Encryption you can do math on: add up encrypted numbers and get the encrypted total, without seeing any individual number.
The idea: Imagine sealed ballot boxes that can be merged: put two together and you get one sealed box holding the sum. With Paillier, multiplying two ciphertexts gives an encryption of the sum of their messages. A tallying server can combine all the encrypted votes into one ciphertext and hand it to the key holder, who decrypts only the total. No individual vote is ever decrypted.
Why it matters: Useful for private voting and for wallets that split one key across several devices.
On the map: additively homomorphic: e-voting, aggregation
Public-key encryption where multiplying two ciphertexts adds their plaintexts: E(a) × E(b) = E(a + b)[1]. Anyone can sum encrypted votes or values without decrypting them.
Where you meet it: e-voting research, private aggregation, and threshold ECDSA wallets that split a signing key between devices[2, 3].
If any of these breaks, this breaks too.
If this breaks, these break with it.
Nothing on the map depends on it: it is an end point, something people use directly.