About Security Reductions
Oblique Drive employs several primitives that generate a second set of data corresponding to a first set of data. The second set of data does not contain any information from the first set of data. For example, Basic Resolver makes extensive use of both the “8421” algorithm as well as the “1110” algorithm, which is examined below. Other protocols and software design are discussed on other pages.
Information of Data Sets
Let first set of data S1 represent any object having original content such as a file or a directory node. For each first set of data S1, a second set of data S2 is generated that does not contain any information from the first set of data S1. In the example below, assume all members of a first set of data S1 have the same length. Addition modulo-2 logical operations are performed between adjacent elements in cyclic order to generate a second set of data S2 in accordance with the relationship R as shown.
The one-way functionality of this transform is demonstrated as follows. It is observed that for all values, the addition modulo-2 sum of the second set of data S2 is always 0. Given the assertion (i.e. ), assume that all members of S1 are independent random numbers extracted from a Gaussian distribution. Because one member of S2 could then be dropped but derived again later by solving for the unknown member, this implies that random data is compressible – a contradiction of the pigeonhole principle. Therefore, the transform cannot be reversed. But is the addition modulo-2 sum of the second set of data S2 always 0? And how does the irreversibility of the transform prove that S2 does not contain any information from S1?
To show this, replace members of S2 with equivalent expressions of operations on members of S1 (i.e. ). The same expressions may then be rearranged according to the associative law (i.e. ). The result is clearly true for all values and confirms the initial assertion (i.e. ). Although one-way security can be achieved in this way, indistinguishability is achieved elsewhere.