```Date: Jun 17, 2013 11:18 AM
Author: Mok-Kong Shen
Subject: A block encryption processing idea taken from linear algebra

The iterative solution of a system of n linear equations can beformulated as follows:x1 := a11*x1 + a12*x2 + ... + a1n*xn + b1x2 := a21*x1 + a22*x2 + ... + a2n*xn + b2    .....................xn := an1*x1 + an2*x2 + ... + ann*xn + bnwhere (in the so-called single-step method) the assignments areperformed sequentially. See V. N. Faddeeva, Computational Methods ofLinear Algebra, p.117, Dover Publ., 1959. (Note that many textbooksof linear algebra present however a different, in fact less general,formulation.)Using this as a hint, we propose to do for block encryption processingof n blocks, x1, x2, ... xn, the follwoing, where the f's areinvertible non-linear functions, the r's are pseudo-random numbers andthe assignments are performed sequentially (the f's and the r's are(secret) key-dependent and different for different rounds, if morethen one rounds are used, computation is mod 2**m for block size ofm 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 isdeemed a justifiable simplicity since the f's are non-linear andfurther the r's are pseudo-random. Note also that the effect ofblock-chaining in the use of the common block ciphers is intrinsicallypresent in our scheme. A viable variant of the scheme is to employ^r instead of +r.M. K. Shen
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