The most strongest public encryption key today, is $256$ bit symmetric (e.g. AES-256) and $512$ bit hash (e.g. SHA-512).

So, if there are 2048-bit hashing and 1024-bit symmetric encryption, it is theoretically unbreakable by the universe by current science.

Today, the theoretically smallest length is planck length (~$10^{-35}$ meter), and the theoretically smallest time is planck time (~$10^{-44}$ seconds). The observable universe is $93$ billion light years ($10^{27}$ meter), and the age of universe is $13.8$ billion years ($10^{18}$ seconds).

Just a simple calculation, we can found that the universe is actually around $10^{186}$ cubic planck length (or planck volume). ($(10^{27}/10^{-35}) ^3$), and the age of universe is $10^{62}$ planck time ($10^{18}/10^{-44}$).

If the smallest particle (planck length) in universe trying to crack the 1024-bit password, and it can crack 1 time in the smallest time unit (planck time). Using all universe particle to crack the password in fastest way, it still not possible to crack a 1024-bit password ($10^{186}$ planck length $10^{62}$ times = $10^{248}$, which is much smaller than $2^{1024}$ bit = $10^{308}$ combination).

Due to birthday problem, 2048-bit hash strength is approximately equivalent to 1024 bit encryption.

So, is that we can conclude that, 2048-bit hash and 1024-bit symmetric encryption is never obsolete. No matter the strongest quantum computer is, it still impossible to crack. But Why there are no 2048-bit hash and 1024-bit encryption available in the public market ?


Because the numbers required to achieve that level of security are much lower, even versus an adversary with a quantum computer. See this question/answer on security.stackexchange for the specifics.

Assuming that 256 bits/512 bits are secure for encryption/hashing, anything greater cannot serve a functional purpose in terms of security (it cannot be "more secure").

The biggest major factor besides security is performance. If the algorithms are not more efficient then their traditionally sized counterparts, then there is no motivation for their creation. Your proposed extremely large algorithms could potentially have performance issues. Using copious amounts of data is not necessarily register or cache friendly. Such large algorithms could also be difficult/expensive to implement on constrained/dedicated hardware.

  • $\begingroup$ Is it conspiracy to stop other develop 2048-bits hash because of performance reason? Assuming that 2048-bit hash are not worse secure than 512 bits one. I think i should have a choose to use 2048-bit hash if i think my data is very important and i have the enough computer power to use it. $\endgroup$
    – bronze man
    Nov 2 '18 at 7:23
  • $\begingroup$ @bronzeman No, it's cost and functional requirements; There is no conspiracy to stop people from using 2048-bit hashes, because there is no benefit to any malicious actor for anyone to use 256/512-bit hashes. Design decisions need to be justified, and there is no justification for designing a 2048-bit hash function, which is why you don't see them. Anyways, depending on your definition of "hash" (e.g. security or simply output size), SHA3 can produce a digest as long as you want it to be. "I think i should have a choose to use 2048-bit hash" why? $\endgroup$
    – Ella Rose
    Nov 2 '18 at 15:50

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