Skew Curve Cryptography – How it Works.

[adacrypt]

Let,

t^4(i) + 7 (j) + t^2 (k) be the equation of motion of the point ‘P’

Note : [ f(t)(I) , g(t)(j) , H(t)(K)] may be anything that Alice
and Bob agree - I have guessed these vector functions here.

A value is assigned to ‘t’ as being the numerical representation of
the plaintext to enciphered.

Using this equation and this value of ‘t’ as the operand Alice and Bob
calculate the displacement of ‘P’ from time ‘t’ = 0 to time ‘t’ = t
i.e. relative to some starting point which they alone are privy.

They would be very foolish to start the motion at (0,0,0) for t = 0
each time so they instead start at some variable point (x, y, z) which
they discard for each fresh plaintext. They save the details of each
(x,y,z) which they save as key material however.

They express the displacement calculated privately as relative to (x,
y, z) between themselves but publicly (to Eve) they give each
ciphertext as being the displacement relative to (0,0,0). This is a
deliberate piece of entanglement designed as the stumbling block to
Eve that secures the cipher.


Without knowledge of (x,y,z) it is impossible for Eve to navigate to
that point and find the true displacement that was given to ‘P’.

Bob however has full knowledge of (x,y,z) since it is an element in
the array of keys in his mutual database and is able to call the
vector (x,y,z) accurately.

Then,

Legitimate Decryption.

True displacement of ‘P’ i.e. relative to (x,y,z) = Ciphertext –
(x,y,z)

The plaintext is found by solving for ‘t’ in any one of the
coefficients

f(t)(i) + g(t)(j0 + h(t) k , ( I would check all three to make sure
they coincide)


‘t’ is decoded back into the plaintext it represents.


This example is coming off the top of my head as I write - its ok
however.

- adacrypt