# 2048 bit hashing and 1024 bit symmetric encryption

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 ?