Nonlinear dynamic substitution devices and methods for block substitutions

Claim 1

A method of encryption by substituting for any one of the 2 n unique clear text books of n bit binary numbers an associated unique encrypted block of n bit binary numbers comprising the steps of: (a) finding a first matrix of 2 n equations, each equation representing the module 2 addition of one of the 2 n clear text blocks with a unique one of 2 n bit numbers to provide an associated unique intermediate n bit block, all of the equations in the first matrix of 2 n equations being characterized by the vector sum modulo 2 of any number of the equations also being one of the equations in the first matrix, the equations including the null equation Θ⊕Θ=Θ and the remaining 2 n -1 equations being orderable as follows: ______________________________________ Equation # ______________________________________ 1 x.sub.m ⊕ x.sub.1 = x.sub.1-p 2 x.sub.1 ⊕ x.sub.2 = x.sub.2-p . . . . . . . . . . . . j x.sub.j-1 ⊕ x.sub.j = x.sub.j-p . . . . . . . . . . . . m x.sub.m-1 ⊕ x.sub.m = x.sub.m-p ______________________________________ where m=2 n -1 (b) modifying a plurality of the nonzero 2 n -1 equations in the first matrix of 2 n equations to provide a second matrix of 2 n equations, the plurality of equations being modified so that the modified plurality of equations collectively map the same clear text blocks to the same unique n bit intermediate blocks as the corresponding unmodified equations, but each in a different manner so that each of the modified equations in the plurality is not the sum modulo 2 of any number of the unmodified equations left over and not included in the modified plurality of equations; the second matrix of 2 n equations consisting of the modified plurality and the remaining unmodified equations from the first matrix of 2 n equations; and (c) for each clear text block to be encrypted, adding modulo 2 to that block, the unique one of the 2 n n bit numbers associated therewith in accordance with the associated equation of the second matrix of 2 n equations to obtain the encrypted block.

Claim 2

A method of encryption by substituting for any one of the 2 n unique clear text books of n bit binary numbers an associated unique encrypted block of n bit binary numbers comprising the steps of: (a) finding a first matrix of 2 n equations, each equation representing the module 2 addition of one of the 2 n clear text blocks with a unique one of 2 n bit numbers to provide an associated unique intermediate n bit block, all of the equations in the first matrix of 2 n equations being characterized by the vector sum modulo 2 of any number of the equations also being one of the equations in the first matrix, the equations including the null equation Θ⊕Θ=Θ and the remaining 2 n -1 equations being orderable as follows: ______________________________________ Equation # ______________________________________ 1 x.sub.m ⊕ x.sub.1 = x.sub.1-p 2 x.sub.1 ⊕ x.sub.2 = x.sub.2-p . . . . . . . . . . . . j x.sub.j-1 ⊕ x.sub.j = x.sub.j-p . . . . . . . . . . . . m x.sub.m-1 ⊕ x.sub.m = x.sub.m-p ______________________________________ where m=2 n -1 (b) modifying a plurality of the nonzero 2 n -1 equations in the first matrix of 2 n equations to provide a second matrix of 2 n equations, the plurality of equations being modified so that the modified plurality of equations collectively map the same clear text blocks to the same unique n bit intermediate blocks as the corresponding unmodified equations, but each in a different manner so that each of the modified equations in the plurality is not the sum modulo 2 of any number of the unmodified equations left over and not included in the modified plurality of equations; the second matrix of 2 n equations consisting of the modified plurality and the remaining unmodified equations from the first matrix of 2 n equations; and (c) for each clear text block to be encrypted, adding modulo 2 to that block, the unique one of the 2 n n bit numbers associated therewith in accordance with the associated equation of the second matrix of 2 n equations to obtain the encrypted block.

Claim 5

The method of claims 1 or 2 wherein in step (b), a plurality of the equations in the first matrix of 2 n equations which are to be modified begins with a first set of four consecutive equations, a fifth equation which is the vector sum modulo 2 of the first three of the four consecutive equations, and a sixth equation which is the vector sum modulo 2 of the last three of the four consecutive equations, the equations being modified by adding vectorially to the six equations, the following equations: to equations 1 and q (x.sub.1 ⊕x.sub.2)⊕(x.sub.1 ⊕x.sub.2)=Θ to equations 2 and 3 (x.sub.1 ⊕x.sub.3)⊕(x.sub.1 ⊕x.sub.3)=Θ to equations 4 and q+1 (x.sub.2 ⊕x.sub.3)⊕(x.sub.2 ⊕x.sub.3)=Θ wherein for purposes of the foregoing equations of the first set the first matrix of equations are ordered so that the first of the four consecutive equations is x.sub.m ⊕x.sub.1 =x.sub.1-p.