In general, this is a dumb trade to make, because more key bits are cheap and that computation costs every user.
Things like what you describe exist-- where initial key scheduling does key stretching, etc.
> Since memory intensity instead of pure computational intensity seems to be employed by some hashing alghorithms I wonder is that would be possible block ciphers as well. The way I understand this, it makes ASIC/FPGA brute-forcing a lot harder/expensive
Anything is possible, but this often does more to hurt low-resource users than brute force also.
1MB memory usage would not hurt most of the low-resource users while having 1MB memory for each of the millions of computational units in a brute-force rig would hurt the attacker a lot more. I assume that it is relatively easy to have a huge number of brute-force cracking units in a simple GPU/FPGA/ASIC rig but if each of them would additionally need lets say 1MB of RAM that would present a serious problem for the constructor of such rig.
I do get that AES will happily run on a 20-year old smart-card simplified cpu without a problem while my fictional 1meg-requiring cipher would be problematic, but then again it's 2019 and 1MB is not that of a problem for the least powerful smartphones or even embedded systems.
1MB means you basically obliterate caches and torture memory bandwidth every time you want to encrypt a tiny block. But ignoring that...
Low cost microcontrollers with 4k or 8k of RAM total are still used in embedded systems and often have hardware AES built in. Even things like ESP32 are often considered relatively big and have 520k of ram.
There are applications and services that have a million or more connected sockets with encryption at a time. This would represent a terabyte of RAM just for this 1MB block cipher scratchpad.
If one were to just use a megabyte during key scheduling or something-- that's feasible, I guess, but it still locks out a lot of the embedded world.
A microcontroller with a few megabytes of RAM to support several crypto sessions with this cipher is going to be a big cost multiple over current micros.
you could imagine a cipher with a computational/memory[0] intensity so high that the brute force attack could be practically infeasible even at lower key-sizes. I am not advocating using smaller keys, just pointing out that there is more to brute-force resistance that simply just the key-length number. (That is probably the numerology the GP was referring to)
[0]Since memory intensity instead of pure computational intensity seems to be employed by some hashing alghorithms I wonder is that would be possible block ciphers as well. The way I understand this, it makes ASIC/FPGA brute-forcing a lot harder/expensive