## A cryptography observation: the odd wheel.

It is well known that the function 1/x generates a huge set of different numbers for x between 0 and 1. For this reason, this function can be used to transfrom a single piece of data into a wide range of possible alternatives. But you have to have a method to extract those alternatives and bind them to the range you require. I do this through the creation of an odd wheel, which is a range of numbers with an odd length. With this range defined, I then take the wider ranged number and subtract the odd wheel from it until my result lies within the range. Then I will have a result which is bound to my desired range, and that varies wildly with small changes in x.

Think of it like the more standard 360 degree circle. If I have an angle greater than 360 degrees, then my actual location on the circle is determined by subtracting 360 from my oversized angle until I get a result between 0 and 360. But, for say cryptographic applications an even numbered range has the potential of leaving one vulnerable to having a propensity for an even or odd result. If my x or my function for calculating the large widely range number has any tendency towards being even or odd, then an Even wheel will pass that tendency directly to my result, leaving me with a less secure range. However an odd wheel will switch whether the result is even or odd each time it iterates through the subtraction, leaving one with a better range as long as the magnitude of the wide ranging input is sufficiently varied.