Bulletproofs are short non interactive zero knowledge proofs that require no trusted setup A Bulletproof can be used to convince a verifier that an encrypted plaintext is well formed For example, prove that an encrypted number is in a given range, without  revealing anything else about the number Compared to SNARKs, Bulletproofs require no trusted setup However, verifying a  Bulletproof is more time consuming than verifying a SNARK proof.

PRCY uses a dual key system to provide stealth addresses to obfuscate addresses. A public address is derived from a private view spend key pair. A public address can contain optionally payment ID, which is usually used by exchanges.
PRCY uses the EC secp256k1 curve to derive public keys from corresponding private keys.

The short answer is that these 12 or 24 words are what you get when you translate from binary (the language computers use,  consisting of 1’s and 0’s) into the language that you can understand, recognize, and (perhaps most importantly) remember. Cryptocurrency is a purely digital fortress of math. It would be strange and difficult if you had to read, copy, or type a string of 256 ones and zeros as your private key to claim ownership of some amount of crypto.

To make things easier and safer for all users, a standard system was developed with security in mind, known as BIP-39, to  conveniently provide you with a set of words, called your mnemonic phrase or mnemonic seed (both names can be used  interchangeably).