Skew Curve Cryptography – Further Analysis.

[adacrypt]

Considering the vector equation of the skew curve and tracking each
component (i, j, k) separately at time ‘t’ while remembering that the
plaintext has numerical representation t = some positive integer
(trying to keep it all as simple as possible here). The tracking is
terminated at time t = t.

Let t^4(i) + 7t (j) + t^2 (k) be the equation of motion of the point
‘P’ along the path bounded by the elapsed time between t = 0 and t =
t.

Note: [ f(t)(i) , g(t)(j) , h(t)(k)] may be any function in ‘t’
that Alice
and Bob agree to - I have guessed these vector functions here.

The initial displacement at time t = 0 is (x, y, z)
Path of a point defined by (i) alone is s = t^4 +x that is bounded by
s = x and s = P(i).
Path of a point defined by (j) alone is s = 7t + y that is bounded by
s = y and s = P(j).
Path of a point defined by (k) alone is s = t^2 + z that is bounded by
s = z and s = P(k)

All three paths intersect at the point P (i, j, k) which is defined by
a position vector P(t) (say) that comprises the ciphertext.

The separate paths serve as curvilinear number lines that Bob may use
to decrypt ‘t’ and decode it back to the plaintext that it
represents. He may use any path (no advantage in having multiple
paths like this but that is the nature of the beast).

Note: curvilinear number lines are less transparent than the
traditional number line – they are not inductively obvious - this is
the whole point of this cryptography

Given the ciphertext into her hand Eve is unable to backtrack to ‘t’
because she does not know the values of x, y, and z or the function
that connects ‘s’ with ‘t’.

Let experienced readers please note I am putting my head on the block
here in the interests of simplifying things for readers who are not
familiar with the applied mathematics. I am open to correction from
readers who are well versed in mechanics and physics as usual however
but remember I am going out on a limb in doing so.

* the most important key here in this cryptography is the initial
displacement (x, y, z) at time t = 0 - this is similar to the change-
of-origin ploy in previous work. The values of x,y,z are changed for
each fresh plaintext - these are strored in arrays as keys for calling
sequentially at run time of the cipher program.

The vector functions on (i, j, k) in 't' are further 'entanglement'
only but important additional keys nonetheless also.

- adacrypt

[adacrypt]

Skew Curve Cryptography – Further Analysis – Late Supplement.

Forgot to say – the skew curve proper (i.e. the combined curve formed
by the instantaneous collisions (intersections ) of the individual
paths) is the graph of all such intersections at P (t) for all time t
between t = 0 and t = t according to the equation of motion, s =

t^4(i) + 7t (j) + t^2 (k)

Amendment.

>Considering the vector equation of the skew curve and tracking each
>component (i, j, k) separately at time ‘t’ while remembering that the
>plaintext has numerical representation t = some positive integer
>(trying to keep it all as simple as possible here). The tracking is
>terminated at time t = t.

*while remembering that the

plaintext has numerical representation t = some positive integer

This should read :- t (max) = some positive integer <= the plaintext
representation.

t(max ) terminates the motion.

- adacrypt