On Distributed Communications Series
IX. Security, Secrecy, and Tamper-Free Considerations
Use of a Function of N-Boolean Variables as a Second-Order Modifier for "Next-Key" Generation
In the foregoing text, little was said about the types and the range of operations possible in modifying the key in the end-to-end auto-key subsystem. This Appendix lends some insight into the added complexity of analysis that can be created for the eavesdropper by simply varying the logical addition operator.
In Fig. 5 three drum bands, each containing 866 bits, are shown. The first band contains the key used to decrypt the last Message Block; the second drum band stores text in the clear that has been derived by use of the old key; and the third drum band stores a new key computed by a "black box," labeled "Z".
A, B, and C, could, for example, represent three magnetic heads on the Multiplexing Station drum, 16 bits apart. Similarly, D, E, and F, would represent a second set of three heads. The box, Z, contains Boolean logic which performs "some" operational function upon the old key for the sake of increasing complexity. Consider the six separate heads to form six separate inputs. We ask, "How many different ways can six inputs be logically organized to form separate and distinct output functions?"
Any Boolean function can be expressed as the logical addition of a series of "min-terms. Each min-term is a logical product of each of the fundamental inputs or its logical complement. Any logical function can be expressed as a series of points on a Veitch Diagram (see Fig. 6).
Thus, we can have
allowable combinations for only six variables. This number almost "explodes" when the number of variables is raised. For example, let N equal the number of variables and compute the number of separate logical functions possible:
Of course, rather complex logic circuitry is required for many of these combinations, but many of the functions can be created with only a small portion of the full complement of 384 diodes.
Thus, it is seen that rather simple straightforward techniques can be used at this point to add another layer of complexity, further compounding the problems of the would-be eavesdropper.