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Topic: A block encryption processing idea taken from linear algebra
Replies: 1   Last Post: Jun 27, 2013 4:28 AM

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Mok-Kong Shen

Posts: 629
Registered: 12/8/04
Re: A block encryption processing idea taken from linear algebra
Posted: Jun 27, 2013 4:28 AM
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Am 18.06.2013 09:00, schrieb Mok-Kong Shen:
> The iterative solution of a system of n linear equations can be
> formulated as follows:
> x1 := a11*x1 + a12*x2 + ... + a1n*xn + b1
> x2 := a21*x1 + a22*x2 + ... + a2n*xn + b2
> .....................
> xn := an1*x1 + an2*x2 + ... + ann*xn + bn
> where (in the so-called single-step or Seidel method) the assignments
> are performed sequentially. See V. N. Faddeeva, Computational Methods
> of Linear Algebra, p.117, Dover Publ., 1959. (Note that many textbooks
> of linear algebra present however a different, in fact less general,
> formulation.)
> Using this as a hint, we propose to do for block encryption processing
> of n blocks, x1, x2, ... xn, the follwoing, where the f's are
> invertible non-linear functions, the r's are pseudo-random numbers and
> the assignments are performed sequentially (the f's and the r's are
> (secret) key-dependent and different for different rounds, if more
> than one rounds are used, computation is mod 2**m for block size of
> m bits):
> x1 := f1(x1 + x2 ... + xn + r1)
> x2 := f2(x1 + x2 ... + xn + r2)
> ................
> xn := fn(x1 + x2 ... + xn + rn)
> Note that we have left out the multiplication with a's, which is
> deemed a justifiable simplicity since the f's are non-linear and
> further the r's are pseudo-random. Note also that the effect of
> block-chaining in the use of the common block ciphers is intrinsically
> present in our scheme. A viable variant of the scheme is to employ
> ^r instead of +r.

An implementation is now available in:

M. K. Shen

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