Encryption 101: A Beginner‘s Guide to Public Key Cryptography

Imagine you wanted to send your friend a top-secret message across the schoolyard. The problem? The school bully might intercept it and read your private note. What we need here is a way to scramble the message so only your friend can decode it.

This is the idea behind encryption – transforming information into unreadable gibberish that only authorized parties can decipher. And public key cryptography provides a clever way of doing this without having to secretly agree on a code ahead of time.

A Tale of Two Keys

Public key encryption uses a pair of keys – one public, one private. Here‘s a simple analogy:

The public key can be compared to a lockbox with an open slot on top. Anyone can put a message inside and lock it closed. But the box can only be unlocked with your private key. So you can freely share your public key to receive encrypted messages that only your private key can decrypt.

This enables all sorts of vital capabilities in our digital world:

  • Private online communication – Encrypt emails, messages and data transfers without pre-shared keys
  • Secure web browsing – Safely transmit credit card details, medical records and other sensitive information
  • Validating identity & authenticity – Digital signatures, software verification, blockchain transactions and more

Next, we‘ll explore exactly how public key encryption works under the hood…

Behind the Math Magic

While analogies can help conceptually, public key crypto relies on complex mathematical functions to work its magic. Here are the principles driving both key generation and encryption.

The Power of Prime Numbers

Many public key algorithms depend on the challenge of factorizing extremely large prime numbers – whole numbers only divisible by 1 and themselves. The public and private key are created using two sufficiently large random primes.

For example, the primes 203,251,893 and 274,897,721 could be picked. It‘s nearly impossible to identify what the original primes were just from looking at their product – 56,119,176,989,443,721.

This forms the core "trapdoor function" of public key encryption. The private key provides the secret trapdoor information to reverse the math.

Harnessing Elliptic Curves

Public key systems like ECC also rely on tricky mathematical problems that are simple to perform in one direction but extremely difficult to reverse engineer.

Instead of prime numbers, ECC utilizes the addition properties of elliptic curves – oddly shaped graphs with nice cryptographic qualities. Randomly choosing a starting point on such a curve once again creates an irreversible one-way function.

Elliptic curve diagram

An elliptic curve for cryptography use

So in summary, the complex math powering encryption keys enables:

  • Key generation – Creating irreversible, "trapdoor" public/private key pairs
  • Encryption – Anyone can use the public key to scramble data
  • Decryption – Only the private key holder can unlock messages

This publicly accessible yet ultra-secure encryption system avoids the need to secretly transmit symmetric keys between communicators. Fascinating stuff!

Now let‘s analyze some common public key algorithms and ciphers.

Comparing Crypto: Asymmetric vs Symmetric

Modern encryption leverages two main types to secure communications and data:

Symmetric encryption uses the same secret key to encrypt and decrypt data. This offers better performance for bulk encryption but the sender/receiver must securely exchange the key.

Public key encryption utilizes key pairs instead, avoiding secret transmission – but operates slower.

So asymmetric and symmetric ciphers have different strengths:

Metric Symmetric Asymmetric
Speed Very fast Slow
Key distribution Challenging Built-in
Scalability Excellent Poor
Use cases Bulk data encryption Key exchange, signatures

Accordingly, most cryptosystems cleverly combine symmetric and asymmetric encryption:

  1. Public key encryption establishes secure connections and verifies identities
  2. Symmetric encryption handles high volume data transfer under this protected tunnel

This gives us the best of both worlds!

RSA vs ECC vs Others

There are many public key algorithms to choose from. Here‘s how the most common ones stack up:

Algorithm Key Sizes Strengths Vulnerabilities
RSA 1024+ bits Most widely used and battle-tested Vulnerable to quantum
ECC 256+ bits Smaller/faster at equiv. security Fewer known attack vectors
Diffie-Hellman 1024+ bits Secure key exchange Keys vulnerable if leaked

As you can see ECC (Elliptic Curve Cryptography) is emerging as a next-gen replacement for RSA in many cases thanks to better efficiency.

But first, let‘s walk through some real world applications to understand the role of public key encryption.

Use Cases: Where Asymmetric Encryption Shines

Public key cryptography uniquely powers many essential security capabilities by removing pre-shared secret keys from the equation. For example:

Securing Web Browsing with HTTPS

Every time you connect to a website these days you‘ll notice HTTPS in the address bar. The S indicates traffic is secured using either TLS or SSL protocols:

  1. Browser requests site certificate containing public key
  2. Server provides certificate after digitally signing it
  3. Browser verifies certificate signature matches server
  4. Session keys exchanged to enable symmetric data encryption

This handshake allows confidently sharing credit card details over an encrypted tunnel.

Sending Confidential Emails

Similarly, services like PGP email leverage public key encryption to provide confidentiality:

  1. Recipient generates key pair and publishes public key
  2. Sender downloads public key to encrypt email contents
  3. Recipient decrypts email using private key

No more worrying about email providers or hackers reading your messages in transit!

Enabling Trust with Digital Signatures

Used in everything from signed documents to software updates, digital signatures also rely on public key encryption:

  1. Private key used to encrypt unique hash of document/code
  2. Signature embedded alongside data
  3. Anyone can recompute hash and verify it matches using public key

This mathematically proves authenticity and integrity from the signing authority.

Authorizing Blockchain Transactions

Finally, the surge in cryptocurrencies and blockchain depends heavily on asymmetric cryptography:

  • Key pairs are generated when wallet addresses are created
  • Owners digitally sign transactions with their private key
  • The network verifies signatures match addresses using public keys

Enforcing access rights and authorization without centralized account management.

As you can see, many crucial technologies depend on public key encryption security models. However, some limitations remain.

Challenges & Weak Points of Public Key Crypto

While transformative, asymmetric cryptography also comes with downsides:

Performance overheads – The computationally intensive math chews through processing capacity, slowing communications compared to symmetric alternatives. Software and hardware acceleration alleviates this though.

Key security & management – Public keys themselves aren‘t secret but they must link reliably to the owner. Compromised or forged certificates break trust models. Strict issuance policies and revocation lists help.

Private keys are also a single point of failure needing air-gapped, encrypted storage since they decrypt all data. Access controls and backups are key for resilience.

Quantum computing uncertainty– Shor‘s algorithm means quantum can crack asymmetric encryption by factoring the mathematical "trap doors." This threat must be mitigated via new quantum-resistant algorithms and larger key sizes.

Defense in Depth Critical

Ultimately defense in depth with fail-safes at all layers helps minimize asymmetric encryption vulnerabilities:

Layers of cryptographic defense

Monitoring systems, key hygiene policies, algorithm agility to counter emerging threats and more…

The Future of Public Key Encryption

Public key cryptography has evolved tremendously since concepts emerged in the 70s.

Once barely cracking 512-bit keys, computers now test the limits of 2048-bit and larger RSA encryption. ECC similarly progresses down a path to a future of 256-bit quantum-safe elliptic curves.

Further optimization will deliver efficiency gains while robust identity systems help secure certificates. Combined with symmetric ciphers and other protections, asymmetric encryption remains critical infrastructure for the digital revolution.

No wonder pioneers Whitfield Diffie, Martin Hellman and Ralph Merkle were given the 2015 ACM Turing Award – computing‘s equivalent of the Nobel Prize – for public key cryptography advancements.

Truly a landmark feat of modern computing!

So in closing, if you made it this far – hopefully you now see public key systems secure the web in so many ways. Fundamentally we owe the ability to browse, shop, share, communicate and transact online safely to asymmetric cryptography, digital signatures and encryption.

Additional References

  1. NSA Suite B Cryptography: https://www.keylength.com/en/4/
  2. NIST Post-Quantum Cryptography Programs: https://csrc.nist.gov/projects/post-quantum-cryptography
  3. IETF RFC 6091 Using ECC for Secure Key Exchange: https://www.rfc-editor.org/rfc/rfc6091.txt