Theory of Eve’s Triangle Enigma – Adacrypt
adacrypt
decrypt the cipher text item that the triangle represents by knowing
one more side. Only Alice and Bob know this side however and she is
reduced to guessing which one of an infinite set of possible sides is
the right one for her to use. This is the essence of vector
cryptography.
The creation of the side that she knows is a proper one-way function
performed by Alice in cryptography. Vector mathematics happens to be
the better way of implementing the triangle model.
The Triangle Model.
One side of the triangle is the cipher text vector, another side is
the trapdoor vector of the one-way function, the remaining side i.e.
the closing side, is the decryption key vector.
There can be many key holders thus creating a polygon of vector sides
but these always reduce to a triangle when every component of the
trapdoor is completed by each authorized key holder entering their key
component. Triangulation is then complete and the decryption can
proceed.
Theory
Alice and Bob believe that the traditional number line of arbitrary
direction is too transparent for cryptography so they decide to use a
directed number line for each plaintext that Alice enciphers. The
numerical representation of the plaintext in hand is assigned to this
line each time. The line is defined by its vector equation and the
integer numbers i.e. the code points are defined by the position
vector of the code point on the line relative to the origin (0,0,0).
A different line is used each time.
Lemma.
A position vector of a point in space is useless unless the origin to
which it is made relative is clearly defined.
This is the basis of vector cryptography.
Although Alice and Bob’s calculated position vector is true relative
to (0,0,0) it can also be declared as being true relative to any point
(x,y,z) in the whole of space quite legitimately. Alice and Bob see
an opportunity of confounding Eve here by conspiring to send the
publicly visible cipher text in position vector form as being relative
to some (x,y,z) instead of (0,0,0) in each case and later returning to
the computation origin (0,0,0) at decryption time. The upshot is a
string of cipher text items in the form of position vectors of
indeterminate origin, each one is different to the next – i.e. they
are totally useless to any interceptor such as Eve.
A different line and a different confusing origin (x,y,z) is used each
time, Alice and Bob agree on the change-of-origin that will be made
each time by adding an agreed vector to the correct origin in order to
give it a confusing displacement, they carefully record the change-of-
origin vector [(x,y,z) – (0,0,0)] each time and store the coefficients
of the latter in arrays of integers that represent the coefficients
of i , j, k. This serves both as encryption data at Alice’s end and
decryption data at Bob’s end. It is highly manageable by the computer
program and is not a problem no matter how convoluted this description
here may sound.
This ploy of a change-of-origin to a position vector is a uniquely
definitive mathematical one-way function. In cryptography it is a
trapdoor one-way function where the trapdoor is the change-of-origin
vector. In Eve’s Enigma, the trapdoor information is one side of the
triangle that she doesn’t know and when this is subtracted from the
visible cipher text vector it yields the third side as the computed
original position vector.
The cipher text string that Eve sees is a string of position vectors
that are of indeterminate origin to her, they each represent a single
side of her Enigma triangle that only Alice and Bob can complete.
Subtracting the change-of-origin vector from the cipher text gives Bob
the position vector that he needs to know and enables him to decipher
the cipher text back into the encryption code point on Alice’s
encryption line.
Decryption
When he receives cipher text from Alice Bob retrieves each
corresponding change-of-origin vector simply by sequentially reading
it as shared information from the arrays of the mutual data base that
they both use. He next subtracts this change-of-origin vector from the
cipher text vector to get Alice’s original position vector (relative
to (0,0,0) and goes on to decode this position vector, the result is
Alice’s original encryption number. He is able to decode this
encryption number back into its ASCII equivalent from the encryption
alphabet that they are using (additional to ASCII) and read the
information that Alice wants him to know. It is a reasonable caveat
that they must both keep their shared information secure from
adversaries.
Comment
The arrays of data in the mutually synchronized database that Alice
and Bob use are routinely shuffled and sliced simply as good practice
although there is nothing by way of cryptanalysis that can overcome
the one-way function that under pins the security of the ciphers that
are to hand, should that not be done.
It can be seen that the same plaintext can be enciphered in an
infinite number ways for sending to multiple receivers who could be
partners or simply trusted third parties, the implications to non-
repudiation schemes is apparent.
Readers with any modicum of vector mathematical understanding will
realize that this cryptography is theoretically unbreakable. It is a
first in main stream cryptography. The methodology contains two
mathematical firsts also by this writer, 1) Vector Factoring and 2) A
Mathematical one-way Function. No plaudits are being solicited for
this achievement but it is necessary to pre-empt plagiarism with this
time-stamped claim here.
This invention is cryptography ‘in waiting’ and will almost certainly
replace the RSA cipher sometime in the future. You don’t have to be
Nostradamus to see that. The greatest enemy to all round early
acceptance of this crypto type now is the intransigence of a dishonest
establishment who still seek to perpetuate the current weak pseudo-
based cryptography of the status quo instead of admitting that the
emperor is stark naked and it was a mistake made forty years ago not
to avail of the powerful new science of computing instead of pursuing
so-called asymmetric cryptography that is only ‘practically’
unbreakable and is dangerously susceptible to advancing increases in
computer power to day. The RSA cryptography uses computer power to
implement itself today but the design thinking of that cipher is old
fashioned, long hand and intensely number-theoretic in concept.
Computer science is being wasted in current cryptography.
This invention of vector cryptography being described here is immune
to increasing computer power for all time, it will benefit from any
increases in computer power that do occur however.
A more complete and expanded version of the theory of vector
cryptography that is only partly described here is available on
http://www.adacrypt.com under “ A New Approach to Cryptography.”
The program source code of an up and running cipher together with a
compiler is downloadable from the same website. – Enjoy – Adacrypt.
Gordon Burditt
>decrypt the cipher text item that the triangle represents by knowing
>one more side. Only Alice and Bob know this side however and she is
>reduced to guessing which one of an infinite set of possible sides is
>the right one for her to use.
There are not an infinite number of possible sides in this situation.
Only a finite number of sides will decrypt to a valid plaintext
(not necessarily the *correct* plaintext, just *any* plaintext),
which in your model is an integer of limited range.
>This is the essence of vector
>cryptography.
>
>The creation of the side that she knows is a proper one-way function
>performed by Alice in cryptography. Vector mathematics happens to be
>the better way of implementing the triangle model.
>
>The Triangle Model.
>
>One side of the triangle is the cipher text vector, another side is
>the trapdoor vector of the one-way function, the remaining side i.e.
>the closing side, is the decryption key vector.
>
>There can be many key holders thus creating a polygon of vector sides
>but these always reduce to a triangle when every component of the
>trapdoor is completed by each authorized key holder entering their key
>component. Triangulation is then complete and the decryption can
>proceed.
>
>Theory
>
>Alice and Bob believe that the traditional number line of arbitrary
>direction is too transparent for cryptography so they decide to use a
>directed number line for each plaintext that Alice enciphers. The
>numerical representation of the plaintext in hand is assigned to this
>line each time.
The numerical representation of the plaintext uses *what possible
range of values*?
>The line is defined by its vector equation and the
>integer numbers i.e. the code points are defined by the position
>vector of the code point on the line relative to the origin (0,0,0).
>A different line is used each time.
>
>Lemma.
>A position vector of a point in space is useless unless the origin to
>which it is made relative is clearly defined.
It doesn't matter whether it is *DEFINED*, it matters whether it
is *KNOWN* to the person attempting decryption. There's a difference.
If you'd quit re-using the shared database, you'd have a one time
pad, which is theoretically unbreakable.
>He next subtracts this change-of-origin vector from the
>cipher text vector to get Alice�s original position vector (relative
>to (0,0,0) and goes on to decode this position vector, the result is
>Alice�s original encryption number. He is able to decode this
>encryption number back into its ASCII equivalent from the encryption
>alphabet that they are using (additional to ASCII) and read the
>information that Alice wants him to know. It is a reasonable caveat
>that they must both keep their shared information secure from
>adversaries.
>
>Comment
>The arrays of data in the mutually synchronized database that Alice
>and Bob use are routinely shuffled and sliced simply as good practice
>although there is nothing by way of cryptanalysis that can overcome
>the one-way function that under pins the security of the ciphers that
>are to hand, should that not be done.
Yes, re-using the data in the synchronized database can overcome
the encryption. Any encryption is crackable if you keep using
a stupid key.
>It can be seen that the same plaintext can be enciphered in an
>infinite number ways for sending to multiple receivers who could be
>partners or simply trusted third parties, the implications to non-
>repudiation schemes is apparent.
No, you don't have any non-repudiation scheme here. This is symmetric
encryption. Bob can encrypt anything he wants, then claim Alice
did it. Further, in order to prove this in court, he'd have to give
up his shared database to the judge, thereby rendering any further
communication between Alice and Bob insecure until they change databases,
and any previous communication crackable by the judge.
>Readers with any modicum of vector mathematical understanding will
>realize that this cryptography is theoretically unbreakable. It is a
Not if you re-use key material.
>first in main stream cryptography.
No, you did NOT invent the One Time Pad, and you sorta copied it
badly.
>The methodology contains two
>mathematical firsts also by this writer, 1) Vector Factoring and 2) A
>Mathematical one-way Function. No plaudits are being solicited for
>this achievement but it is necessary to pre-empt plagiarism with this
>time-stamped claim here.
>This invention is cryptography �in waiting� and will almost certainly
>replace the RSA cipher sometime in the future.
Bullshit. RSA is public-key encryption, and your encryption is
symmetric. Your encryption will never replace RSA in any application
that depends on the public-key properties of RSA.
>You don�t have to be
>Nostradamus to see that. The greatest enemy to all round early
>acceptance of this crypto type now is the intransigence of a dishonest
>establishment who still seek to perpetuate the current weak pseudo-
>based cryptography of the status quo instead of admitting that the
>emperor is stark naked and it was a mistake made forty years ago not
>to avail of the powerful new science of computing instead of pursuing
>so-called asymmetric cryptography that is only �practically�
>unbreakable and is dangerously susceptible to advancing increases in
>computer power to day. The RSA cryptography uses computer power to
>implement itself today but the design thinking of that cipher is old
>fashioned, long hand and intensely number-theoretic in concept.
>Computer science is being wasted in current cryptography.
>This invention of vector cryptography being described here is immune
>to increasing computer power for all time, it will benefit from any
>increases in computer power that do occur however.
Vector cryptography is not a one time pad, and it is not theoretically
unbreakable.