Have you ever wondered how websites prove their identity or how you can securely pay online? Public key cryptography makes these daily activities on the internet possible! This comprehensive guide will explain step-by-step how this ingenious form of encryption works.
Introduction to Public Key Cryptography
Public key cryptography is a system that uses a pair of mathematically linked keys (a public key and a private key) to enable secure communication over insecure channels. It allows you to encrypt data at one end and then have only the intended recipient with the private key be able to decrypt it at the other end.
This guide will cover:
- The origins and historical context that inspired public key cryptography
- How public key cryptography works on a technical level
- The specific mathematical algorithms that power different public key schemes
- The many applications made possible thanks to this technology
- Comparisons to previous encryption techniques and the advantages introduced
By the end, you‘ll have a deep understanding of the ins and outs of this critical encryption method!
History and Origins
Public key cryptography was publicly introduced in 1976 by Whitfield Diffie, Martin Hellman, and Ralph Merkle. This built on earlier classified research into asymmetric key exchange by researchers at GCHQ in the UK.
At the time, all non-classified encryption was based on private key cryptography alone. This required securely exchanging a common private key to encrypt and decrypt information between two parties. There were several downsides to this approach:
- Private keys had to be kept perfectly secret between parties
- Distribution of private keys was risky and complex
- Every communication pair needed a separate private key
- The number of keys scaled very poorly as networks grew bigger
Diffie, Hellman and Merkle devised an innovative solution to these limitations. By using a public/private key pair, the need to secretly exchange permanent keys was eliminated! This opened the door to practical encryption on a much wider scale.
How Public Key Cryptography Works
Public key cryptography is also called asymmetric key cryptography due to its use of mismatched keys. It requires two separate keys:
| Key | Description |
|---|---|
| Public key | This key is made freely available to anyone and is used to encrypt messages |
| Private key | This key is private and only available to the intended recipient of the message. It is used to decrypt messages encrypted by the public key. |
Here‘s how it works step-by-step:
- A recipient generates both a public and a private key (mathematically linked together via a one-way function)
- They widely share their public key without needing to keep this key secret from anyone
- To send an encrypted message, the sender looks up the recipient‘s public key and uses it to encrypt the message
- The resulting encrypted message can only be decrypted and read by using the recipient‘s corresponding private key
- Even without exchanging any secret keys beforehand, the sender was able to encrypt a message that only the intended recipient can read!
This one-way encryption powered by separate public/private keys is the core genius behind public key cryptography. Billsions of dollars worth of transactions occurs because of this technique!
Mathematical Foundations
Several clever mathematical approaches have been used over the years to create functional public key schemes:
RSA
The RSA algorithm published in 1977 remains one of the most widely used today. It relies on the practical difficulty of factoring extremely large prime numbers to mathematically link its key pair. Its security comes from the infeasibility for any modern computer to attempt to factor a number hundreds of digits long!
Elliptic Curve Cryptography
ECC schemes utilize properties of elliptic curves over finite fields to create efficient algorithms. Formulated in 1985, ECC offers equivalent security to RSA but via much smaller key sizes, lowering storage and bandwidth demands. However, attacks against ECC are viewed as more theoretically viable.
Diffie-Hellman Key Exchange
Introduced before RSA in 1976, the Diffie-Hellman key exchange elegantly enabled two parties to securely establish a shared secret key. It would later inspire algorithms for varied complex protocols like HTTPS, SSH, and VPNs.
Advantages over Previous Ciphers
To understand the leap in cryptographic capability that public key encryption enabled, let‘s compare some weaknesses it overcame:
| Cipher Type | Weaknesses |
|---|---|
| Substitution ciphers like Caesar/ROT13 | Provided no security against dedicated adversaries |
| Monoalphabetic ciphers like Atbash | Letter frequency analysis could routinely break encryption |
| Polyalphabetic ciphers like Vigenère | Eventually vulnerable to cryptanalysis techniques like Kasiski examination |
| One-time pads | Required secure distribution of disposable keys |
By contrast:
- Public key encryption is resistant to all types of cryptanalysis
- Secure key distribution is no longer an obstacle
- The asymmetric design better protects against compromised keys
This unprecedented resilience ushered in the era of robust encryption still relied on 40+ years later!
Applications Enabled by Public Key Cryptography
Thanks to public key cryptography‘s abilities, we can now:
- Securely browse the web (HTTPS)
- Trust identity certificates
- Privately pay online with ease
- Validate software digitally
- Create unforgeable digital signatures
- Exchange secret keys securely
Additional uses include:
- Cryptocurrencies like Bitcoin
- Secure emails via PGP
- Secure remote connections through VPNs and SSH
The list continues growing as developers find creative new applications for public key encryption schemes!
Key Takeaways
- Developed in the 1970s to solve key exchange problems
- Uses mathematically-linked public/private key pairs
- Public key encrypts, private key decrypts messages
- Enables convenient secure communication channels
- Withstood 40+ years of attacks so far!
Hopefully you now appreciate the critical role that public key cryptography plays in enabling secure digital transactions. The concepts introduced here provide just a high-level overview of this complex, ever-evolving domain. Please explore further – there‘s always more to uncover with cryptography!
