The One-Way Function.



Two points in space can be defined by the position vector that
connects the two points.

In everyday standard usage one of the points is taken to be fixed at
(0,0,0) and every other point in the whole of space can be expressed
as being relative to this point.

But users are not bound to always uses (0,0,0) as the standard
reference and they can agree between themselves to use another private
reference point at say (x,y,z ) to define points in space whenever
they need to. The position vector is then totally different to what
it would be relative to (0,0,0). Only the users know just how
different because they alone are privy to (x,y,z) which could be any
point in the infinity of space.

With knowledge of (x,y,z) any person who knows this can navigate to
(0,0,0) and find the correct position vector relative to (0,0,0) when
that is needed but (x,y,z) could be any one of an infinite number of
confusingly different values in the whole of space when users decide
to keep it secret.

There is no mathematical means whatever by which (x,y,z) can be
deduced only the users know and they alone can provide the information
(but of course they are not telling).

When the users are Alice and Bob in a secure communications scheme
this ploy is called a change-of-origin. I liken it to a transfer of
data from a human memory to a computer memory that they alone can
implement and supply the correct values of (x,y,z) that enable
decryption to proceed with a correct result.

They calculate ciphertext according to (0,0,0) but publish it as being
relative to (x,y.z) and go back to (0,0,0) again at decryption time.

I am calling this a definitive one-way mathematical function in
cryptography – one-way simply because that is what it is i.e. non-
invertible by any mathematical means albeit a proper mathematical
function per se at the same time.

This powerful ploy guarantees my cipher against the attack described
as attack 1) that is foremost in basic design priority, called known
ciphertext attack.

I have no evidence that there is such a thing in academia as a “one-
way” function in mathematical parlance. (Never mind the Cryptography
Handbooks – they are not quotable outside of cryptography).

Anybody? I would appreciate any information but please quote the
source.

- adacrypt
.