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| A steganographical application of the base representations of integers | |
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| Tweet Topic Started: Mar 22 2014, 07:10 PM (126 Views) | |
| mok-kong shen | Mar 22 2014, 07:10 PM Post #1 |
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NSA worthy
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Recently there has been a discussion in our forum on the use of the common base representation of integers for encryption processing, resulting in my implementation of NUMCODING (http://s13.zetaboards.com/Crypto/topic/7155855/1/) In the following we sketch a potential application of base representations of integers (see http://s13.zetaboards.com/Crypto/topic/7149584/1/ (Version 1.1.1)) to steganography, namely via letting the coefficients in the base representation of an integer (that is to be inconspicuously transmitted to the recipient) be encoded as certain agreed-upon kinds of objects to be placed in an appropriate cover picture. Let u be the integer to be sent and I = u + 1 > 0. Let there be m + 1 different types of objects agreed-upon by the communication partners and designated by their type indices k (0 <= k <= m). (Objects of different types may differentiate from one other according to their categories (e.g. apple, melon etc.), colours, sizes, orientations, etc.) There are two possible cases: (1) The sender is able to place objects into the picture in a certain ordering that can be discerned by the recipient. He uses the common base representation of I, with base value b = m + 1: I = a0 + a1*b + a2*b^2 + a3*b^3 + ....... and puts at the i-th position of the ordering an object of type index k = ai. (2) Establishing a discernable ordering of the objects in the picture is difficult or infeasible in practice. The sender uses a multiple base representation (see http://s13.zetaboards.com/Crypto/topic/7149584/1/ (Version 1.1)) of I, with an agreed-upon list of base values bi such that the number of objects of type index k that could occur in a picture is limited to be less than bk (0 <= k < m). (objects of type index k = m doesn't have such a limit): I = a0 + a1*b0 + a2*b0*b1 + a3*b0*b1*b2 + ....... + am*b1*b2*b3...*b_(m-1) and puts into the picture a total number, equal to ai, of objects of type index k = i. It should be remarked that (1) is a special case of (2) and common base is a special case of multiple base. This being so, it is certainly conceivable that under circumstances it may be desirable to employ (2) instead of (1), even where an ordering could have been exploited. (As stated, one has in (2) certain flexibility of limiting the number of occurrences of different objects in the picture.) For helpful critiques and comments I should be very grateful. [Addendum] For case (1) there is a method employing a set of objects of (fixed) numbers, i.e. 2 of one kind, 5 of another kind, etc.. The permutatiions of the ensemble of objects have a lexcicographical ordering and hence each permutation has a unique index in the list of all permutations. I published a C code for that elsewhere in 2012. I have now ported it to Python, see http://s13.zetaboards.com/Crypto/topic/7174259/1/. Edited by mok-kong shen, Mar 25 2014, 05:22 PM.
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7:28 PM Jul 11