Cryptography

Cryptography is the practice of securing information in the presence of adversaries. It sits underneath everyday systems such as online banking, messaging apps, software updates, and password storage. Modern cryptography is less about secret codes and more about well-defined security goals, carefully designed algorithms, and protocols that remain safe even when attackers know exactly how the system works.

At its core, cryptography answers a few practical questions: How can two parties communicate privately over an insecure network? How can you prove a message was not altered? How can you verify identity without exposing secrets? The tools that address these questions include symmetric and asymmetric encryption, hash functions, digital signatures, and advanced constructions like zero-knowledge proofs.

From classical ciphers to modern cryptography

Classical cryptography includes historical ciphers such as substitution and transposition methods. These techniques relied heavily on obscurity and were often broken through frequency analysis or operational mistakes. Their main limitation was that “security” was not formally defined and rarely robust against determined analysis.

Modern cryptography shifted the field toward mathematically grounded designs and explicit threat models. A basic principle is that algorithms are public and only keys are secret. Security is evaluated against realistic attacker capabilities, such as intercepting traffic, modifying messages in transit, or even tricking systems into encrypting chosen inputs.

This shift matters because it aligns cryptography with real engineering. A secure system should not depend on hiding how it works; it should withstand scrutiny.

Symmetric encryption: fast confidentiality with shared keys

Symmetric encryption uses the same secret key to encrypt and decrypt data. It is typically the most efficient option and is used to protect large volumes of data, from disk encryption to bulk network traffic.

Block ciphers and modes of operation

A common building block is a block cipher, which transforms fixed-size blocks of plaintext into ciphertext using a key. Because real messages are longer and structured, block ciphers are used with modes of operation that define how blocks are chained and how randomness is incorporated.

In practice, the security of symmetric encryption depends on more than the cipher itself. It hinges on correct use of nonces or initialization vectors (IVs), avoiding key reuse across contexts, and selecting an authenticated mode.

Authenticated encryption

Confidentiality alone is not enough. Attackers can often tamper with ciphertexts in ways that cause predictable changes after decryption. Authenticated encryption with associated data (AEAD) addresses this by providing both confidentiality and integrity. It encrypts the message and produces an authentication tag that detects modifications. “Associated data” refers to metadata that must be authenticated but not encrypted, such as packet headers.

The practical takeaway is simple: when designing systems, choose encryption that also verifies integrity, not just secrecy.

Asymmetric cryptography: public keys and scalable trust

Asymmetric cryptography, also called public-key cryptography, uses a key pair: a public key that can be shared widely and a private key that must remain secret. This enables secure communication and authentication without requiring both parties to have pre-shared a secret key in advance.

Public-key operations are typically slower than symmetric encryption, but they solve the hard problem of key distribution at scale.

RSA: a foundational public-key system

RSA is one of the most widely recognized public-key systems. Its security is based on the difficulty of factoring a large composite number into its prime factors. RSA can be used for encryption and digital signatures, though modern deployments require careful padding and encoding rules to avoid subtle vulnerabilities.

A conceptual view: RSA lets someone encrypt a message using your public key such that only you, holding the private key, can decrypt it. For signatures, you use the private key to sign data, and anyone can verify the signature using the public key.

Elliptic curve cryptography: smaller keys, strong security

Elliptic curve cryptography (ECC) achieves comparable security to RSA with much smaller keys, which can improve performance and reduce bandwidth and storage requirements. ECC is used for key exchange and digital signatures in many modern protocols.

Instead of relying on factoring, ECC relies on the hardness of problems related to elliptic curve discrete logarithms. The underlying math differs, but the practical value is similar: you get public-key functionality with strong security properties, provided curves and parameters are chosen correctly and implementations are constant-time to resist side-channel attacks.

Hash functions: integrity, fingerprints, and building blocks

A cryptographic hash function maps an input of any size to a fixed-size output. It is designed to be:

• One-way: hard to recover the input from the hash.
• Collision-resistant: hard to find two different inputs with the same hash.
• Sensitive to input changes: small changes in input radically change the output.

Hash functions are used to detect modifications, deduplicate data, and serve as core components in many protocols.

Password hashing is not just hashing

A critical practical distinction: storing passwords requires specialized password hashing that is intentionally slow and typically uses a per-user salt. Fast general-purpose hashes are not appropriate because attackers can try billions of guesses quickly. Modern systems use dedicated password-hashing approaches designed to resist large-scale guessing attacks.

Hashes in protocols and signatures

Hashes make it efficient to sign large data. Instead of signing an entire file, a system typically hashes the file and signs the hash. This supports software updates, document signing, and secure logging, where integrity must be verifiable long after the fact.

Digital signatures: authenticity, integrity, and non-repudiation

A digital signature provides a way to prove that a message or document came from a holder of a specific private key and that it was not altered after signing. Verification uses the corresponding public key.

In real systems, signatures do more than authenticate a person. They authenticate software publishers, servers, devices, and even automated processes. This is how operating systems verify updates, how certificate authorities vouch for websites, and how many secure messaging systems ensure that identity keys have not been swapped.

A key operational detail is key management. A perfectly sound signature algorithm fails if private keys are mishandled, leaked, or reused across incompatible contexts.

Cryptographic protocols: where systems succeed or fail

Cryptography is not only about algorithms; it is about protocols, the rules that define how parties use cryptographic primitives to achieve security goals.

Secure key exchange and session security

Many real-world connections use asymmetric cryptography to establish a shared secret, then switch to symmetric encryption for performance. This pattern appears in secure web browsing and private messaging. The protocol must ensure that attackers cannot perform man-in-the-middle attacks, downgrade security settings, or replay messages.

Authentication, authorization, and certificates

Public keys often need an identity binding: whose key is this? Certificate-based systems address this by having trusted entities sign statements connecting a public key to a domain or organization. If that trust layer fails, attackers can impersonate services even if the underlying cryptography remains intact.

Zero-knowledge proofs: proving without revealing

Zero-knowledge proofs allow one party to convince another that a statement is true without revealing why it is true or leaking the underlying secret. For example, a prover might demonstrate knowledge of a secret key or satisfy a condition about private data without exposing the data itself.

These proofs are increasingly relevant in privacy-preserving authentication and systems that need verifiable computation with minimal disclosure. The key idea is not magic; it is a rigorous protocol design where the verifier learns only the truth of the claim, nothing more.

Practical security: what matters beyond the math

Even when the underlying cryptography is strong, systems fail for predictable reasons:

• Poor randomness: weak keys, repeated nonces, or predictable values can destroy security.
• Implementation bugs: parsing errors, padding mistakes, or memory corruption can bypass cryptography entirely.
• Side-channel leaks: timing, power, and cache patterns can reveal secrets unless implementations are hardened.
• Key management failures: lost keys, leaked private material, and weak access controls undermine every layer.

Good cryptography is therefore as much about disciplined engineering as it is about elegant theory. The strongest algorithms help, but secure outcomes come from choosing appropriate primitives, composing them correctly in protocols, and operating them safely over time.

Why cryptography remains essential

Modern digital life depends on confidentiality, integrity, and authentication at global scale. Symmetric encryption protects data efficiently, asymmetric cryptography enables scalable trust, hash functions provide integrity and structure, digital signatures establish authenticity, and zero-knowledge proofs expand what can be verified without sacrificing privacy.

Cryptography is not a single tool but a toolbox. Used correctly, it makes hostile networks usable, and it turns fragile digital interactions into systems people can rely on.