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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
A block encryption processing idea taken from linear algebra
Posted: Jun 18, 2013 3:00 AM
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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,

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.

M. K. Shen

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