What is the 'key exchange problem' that public-key cryptography solves?

How to securely share a secret key over an insecure channel — symmetric encryption requires both parties to share a key first, but if they could securely share a key, they could just share the message directly How to create a key that can be used for both encryption and decryption How to ensure both parties receive the same key when it's generated randomly The challenge of storing many different keys securely in one place

How does Diffie-Hellman key exchange work conceptually?

Both parties share a public color (starting value), each mixes in their private color, exchanges the mixed results publicly, then adds their private color to the other's mixture — only they end up with the same final combined color One person generates a key, encrypts it with the other's password, and sends it Both parties independently generate identical keys using a synchronized random number generator A trusted third party generates a key and sends a copy to each party separately

How does RSA encryption work conceptually?

Based on the difficulty of factoring large numbers — the public key is the product of two large primes; the private key derives from those primes; encryption and decryption use modular exponentiation Uses the initials of its inventors (Rivest, Shamir, Adleman) as the encryption key Encrypts by converting each letter to its ASCII value then multiplying by the key Uses a pair of randomly generated numbers — one to encrypt and one to decrypt

What is 'elliptic curve cryptography' (ECC) and why is it used in mobile devices?

A public-key system based on algebraic geometry — it provides the same security as RSA with much smaller keys (256-bit ECC ≈ 3072-bit RSA), making it efficient on battery-constrained mobile devices A cipher that draws elliptical curves through data points to create a unique encryption path A mobile-specific encryption system that runs in circular patterns to save processing power Encryption that curves around data to protect it from side-channel attacks

What is a 'hybrid encryption system' and why does it combine asymmetric and symmetric cryptography?

Using asymmetric cryptography (slow but solves key exchange) to securely share a symmetric key, then using symmetric cryptography (fast) for the actual data — gets the benefits of both Encrypting data twice — once with a symmetric key and once with an asymmetric key for double security A system that works both on-premise and in the cloud — hybrid refers to the infrastructure Mixing public domain and proprietary cryptographic algorithms for licensing efficiency

What is a 'digital signature' and what does it prove?

A cryptographic mechanism using a private key to 'sign' data — proves that the signer holds the private key (authentication) and that the data hasn't been modified (integrity) A digital copy of a handwritten signature scanned and attached to documents An encrypted password attached to files to verify who created them A certificate proving that a document was created on a specific date

What is 'forward secrecy' (or perfect forward secrecy) in key exchange?

Using temporary session keys that are discarded after use — if an attacker captures encrypted traffic now and later obtains the private key, they still can't decrypt old sessions Encrypting data before it's sent so it's secure before even leaving your device A key backup system that ensures you can always recover your data in the future Secrecy that extends forward in time — your future communications will be secure

What is the 'discrete logarithm problem' and why is it hard?

Given values g, p, and g^x mod p, find x — computing g^x mod p is fast, but reversing it to find x (the discrete log) is computationally infeasible for large numbers The problem of finding all factors of a large discrete (integer) number The difficulty of computing logarithms by hand without a calculator A problem in computing where numbers must be processed separately (discretely) rather than in bulk

What is a 'public key infrastructure' (PKI) and why is it needed?

A system of certificate authorities, certificates, and trust chains that allows anyone to verify that a public key genuinely belongs to who claims it — preventing man-in-the-middle attacks A government system for distributing public encryption keys to citizens A network of servers that store public keys so everyone can access them The rules about what information can be publicly shared with encryption software

What is 'PGP' (Pretty Good Privacy) and how is it used?

An email encryption and digital signature system using public-key cryptography — users publish their public keys; senders encrypt with the recipient's public key; recipients decrypt with their private key A lightweight encryption system for casual users who want 'pretty good' (not military-grade) security A government-approved email encryption system in the US A password manager that generates 'pretty good' passwords for online accounts