Which consensus algorithm requires validators to solve cryptographic puzzles?

The consensus algorithm that requires validators to solve cryptographic puzzles is Proof of Work.

Proof of Work operates on a system where participants, often called miners, compete to solve complex mathematical problems, which are essentially cryptographic puzzles. The first participant to successfully solve the puzzle gets the right to add a new block to the blockchain. This process is crucial for achieving consensus in decentralized networks as it helps secure the blockchain by making it computationally expensive to attempt to manipulate or alter the previous blocks, thereby ensuring integrity and trust among participants.

The other consensus algorithms listed do not rely on solving cryptographic puzzles. For instance, Proof of Stake allows validators to create new blocks based on the number of coins they hold and are willing to "stake" as collateral, rather than solving puzzles. Proof of Elapsed Time uses a fair lottery system where the next block creator is a randomly chosen participant who has waited a predetermined amount of time. PBFT (Practical Byzantine Fault Tolerance) is designed for a different kind of consensus based on votes rather than puzzle-solving, focusing on ensuring agreement among participants even if some behave maliciously.