# Spancrypt_1 – Scalable Key Cryptography.

All current cryptography is what I personally call “Encapsulation
Cryptography”. By this I mean that the key and cipher-text are
embedded together by some extraordinary means. The key has to be made
intractable to an adversary who knows that it is there also for the
finding by some other extraordinary mathematical means that is
available to him. The “means” per se is usually some very cunning
piece of mathematics that is selectively reversible to only two people
i.e. the entities of a secure communications channel. There is a huge
dearth of such mathematics however and with the advance of computer
power threatening even the few current ciphers in existence, the
situation is becoming parlous to the powers that be in secure
communications. All current cryptography requires massive
‘entanglement’ of some form to keep it safe from theft while the
encapsulated key is in transit.

It is safe to say that all future cryptography will be computer-driven
and will also be number-theoretic. Finding these extraordinary
mathematical means of encapsulation of keys is extremely difficult and
the result is that at the time of writing there is no cryptography
being used in main stream secure communications today that has the
much-sought cryptographic strength of being “theoretically
unbreakable” and is instead only “practically unbreakable”.
Furthermore, even that second-class state of secure communications is
under threat from increasing computer power and it could happen very
quickly that it becomes worthless with only very short notice.

In passing, I have invented cryptography that fits the bill but is not
yet in use, this is called “vector cryptography” and is theoretically
unbreakable but that is not what I want to talk about here.

Modern cryptography does not make proper use of computers and is
seriously remiss in that respect. There is palpable intransigence
also on the part of the academic establishment in not accepting that
there is better cryptography on the table that they are slow to accept
for fear of having to admit that they have been barking up the wrong
tree for nearly half a century. They have targeted complexity and
heavy mathematics as the solution to the problem of achieving perfect
secrecy of communications and have not made proper use of the enormous
of mutual databases that is possible with even the smallest of today’s
computers.

Separation Principle.

Mutual database technology does not require the huge entanglement of
current cryptography and works by keeping the key and the ciphertext
separate from each other meanwhile and bringing them together only at
the precise moment of decryption. The keys are kept in the mutual
databases of the entities i.e. stored as static arrays of data and
only a much watered-down form of the ciphertext now needs to go public
as email transmitted by ordinary public electronic means. If the
ciphertext is intercepted enroute it is totally useless to any
databases. As long as Alice and Bob keep their databases safe from
theft they can enjoy perfect security of communications at all times.
Clearly, this important caveat must be observed.

The upshot of separating the key from the ciphertext is that there is
no longer the need for the difficult mathematics that was needed to
make the key embedded in the ciphertext intractable to an adversary
and instead only a very benign relationship between them will suffice,
i.e. the simple inversion process of decryption need be nothing more
difficult than school-level arithmetic and subtraction. Obfuscation
is done by the mutual databases in the entities’ computers keeping the
keys separate and widely apart from the ciphertext, rather like the
chip’n pin technology of cash transaction systems.

In the cipher being promoted here I have chosen a simple spanning
algorithm to define a relationship that exists between the keys and
plaintext in ad hoc fashion and is inverted simply by reversing the
algorithm. A key and a ciphertext are called in paired, sequential,
synchronous order and decrypted into message-text one by one at high
speed. The user may use any other different algorithm they like in a
similar way. I have called this cipher “Spancrypt_1” because the name
is then a convenient reminder of the spanning process that uses it.
This form of spanning substitutes as a simple form of graphic number
addition in linear algebra that leaves no structural footprints that a
the sheer simplicity with which any reader may write a theoretically
unbreakable cipher of their very own. There is no glory in complexity
of method ever in mathematics, sufficient unto the need is enough.

The scheme is secured by the randomness of the long key-string, this
is generated automatically (at the design stage) by the encryption
algorithm and is simply a long string of non-repeating integers – it
is easy to procure. Any subset of this long key string (14250
integers in the one to hand) enables a message-length of the same size
to be encrypted. Larger messages are obtained by scrambling this long
key and re-using it again and again if needs be.

A downside, if it may be called that of my scheme, is that it requires
a one-off secure delivery of Alice’s copy software but that’s it then
for all time thereafter, there is no more need for any further
troublesome key exchanges by the entities in the entire future of the
secure channel after that. The scheme is extensible to the whole of
Unicode.

contains the cipher “Spancrypt_1”. The cipher has a tutorial/
diagnostic version that shows step-by-step working of the cipher
algorithm. This version also includes a graphic analysis of both the
plaintext and the associated ciphertext for six test files of
plaintext. It can be easily seen that there is no threat from attacks
by statistical experiment, by chosen plaintext attack or by Kasiski/
Babbage attack. Linear analysis, differential analysis and indeed all
numerical methods are non-starters because of the sporadic periodicity
that has been wrought by mathematical ‘spanning’ on the characters of
ASCII that normally have such predictable unit periodicity, by the
cipher.

This cipher works by creating a different number-line i.e. a number-
line that is of arbitrary direction but of different periodic scale,
for each and every plaintext character that is encrypted. This totally
precludes predictable regular structure that might be inductively
cryptanalysed by adversaries. The cipher being called “Spancrypt_1”
belongs in the group of ciphers called “Scalable Key” under the
generic class description of “Scalar Cryptography”. The cipher
belongs in the crypto class of “Symmetric Stream Cipher”

Note; Any set of non-repeating integers (not necessarily consecutive
numbers but ideally so) may be configured within suitable bounds to
comprise a random set of keys (variable name ‘StepChange’ in the
program source-code) in the context of the cipher algorithm; this
means any reader can write another similar cipher of any capability

that is more a practical daily work version.

Discerning readers who take the trouble will notice how the
distribution of the plaintext is totally diffused by the ciphertext in
this cipher, i.e. in a file of 10851 plaintext, 1826 space characters
(‘-‘) and 1824 ‘e’ Characters (‘e’) disappear (in relative frequency)
without visible trace. Together with the randomness of the keyset and
the sporadic periodicity of the ciphertext this makes it a totally
unbreakable yet simple cipher. – enjoy - adacrypt
.

## Relevant Pages

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