Assumption of difficulty of attack in restricted short time
One area that tries to address such questions is fine-grained cryptography [DVV]. Here the working assumption is that the protocols should be secure "against adversaries with an a-priori bounded polynomial amount of resources but the honest algorithm requires less resources than the adversaries they are designed to fool". A classical example of such a protocol is the Merkle puzzle, which is a key-exchange/public-key scheme that requires $O(n)$ time/queries for the parties carrying out the protocol but it takes an adversary $\Theta(n^2)$ time/queries. 

More recently, there have been attempts at building public-key cryptography where the gap is arbitrary (e.g., $O(n^c)$ vs $O(n^{c+1})$ for any constant $c$) and these rely on computation problems such as the orthogonal vector problem [B+] where there is a gap between computation and verification (and this gap is inherent conditioned on SETH). This has also resulted in an interesting notion of proofs of work called useful proof of work [B+] where the goal is to utilize otherwise wasteful work (as for example in Bitcoin).

You can find a nice overview of the area by Alon Rosen here.

[B+] Ball et al, Proof of useful work, Crypto'18

[DVV]: Degvekar, Vaikuntanathan and Vasudevan, Fine-grained Cryptography, Crypto'16.