Lumpy Data and Randomness  

Today’s students may not use the terms ‘lumpy’ data or its opposite ‘smooth’ data but they still exist however. National coinage is an example of a medium that changes in sudden steps like the jump between one cent and a nickel, then to a dime etc. Postage stamps go like that also – there are lots more of examples of lumpy data in everyday life. Smooth data on the other hand usually changes in a ‘ramped’ fashion – a sloping line that may be the visible ramp change itself, or it may be hidden from view on a curved graph but findable as the ‘slope’. Discontinuous data just stops dead periodically or goes asymptotic and is neither of these.

Putting these on the ‘back burner’ now just for the present and taking a look at randomness as an essential force in cryptography.

Microsoft Encarta has the best description of randomness that anybody could ask for, I quote

-random: without a pattern; done , chosen, or occurring without a specific pattern. plan, or connection.

-randomize –make random: to arrange or select items so that no specific pattern or order determines the resulting arrangement or the selection process.

-random number – number from a sequence without a pattern: any series of numbers that have no pattern in their progression.

These definitions are quoted verbatim so as to demonstrate that there is no out-of-context prevarication anywhere in the present text. This exposure is being made here after a lot of searching in many so-called good information sources. Let the reader please not feel patronised by it.

Personal comment: ‘random’ is a lagging property that comes after the event and is either totally true or totally false. A lot of textbooks talk about randomly selecting numbers as if randomness was being generated by the process when in fact it applies as the static state of the outcome – the very existence of randomness per se is still ‘sub judice’ by the authorities in mathematics and therefore cryptography also. Textbooks often imply also that there are ‘orders’ of randomness when this is not so in maths or cryptography.

In the vector cryptography being expounded here, each item of cipher-text is a set of three integers. The long string of public keys that comprises the message ciphertext is an infinite sequence, by definition, of these sets. The rule of the sequence is the algorithm of the cipher that is known only to Alice and Bob and the pattern of the sequence is the relationship that exists in the individual sets of three integers in how the sets compare to each other – set with set, that is.

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