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| Note on obtaining key sequences from mathematical constants | |
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| Tweet Topic Started: Mar 27 2014, 06:40 PM (172 Views) | |
| mok-kong shen | Mar 27 2014, 06:40 PM Post #1 |
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NSA worthy
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Long sequences of decimal digits of certain mathematical constants are easily available on the Internet. The digits of sqrt(2), Pi and e are commonly believed to be normal (see http://en.wikipedia.org/wiki/Normal_number). An often recurring idea in discussions is therefore to choose a secret offset and use the digits of such constants beginning at the offset as a key sequence. However, opinions are often heard doubting the security, i.e. whether the opponent couldn't under circumstances somehow find the sequence. I suppose a simple practical way to enhance the security is decimation. Borrowing the underlying idea of the shrinking generator, with two decimal digit sequences (both could IMHO even be from the same mathematical constant but at different locations) one could use one sequence A to decimate the other sequence B according to a rule like the following: If the current digit of A is d and d >= k (k is a chosen constant in [1,9]), then skip one digit of B and output the next digit of B (with updating of the current digit of A to its next digit). |
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| fiziwig | Mar 27 2014, 07:17 PM Post #2 |
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Elite member
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Another approach would be to use two constants and two offsets and generate the sum (mod 10) of the digits of the two constants. So you could, for example, start with digit number 36,893,251 of pi and digit number 82,643,992 of sqrt(2) then add subsequent digits (mod 10) to create a new sequence. The enemy would have to know which two constants you used and which two starting points. That seems like it would be pretty secure. |
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| jdege | Mar 27 2014, 07:56 PM Post #3 |
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NSA worthy
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You have to assume that Eve would know everything about your system, except for the two numbers. We can accept as given that the generated key sequence would be random, so the only remaining issue is whether the system is subject to search. It's generally accepted that 128-bit keys are proof against exhaustive search. You're multiplying two 8-digit numbers. 16 digits is equivalent to a 53-bit key. Weaker than DES. Maybe four 8-digit numbers? |
| When cryptography is outlawed, bayl bhgynjf jvyy unir cevinpl. | |
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7:27 PM Jul 11