Is time complexity more important than space complexity?

I've noticed quite a few cryptographic algorithms speak mainly of the time complexity of an algorithm. For example, with a hashing function h, find x given y = h(x). We normally speak on how long it will take. Or the time to find the discrete log for a public key.

Edit:

While writing this question, I pondered that maybe because for most algorithms in cryptography (that I have seen) , have O(1) space time complexity. i.e. If the solution does not work, we throw it away and encrypt.

Clarification on this will be really helpful.

In fact, when we are talking about algorithms in general, time-complexity is discussed much more frequently than space-complexity. Let me provide a few ideas to support that more general phenomenon which applies to the cryptography as well.

• There are much more about time-complexity to talk about in computer science and software industry while space-complexity is more restricted to hardware. It occurs to me that there are over 10 times more tasks/techniques/concepts/results/articles about time-complexity than space-complexity. Overwhelmingly, programming contests are about time-complexity.

• Space/memory can be reused easily. Available space can be expanded easily. On the other hand, time needed for computing cannot be shorten that easily. Parallelization helps, but it cannot speed up the serial part of the program. Practically and relatively speaking, we are enjoying the cheap memory now while we are still hungry for computing speed.

Now come to the cryptography side of the question.

• As you have observed, most algorithms in cryptography have $O(1)$ space time-complexity. Although space might be critical such as in embedded devices, there is not much value of space-complexity in general.

• On the other hand, the time-complexity is the critical factor of a cryptographic algorithm, especially in encryption/decryption. It should produce data fast enough. Authorized users should be able to retrieve the plaintext fast enough while adversaries do not have fast algorithms to decrypt the ciphertext.

StackExchange Computer Science Q#110540, answer score: 8