Bremermann's limit
Encyclopedia
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 c
2/h ≈ 1.36 × 1050 bits per second per kilogram. 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 under 10−36 seconds. However, a 256 bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512 bit key would increase the cracking time to approaching 1072 years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used).
Hans-Joachim Bremermann
Hans-Joachim Bremermann was a German-American mathematician and biophysicist. He worked on computer science and evolution, introducing new ideas of how mating generates new gene combinations...
, is the maximum computational speed of a self-contained system in the material universe. It is derived from Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
's mass-energy equivalency and the Heisenberg uncertainty principle, and is c
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
2/h ≈ 1.36 × 1050 bits per second per kilogram. This value is important when designing cryptographic
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...
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
Brute-force search
In computer science, brute-force search or exhaustive search, also known as generate and test, is a trivial but very general problem-solving technique that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's...
.
For example, a computer the size of the entire Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
, 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 under 10−36 seconds. However, a 256 bit key (which is already in use in some systems) would take about two minutes to crack. Using a 512 bit key would increase the cracking time to approaching 1072 years, without increasing the time for encryption by more than a constant factor (depending on the encryption algorithms used).