital Signature Algorithm quantum-resistant signing through hash functions

New asymmetric schemes get introduced to advance capabilities and security as computing evolves.

### Applications of Public Key Cryptography

Many crucial systems serving billions of users rely on asymmetric encryption properties:

**HTTPS and SSL/TLS**: Enables trusted secure web connections**Email and messaging encryption**: Protects communications via linked key pairs**Document signing**: Binds identities to documents through uncompromised math proofs**Authentication**: Proves identities by possessing associated private keys

In many implementations, asymmetric encryption handles authentication and the exchange of symmetric encryption keys to benefit from both schemes.

### Conclusion on Cryptography

This exploration of the foundations of cryptography, including symmetric and asymmetric encryption alongside hash functions, sheds light on how mathematical techniques safeguard data in modern communications and computation. As these schemes continue advancing in sophistication to meet evolving threats, cryptography will continue powering trust in digital systems through state-of-the-art security protections.