 So this talk is about laziness. Imagine that you have a contract, and you're asked to develop a very efficient crypto system. So you have a list of requirements. What is a crypto system? So it's a set of three algorithms, key generation, encryption, decryption. And you have also some security requirements. So you have to develop something which is very secure. And that's your contract. So if you have such a contract, you're super happy because you have nothing to do. So essentially, you just take the lazy crypto system, which does nothing. So the key generation returns nothing. Encryption returns nothing. Decryption returns nothing. It satisfies the requirements. So you have three algorithms. It's perfectly secure. So it's just something missing. So what is missing is correctness. It doesn't satisfy correctness. So that's why we have a definition for correctness. Correctness describes what is a job to be done. So it describes the job of the primitive. So correctness describes what's happened in honest environment. But now in some papers, we have more and more of fun. Some people describing correctness in an adversarial setting described as a kind of game played by an adversary. So when we do such a thing, we can have some surprise. So there are several examples like this. I just picked one. So this is an example taken from this conference. The first talk of this conference describes a ratcheted key exchange. There is a very, very complicated definition of what is a ratcheted key exchange, what is correctness, what is security. So that's the correctness definition. So correctness definition. So a ratcheted key exchange is described by three algorithms, initialization, sending, and receiving. And correctness says that for every adversary, this game should return zero all the time. So where is there any output in this game? So you can see there is a stop with zero here. There is a recry, which is a shorthand for stop with zero unless this predicate is true. And there is here a shorthand for stop with one if the predicate is true. So the only way to return one is to reach this line. So if you make sure that you never reach it by sending all the state to bottom, so you have a lazy cryptosystem, which works. So lazy cryptosystem is correct, is perfectly correct. I'm running out of time, so I have no time to prove that it's perfectly secure, but believe me, it's very secure. So that's the kind of problem you can encounter if you describe correctness with some adversarial setting. So just be careful if you describe it this way. Thank you.