Example: Modulo 2 addition, denoted by the symbol H, is defined by the following rules which apply to the binary symbols 0 and 1; 0˜0 = 1˜1 = 0 and 0˜1 = 1˜0 = 1. Modulo 2 adding a PN sequence to a binary symbol stream changes the binary symbol half the time and leaves it unchanged the other half of the time. Hence, observing the scrambled symbol stream without knowing the PN sequence tells you nothing about what the underlying data symbols really are.

By replacing the binary symbol 0 with the number +1 and replacing the binary symbol 1 with the number -1, the rules of modulo 2 addition become equivalent to the rules of ordinary multiplication. That is 0H0 =1H1 = 0 becomes 1x1 = -1x-1 = 1 and 0H1 = 1H0 = 1 becomes 1x-1 = -1x1 = -1. Hence, Privacy Scrambling may be viewed as the modulo 2 summing of two binary streams having equal rates or the multiplication of a bipolar voltage symbol signal with a bipolar voltage PN sequence again each bipolar signal having the same rate. In electronic circuits it is much easier to implement Privacy Scrambling using modulo 2 adders, but in explaining scrambling simple multiplication sometimes makes for better understanding. For instance, unscrambling a private message is accomplished using a synchronized PN generator at the receiver. The received private signal is of the form PNs(t-t)s(t-t). The receiver forms PNs(t-x)PNs(t-t)s(t-t) which equals s(t-t) when x equals t.

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