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When assuming a block cipher primitive is secure, or a number theoretic problem is hard, this assumption is usually based on how far we are from breaking the primitive or solving the problem using known techniques - using known algorithms and hardware.

But, from a meta-cryptographic point of view, how do we justify the assumption that there doesn't exist any significantly more efficient algorithms, or any significantly better hardware? I am not asking for opinions on the matter (or for arguments that fix the algorithms and prove that the necessary hardware would be physically impossible) but for justifications based on e.g. the sociology of cryptography or economics of cryptography, using scientific (justified and repeatable) methods and based on the premise that all research is done in the context of pre-existing research.

  • How likely is it that a single small team, basing their research solely on the state of the public research and their own results, would come up with results years or decades ahead of everyone else in the field?
  • Is it possible for large organizations to internally accumulate enough research, to give the researchers within that organization a significant head start over independent researchers in the field?
  • If "yes" on the previous question, are there ways to reliably tell if an organization has such significant amounts of secret accumulated knowledge? Is it possible to use the numbers of papers and patents the organization outputs, as a reliable indication that it doesn't have a strategy of accumulating knowledge only internally? What about flows of personnel between organizations, i.e. people changing jobs?
  • What is the likelihood that an organization exploiting weaknesses it has found in cryptographic primitives, would be caught in the act? If the organization is only using the weaknesses for intelligence gathering? Does it matter if the weaknesses require passive attacks or active attacks to be conducted?
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Nice questions – which won't get perfect answers because they'll include opinions/guesses. (1) We can only guess, but it is likely to be possible as it happened before, (2) yes, practically seen it happen, (3) depends on the organization; but generally there is no reliable way to tell because you can't look deep enough into some governmental institutions and their blacksites, (4) That's the Snowden question rebooted. You're safe until someone notices… the more resources you have to counteract intelligence gathering, the less likely someone will be able to point the finger without losing it. –  e-sushi Feb 20 at 15:44
These kinds of things are very similar to what is studied in social sciences and economics. In principle, we don't have to guess. However, if no such research has been done, either due to lack of interest or lack of opportunity to collect the necessary data, that would also be an interesting answer. –  Henrick Hellström Feb 20 at 15:48
Also, it would be possible to formulate a valid hypothesis based on anecdotal experience, either if it demonstrates that no such study could ever eliminate a significant amount of inherently unknown hidden statistics, or, conversely, if it indicates exactly what kind of evidence should be collected to reach a reliable answer. –  Henrick Hellström Feb 20 at 15:53
I agree, and I'm already looking forward to the answers this gets. Scientific papers handling the points you mentioned are rare and not always easy to find. Especially in relation to cryptography, I'm personally not aware of any scientific paper that really answers all your questions. Yet, I may well be corrected in one of the answers. Alike papers are surely nice to have – not only for reference purposes. (To be honest: first thing that popped up in my mind when I saw your question, was the hope that you may be asking because you're thinking about starting a related research paper yourself… ) –  e-sushi Feb 20 at 16:19
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