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From: Mok-Kong Shen on 18 Jul 2010 14:23
Mok-Kong Shen wrote:
> [Addendum] Concerning item (3) of my post I like to add for
> completeness that one way of obtaining a sufficiently good PRNG
> for the purpose of the present context is IMHO what I proposed in
> the thread "A simple scheme of combining PRNGs" of 01.06.2010.
> As to the use of the Hill matrix, if one uses a 4*4 matrix, there
> are 16 (dynamically generated pseudo-random) elements corresponding
> to the 4 elements each of plaintext and ciphertext elements. There
> is thus here alone a very high degree of indeterminancy that thwarts
> the analysis. Note also that the assumed availability of a PRNG
> enables one to employ, if desired, some simple means of multiple
> encryption (i.e. in addition to the Hill matrix), e.g. xoring with
> the PRNG output, bit rotation in words and permutation of words in
> larger block of words.

Note that a 4*4 matrix results in a block effect of block length 128
bits (or 256 bits for 64 bit words).

M. K. Shen


From: Mok-Kong Shen on 24 Jul 2010 13:12
Mok-Kong Shen wrote:
> Mok-Kong Shen wrote:
>> [Addendum] Concerning item (3) of my post I like to add for
>> completeness that one way of obtaining a sufficiently good PRNG
>> for the purpose of the present context is IMHO what I proposed in
>> the thread "A simple scheme of combining PRNGs" of 01.06.2010.
>> As to the use of the Hill matrix, if one uses a 4*4 matrix, there
>> are 16 (dynamically generated pseudo-random) elements corresponding
>> to the 4 elements each of plaintext and ciphertext elements. There
>> is thus here alone a very high degree of indeterminancy that thwarts
>> the analysis. Note also that the assumed availability of a PRNG
>> enables one to employ, if desired, some simple means of multiple
>> encryption (i.e. in addition to the Hill matrix), e.g. xoring with
>> the PRNG output, bit rotation in words and permutation of words in
>> larger block of words.
>
> Note that a 4*4 matrix results in a block effect of block length 128
> bits (or 256 bits for 64 bit words).

To employ a non-singular Hill matrix, one could in our case, where
it is dynamically generated and used only for one single pair of
vectors of plaintext and ciphertext, conveniently have it in the form
as a product LU of two triangular matrices (say, with odd numbers on
the diagonal of U and 1's on the diagonal of L) without explicitly
multiplying them together. Further, one can simplify the computation
on decryption a bit, if the diagonal elements of U are also chosen to
be all 1's, since no calculation of the inverse of them will then be
necessary. This means that in the case of 4*4 one will have only 12
instead of 16 pseudo-randomly generated numbers to process a plaintext
vector of 4 elements. The indeterminancy is thus reduced from a factor
of 4 to 3, which is apparently nevertheless yet ample enough for the
purpose of thwarting analysis.

M. K. Shen


From: Greg Rose on 24 Jul 2010 13:34
In article <i2f6tj$gl9$03$1(a)news.t-online.com>,
Mok-Kong Shen <mok-kong.shen(a)t-online.de> wrote:
>Mok-Kong Shen wrote:
>> Mok-Kong Shen wrote:
>>> [Addendum] Concerning item (3) of my post I like to add for

Hey, this appears to be a new world record, M-K
replied to his reply to his reply to his addendum
to his original post! Reminds me of Gollum.

Greg.

--
From: Mok-Kong Shen on 24 Jul 2010 13:40
Greg Rose wrote:
>
> Mok-Kong Shen<mok-kong.shen(a)t-online.de> wrote:
>> Mok-Kong Shen wrote:
>>> Mok-Kong Shen wrote:
>>>> [Addendum] Concerning item (3) of my post I like to add for
>
> Hey, this appears to be a new world record, M-K
> replied to his reply to his reply to his addendum
> to his original post! Reminds me of Gollum.

If you have something scientific to say, then say so. If not, then
please don't waste bandwidth in this way, especially in view of the
fact that you also function as a moderator of another group, if I
don't err.

M. K. Shen

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