Gray code number frameworks otherwise called the binary reflected dark code (BRGC) system is a number framework in which two progressive codes vary in only one

bit position. Its generalization has been done such that some combinatorial articles were orchestrated with the end goal that no two back to back components in the rundown vary in some a priori properties.

The

bit position is decided by the quantum position with certain functions, where [|[alpha]|.sup.2] decides the probability that the

bit position is in the '0' state and [|[beta]|.sup.2] decides the probability that the

bit position is in the '1' state.

Thus, the sum for each

bit position in an elementary adder is generated serially only after the previous

bit position has been summed and a carry being propagated into the next position.

The digital image encryption algorithm proposed in this paper includes the following: first, bit permutation, the use of the butterfly network to achieve each pixel

bit position permutation; second, pixel location scrambling transforms.

[j.sub.m]}is the set of indexes whose corresponding

bit position in y is 1, and [R.sub.0] = {[j.sub.m+i] [j.sub.m+2], ...

[??], for x [member of] {0,1}, a special case of [i.sub.x] for i = 0: Transitions for the rightmost bit are simplified, since there is no

bit position with j < i and hence we do not need to use [??], [??], [??], [??].

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], a special case of [i.sub.x] for i = 0: Transitions for the rightmost bit are simplified, since there is no

bit position with j < i and hence we do not need to use [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

If the pattern is not found, the window slides one

bit position. If the pattern is found, the window is reset to the bit after the found pattern, and the search resumes.

With a bit permutation BP, a value of the

bit position i is moved to the

bit position j, where

If r at each received

bit position is known to the receiver, we call this case known channel state information (CSI).

3-Analysis of Hamming Weight According to

Bit Position (Strong S-box).

Thus F bit-slice files one for each

bit position of the set signatures are used.