# Does a bigger key mean more security - if we do not change the structure of the algorithm?

Let's say I have 128-bit cipher in which each round needs to get 768 key bits. Let's consider 10 rounds.

It can be easily 128-bit key cipher. I can do key schedule and produce 7680 bits of keys (let's say with HKDF). But I can also use for example 512-bit key. Then I still need key schedule, but the main key is stronger. And cipher still works on the same 128-bit blocks with the same speed (because it is using still 768 key bits in every round).

Will only by increasing the size of the main key from which I create the round keys I make the algorithm more secure? It is harder to broke main key in this case, but rounds remains the same weak (attacker still have to broke just 768-bit in every round). So maybe we should say that it make stronger key schedule only, not actual cipher? Is it make sense to increase the main key size in that case?

• In differential and linear attack, if the last round attackable, it doesn't change how many rounds or original key you use. Apr 28, 2021 at 9:39

Generally speaking, more than 128 bit security is not required - except maybe for protection against multi-target attacks where large amounts of ciphertext become available to the adversary. The reason for this is that no system will be able to perform $$2^{128}$$ operations. So if there is an analysis that threatens the structure or number of rounds used, then increasing the rounds or updating the algorithm will likely strengthen the security of the cipher more than increasing the key size.