Bremermann's limit

Bremermann's Limit, named after Hans-Joachim Bremermann, is the maximum computational speed of a self-contained system in the material universe. It is derived from Einstein's mass-energy equivalency and the Heisenberg Uncertainty Principle, and is approximately 2 × 10⁴⁷ bits per second per gram. This value is important when designing cryptographic algorithms, as it can be used to determine the minimum size of encryption keys or hash values required to create an algorithm that could never be cracked by a brute-force search.

For example, a computer the size of the entire Earth, operating at the Bremermann's limit could perform approximately 10⁷⁵ mathematical computations per second. If we assume that a cryptographic key can be tested with only one operation, then a typical 128 bit key could be cracked in 10⁻³⁷ seconds. However, a 256 bit key (which is already in use in some systems) would take about a minute to crack. Using a 512 bit key would increase the cracking time to 10⁷¹ years, but only halve the speed of cryptography.

References

* Bremermann, H.J. (1962) "Optimization through evolution and recombination" In: Self-Organizing systems 1962, edited M.C. Yovitts et al., Spartan Books, Washington, D.C. pp. 93-106.

* Bremermann, H.J. (1965) "Quantum noise and information". 5th Berkeley Symposium on Mathematical Statistics and Probability; Univ. of California Press, Berkeley, California.