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September 8, 2014

2

The Whole Universe Can’t Search 500 Bits

by omohundro

2014-08-31_214929

 

Seth Lloyd analyzed the computational capacity of physical systems in his 2000 Nature paper “Ultimate physical limits to computation” and in his 2006 book “Programming the Universe”. Using the very general Margolus-Levitin theorem, he showed that a 1 kilogram, 1 liter “ultimate laptop” can perform at most 10^51 operations per second and store 10^31 bits.

The entire visible universe since the big bang is capable of having performed 10^122 operations and of storing 10^92 bits. While these are large numbers, they are still quite finite. 10^122 is roughly 2^406, so the entire universe used as a massive quantum computer is still not capable of searching through all combinations of 500 bits.

This limitation is good news for our ability to design infrastructure today that will still constrain future superintelligences. Cryptographic systems that require brute force searching for a 500 bit key will remain secure even in the face of the most powerful superintelligence. In Base64, the following key:

kdlIW5Ljlspn/zV4DIlsw3Kasdjh0kdfuKR4+Q3KofOr83LfLJ8Eidie83ldhgLEe0GlsiwcdO90SknlLsDd

would stymie the entire universe doing a brute force search.

 

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