# Re: can we find one-way trapdoor funcation family from the theory of calculus

**From:** Andrew Swallow (*am.swallow_at_btopenworld.com*)

**Date:** 11/21/05

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**Previous message:**Juuso Hukkanen: "Re: can we find one-way trapdoor funcation family from the theory of calculus"**In reply to:**Unruh: "Re: can we find one-way trapdoor funcation family from the theory of calculus"**Next in thread:**Pubkeybreaker: "Re: can we find one-way trapdoor funcation family from the theory of calculus"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Date: Mon, 21 Nov 2005 20:19:58 +0000 (UTC)

Unruh wrote:

*> Andrew Swallow <am.swallow@btopenworld.com> writes:
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*>
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*>
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*>>Unruh wrote:
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*>
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*>
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*>>>Andrew Swallow <am.swallow@btopenworld.com> writes:
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*>>>
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*>>>
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*>>>
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*>>>>Unruh wrote:
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*>>>>
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*>>>>
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*>>>>>"Pubkeybreaker" <Robert_silverman@raytheon.com> writes:
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*>>>>
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*>>>>[snip]
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*>>>
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*>>>
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*>>>>>>Trying to determine, therefore, if it can somehow be made into a
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*>>>>>>one-way function
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*>>>>>>is just total nonsense.
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*>>>>>
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*>>>>>
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*>>>>>No, but then that was not what they were saying. An integral is a
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*>>>>>transformation on a functions. Can such transformations be used to make a
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*>>>>>one way function?
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*>>>
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*>>>
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*>>>>You could use something like the sin function. If your number is bigger
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*>>>>than 360 then sin(x) cannot be inverted because it is a m:1 function.
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*>>>
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*>>>
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*>>>Unfortunately a trapdoor function is one that can be inverted, just not
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*>>>very easily.
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*>>>
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*>>
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*>>Try sin(x + 13N) where N is large
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*>>To get from arcsine to x you need to know N.
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*>
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*>
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*> If you know the value for one x (well, actually two x), you know the value for all x. This is a
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*> pretty useless trapdoor function. Ie, a single known plaintext/encrypted
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*> pair breaks the scheme.
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*> Not only do you need unpredictability, you need resistance to known pairs.
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*>
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*>>In a strong system N would be a function rather than a constant.
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*>>Replacement of sin by a binary or integer function would also help.
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*>
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*>
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*>>Andrew Swallow
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That is why N has to be a function.

Andrew Swallow

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