Re: Alice Encrypts - Adacrypt
- From: Bryan Olson <fakeaddress@xxxxxxxxxxx>
- Date: Wed, 11 Apr 2007 00:08:24 -0700
AdaCrypt wrote:
This involves demonstrating the Algebraic Primary Factors of a Vector
and how a 'seeding pair' is found at each interception of an inclined
plane by the fixed reference frame defined by the X, Y, Z, axes.
Forming the equations of more 'Factor Lines' that emanate from these
seeding pairs comes next and developing these lines recursively to
form the full infinite set of factors of any vector completes the
factoring process. In practice here, only vectors that have three non-
zero coefficients of i, j, k will be chosen as defining normals of
planes for encryption work.
How it works.
Alice takes a suitable vector (more about this later) and proposes it
as being the defining normal of a plane that passes through the
origin.
I think I understand some of that. We're working in 3-space; as
usual we call the axes (X, Y, Z), and i, j and k are the unit
vectors along the X, Y and Z axes respectively. The scheme shares
a vector v = [a, b, c], which is shorthand for ai + bj + ck, and
from v determines the plain normal to v and containing the origin.
That makes sense because for any non-zero vector in 3-space,
there is exactly one plain normal to the vector and containing
the origin.
How hard is finding this plain, given the vector? Not very. The
plain normal to vector [a, b, c], and containing the origin, is
the set of points (x, y, z) satisfying:
x*a + y*b + z*c = 0.
Proof:
This set of points contains the origin:
0*a + 0*b + 0*c = 0.
This set of points is a plain:
All terms are linear, and any real values for any two of
the three parameters {x, y, z} are satisfiable, and
determine the third.
This plain is normal to v = ai + bj + cz:
A plain containing the origin is a vector space, and for
any (x, y, z) in the plain, the dot product with
[a, b, c] is x*a + y*b + z*c which is zero.
By means of a special factoring process that has been
developed already she finds the seeding pairs mentioned above and
edits them so as to define a directed number line that she will use
as her encryption transformation line for the current plaintext of her
secure message to Bob.
You lost me.
Note that this plane is now a vector space of non-parallel vectors
that has an infinite number of members.
Wrong, though it scores two out of three. True: "this plain" is a
vector space, because it is a plain containing the origin. It has
an infinite number of members, as does any non-trivial vector space
over the reals. What goes wrong is the bit: "of non-parallel
vectors". That is false at best. What vector space does not
contain any parallel vectors?
Alice however will only use
it one member of the set. She will take her current character from
ASCII or Unicode, renumber it according to her own encryption alphabet
(more later) which also binds her to a digital signature, assigns the
new number to this private line that she has just defined for herself,
notes the position vector of her number (code point now) on the line
and she will nominate that position vector Pn as her ciphertext vector
Well, this -- and the rest -- reads like gibberish. I know most of
words, and bits may mean something, but whole strikes me as nonsense.
-Bryan
for that plaintext. She will not use the same plane again for.
anything else.
In order to obscure her ciphertext vector now called Pn while it is in
transit to Bob she will give it a hefty change of origin from another
domain of 8000 such vectors that are scrambled, sliced and re-
circulated continuously during the session. A fresh change of origin
is given to each Pn of ciphertext that she generates.
For her next plaintext Alice will repeat this process, over and over
again, using a new normal vector, a new plane, a new number line, a
new Pn , and a new change of origin. Her actual encryption software
has a huge amount of extra entanglement built in on top of all this
also but let the reader note well, nothing extra is ascribed as
security to this extra contrived entanglement, the change of origin is
a stand alone one-way function guaranteeing perfect secrecy as long as
Alice and Bob keep secret their shared knowledge.
It is so on like this to completion of the encryption of Alice's
message into a long string of vectors as demonstrated earlier
elsewhere,
The writer is not satisfied with this textual account alone and is
preparing a website supplement of everything to do with the
encryption / decryption process for the perusal of and criticism by
the community. That may take a few weeks unfortunately. In the
meantime perhaps you will be able to follow the algorithm from what is
written here.- Adacrypt
PS .The Algebraic factors need large calliper brackets that I cannot
produce here so they are not being shown here just yet.
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