Symmetric encryption is, mathematically, the easy part of secure communication: if two parties already share a secret key, scrambling and unscrambling messages with it is fast and well understood. The genuinely hard problem sits earlier — how do two parties who have never met, communicating only over a channel someone else might be listening to, ever agree on a shared secret in the first place, without simply handing that secret to the eavesdropper along the way? Asymmetric, or public-key, cryptography is the answer, and it works through a mathematical trick that has no obvious real-world analogy.
A lock anyone can close, that only one key can open
In asymmetric cryptography, each party generates a mathematically linked pair of keys: a public key, which can be shared openly with anyone, including an eavesdropper, and a private key, which is never shared with anyone. Data encrypted with someone's public key can only be decrypted with their corresponding private key — so anyone can use your public key to send you something only you can read, without either of you ever having exchanged a shared secret beforehand. The mathematical relationship between the two keys is deliberately chosen to be easy to compute in one direction (generating a public key from a private one, or encrypting with the public key) but computationally infeasible to reverse (deriving the private key from the public one), typically relying on problems like factoring extremely large numbers that stay hard even with substantial computing power.
Hashing solves a different problem entirely
Cryptographic hashing addresses a separate need: verifying that data hasn't been altered, rather than keeping it secret. A hash function takes an input of any size and produces a fixed-size output, or "digest," such that even a tiny change to the input produces a completely different digest, and — crucially — it's computationally infeasible to work backward from a digest to reconstruct the original input, or to find two different inputs that produce the same digest. This makes hashing useful for storing passwords (verify a login attempt without ever storing the actual password) and for confirming that downloaded software or transmitted data arrived unmodified, entirely independent of the key-exchange problem asymmetric cryptography was built to solve.
What we're still unsure about
The mathematical foundations of modern asymmetric cryptography and hashing are extensively analysed and, for the algorithms currently in wide use, considered secure against any known attack given current computing power. What remains a genuinely live and consequential uncertainty is how long that security will hold: sufficiently powerful quantum computers are theorised to be able to break the mathematical hard problems (like large-number factoring) that today's most common public-key systems rely on, and while "post-quantum" cryptographic algorithms are actively being developed and standardised in anticipation, exactly when quantum computers might reach the scale needed to pose a genuine threat, and how smoothly the transition to quantum-resistant systems will go, remain open questions.
This sits inside Cryptography (Symmetric, Asymmetric, Hashing), one of seven topics in Cybersecurity, one of seven domains in Computer Science, one of seventeen subjects the app can quiz you on.