In symmetric cryptography, how do Alice and Bob exchange a message — and what is the catch?

Both share a secret key sk. Alice encrypts with c = E(m, sk), Bob decrypts with m = D(c, sk). The catch: the shared key must somehow be agreed on or transmitted before any encrypted communication can start.

The mechanics are simple: same key, same algorithm, both sides. Symmetric = key is symmetric between sender and receiver.

The key-exchange chicken-and-egg problem:

• If you have no secure channel yet, how do you agree on the key?
• Hand-delivery, sealed envelopes by courier, pre-loaded smartcards — all real options but operationally painful.
• Diffie-Hellman key exchange (1976) solved this for the modern internet: two parties can derive a shared secret over a public channel without prior contact. (This is asymmetric cryptography's domain.)

Why we still want symmetric crypto even in the age of public-key:

• Speed: AES on modern CPUs (with AES-NI) is ~10 GB/s; RSA is ~1000× slower.
• Compactness: A 256-bit symmetric key has the same security as a ~15,000-bit RSA key.
• The standard pattern in TLS, SSH, Signal, etc.: use asymmetric crypto to bootstrap a symmetric session key, then encrypt the actual data with the symmetric key. Best of both.

Tip: Whenever you see "symmetric vs asymmetric", the right answer is usually "both" — modern protocols are hybrid by design.