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I'm somewhat new to encryption. When looking at encryption programs for big data, I frequently see a maximum of 256 bits.

Why do we generally restrict our (symmetric) keys to 256 bits? Can more powerful encryption algorithms be used practically, or is there a specific reason for that 256 bit maximum?

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  • $\begingroup$ Are you asking "why do we generally restrict our (symmetric) keys to 256 bits"? If you aren't asking that, what are you asking? $\endgroup$ – poncho Jul 31 '15 at 21:30
  • $\begingroup$ I hope you don’t mind… but to be sure everyone grasps what you’re asking, I’ve added that “reformulation” to your question. Please feel invited to modify my edit in case I missed something. Btw: Welcome to Crypto.SE, Erich! $\endgroup$ – e-sushi Aug 1 '15 at 0:03
  • $\begingroup$ I think the actual issue is more with the blocksize of the cipher and not the key size $\endgroup$ – Richie Frame Aug 1 '15 at 6:16
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There is no need to go beyond 256 bits if the cypher is strong (can only be attacked by brute force).

This is because there are fundamental physical limits on the energy required to perform a computation. The Landauer limit is one: to switch one bit takes $kT\ln2$, where $k$ is the Boltzmann constant ($1.68\times10^{-23}$), $T$ is the temperature in Kelvin, and $ln2$ is the natural log of 2. On average brute forcing a 256-bit key will take $2^{255}$ operations (half of $2^{KeyLength}$).

Assume a computer exists which operates at this limit, is at the temperature of the cosmic microwave background (about 3K), and only needs to do one operation to test a key. It will then take $2^{255}\times 1.68\times 10^{-23}\times 3 \times \ln 2$ Joules, which comes out to about $2.02\times 10^{54}J$.

For comparison, the if the entire mass of the Earth were converted to energy it would only release $5.4\times 10^{41}J$. So you'd be annihilating 10,000,000,000,000 earth-sized planets just to brute force one key. Or building a Dyson sphere and capturing the total energy output of the Sun for 10,000,000,000,000,000,000 years.

In short, there are so many possibilities that the key length is sufficient, presuming you want your secrets to outlive the Sun.

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