How many keys are needed for asymmetric encryption with $n$ participants?

Only $n$ key pairs (one per participant), making key management $O(n)$ instead of $O(n^2)$.

In asymmetric cryptography:

• Each participant generates one key pair (public key + private key)
• The public key is shared openly; the private key stays secret
• To communicate with anyone, you just need their public key

$$\text{Key pairs} = n$$

Comparison for $n = 100$:

This massive reduction in key management complexity is a key advantage of asymmetric crypto. The trade-off is that asymmetric encryption is roughly 1000x slower than symmetric encryption, which is why hybrid encryption exists.

Go deeper:

• Public-key cryptography — how one key pair per person replaces per-pair secrets.