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I have a very elementary understanding about encryption so this question may have false assumptions,

Lets take an encryption algorithm that is impractical to break through bruteforce with today's hardware, assuming that moore's law is and will be valid in the near future, can we predict to some extent when will the computing power necessary to make the algorithm widely obsolete achieved?

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    There are these calculations where the amount of energy required to brute force an algorithm is larger than the amount of raw energy in the solar system. In those cases Moore's law can do nothing but to roll over and admit defeat. See for instance this article just to give an understanding on how mind boggling the numbers are. – Maarten Bodewes Oct 20 '14 at 1:42
  • @owlstead you don't realise how helpful and awesome your comment was – Jonathan Oct 20 '14 at 2:03
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Given the constraints in your question, yes, it can be predicted.

For symmetric-key encryption algorithms, the answer is "never".

Assuming Moore's Law is valid for the next century (an extremely optimistic assumption -- such a computer would be drawing much of the energy output of the Sun to power itself) and that current computers can test a million keys a second (a reasonable assumption), a computer in 2114 will be able to test 7.3*10^25 keys/sec. At that rate, it will take approximately 146,000 years to brute-force a 128-bit symmetric cypher (the minimum considered "secure" right now).

Asymmetric cyphers are a different matter. Since they depend on certain mathematical operations (eg. computing discrete logs or factoring numbers into large primes) being difficult, they're vulnerable to improvements in the algorithms for performing those operations. Improvements in computing power are relatively easy to predict; mathematical breakthroughs are rather less so.

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