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ciphergoth comments on Bullying the Integers - Less Wrong Discussion

13 Post author: sixes_and_sevens 15 December 2010 05:40PM

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Comment author: ciphergoth 16 December 2010 08:02:03AM 2 points [-]

Many of the people who thought it was impossible to break RSA in polynomial time were arrogant, they thought they understood the world much better then they actual did. Many of the people who thought that it was obvious that RSA would one day be solved in polynomial time were also arrogant.

Could you quote some of those people? I'm not aware of a lot of knowledgeable people making unwarrantedly strong assertions.

Comment author: Davorak 16 December 2010 08:34:49AM *  1 point [-]

My assertion was also not specific to people knowledgeable in the field, just like the op's colleague is not very knowledgable in RSA(at least I had assumed so). I consider the probability of a non-expert having said this to be to be close to 100%.

Be forewarned I am not an expert in the feild, but here are some interesting tidbits:

Thesis (Quantitative Church’s thesis). Any physical computing device can be simulated by a Turing machine in a number of steps polynomial in the resources used by the computing device"

Then:

If the precision of a quantum computer is large enough to make it more powerful than a classical computer, ...

edit: Shor is suggesting that quantum computers break the Church thesis which implied that for any device it was impossible to solve RSA in poly time. end edit.

Both from quotes are from "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer" - Peter W. Shor

Comment author: ciphergoth 16 December 2010 10:05:24AM *  0 points [-]

Note that AFAIK Church did not state this "Quantitative Church’s thesis" - it's hard to be sure because of the paywall, but I'd guess that this paper was the first to explicitly state it, and it did so in order to argue that it may not be true.

Comment author: Davorak 16 December 2010 10:45:01AM 0 points [-]

I could not tell which paper you are talking about. The paper I posted? It is not behind any pay wall for me. If not the paper I post which paper are you talking about I can try to look at it at work latter.

Comment author: ciphergoth 16 December 2010 12:34:18PM 0 points [-]

Don't know what went wrong there - I have the paper now. Turns out I'm quite wrong, this idea is credited to:

P. van Emde Boas (1990), Machine models and simulations, in Handbook of Theoretical Computer Science, Vol. A, J. van Leeuwen, ed., Elsevier, Amsterdam, pp. 1–66.

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