Kryptografie/Schlüssellängen

AES256 and AES128

I would never consider using AES256, just like I don't wear a helmet when I sit inside my car.
It's too much bother for the epsilon improvement in security.

Recommendations on keylengths need to be adapted regularly

Since this document first of all is static and second of all, does not consider itself to be authoritative on keylengths, we would rather refer to existing publications and websites.
Recommending a safe key length is a hit-and-miss issue.

Furthermore, when choosing an encryption algorithm and key length, the designer/sysadmin always needs to consider the value of the information and how long it must be protected.

In other words: consider the number of years the data needs to stay confidential.

The ECRYPT II publication gives a fascinating overview of strengths of symmetric keys in chapter 5 and chapter 7.

Summarizing ECRYPT II, we recommend 128 bit of key strength for symmetric keys.
In ECRYPT II, this is considered safe for security level 7, long term protection.

In the same ECRYPT II publication you can find a practical comparison of key size equivalence between symmetric key sizes and RSA, discrete log (DLOG) and EC keylengths.

ECRYPT II arrives at the interesting conclusion that for an equivalence of 128 bit symmetric size, you will need to use an 3248 bit RSA key (II & SYM, 2012).

There are a couple of other studies comparing keylengths and their respective strengths.

The website https://www.keylength.com/ compares these papers and offers a good overview of approximations for key lengths based on recommendations by different standardization bodies and academic publications.
Figure #fig:keylengths.com[1] shows a typical comparison of keylengths on this web site.

"Screenshot for 128 bit symmetric key size equivalents"

Summary

Asymmetric public-key cryptography: we consider any key length below 3248 bits to be deprecated at the time of this writing (for long term protection)

For elliptic curve cryptography: we consider key lengths below 256 bits to be inadequate for long term protection

For symmetric algorithms: we consider anything below 128 bits to be inadequate for long term protection