Appendix-C. A Worked Example. - Scalable Key Cryptography.
adacrypt
the receiving entity respectively in some crypto circles although a
lot of people do not use the expressions and I suspect it is because
it is often disconcerting to talk with such familiarity about complete
strangers. It does save the repeated verbalising of large mouthfuls
of the English language and I shall use them here for that reason.
Alice is the administrator of an office secure network.
She has set the scope of her infrastructure encryption scheme at 14250
characters of message length capability. => she wants to be able to
send messages this long if needs be =>
X = 14250 + 63 = 14313
Lower Bound of N = 14313 + 127 = 14440
Upper Bound of N = 2(14313 + 32)= 2 x 14245 = 28690
So, the range of N is 14440 … 28690 inclusive (14440<= N <=28690)
The encryption algorithm is,
[(PlainText +X) + (Key+ X)(Mod N) = a residue (modulo N)
Cipher text = residue – N
Let us say that Alice wants to encrypt the letter Q (Capital Q) ( 81
in ASCII)
Let us say also that the instantaneous key she is using is the
‘$’(dollar sign) (36 in ASCII)
Let us say also that the instantaneous modulus N is 17359.
Then,
[(81 +14313) +(36 +14313)] (MOD 17359) = (14394 + 14349)(MOD 17359) =
11384
Cipher text = 11384 – 17359 = -5975 (in practice this is made positive
by multiplying it by (-1)
ð Cipher text = 5975
The decryption algorithm is,
Plaintext = Cipher text + 2N – 2X - Key
Cipher text = 5975 x (-1) = -5975
Then,
Plaintext (as message text) = -5975 + (2 x 17359) – (2 x 14313) – 36 =
81
Decoded back in ASCII 81 => ‘Q’ as expected.
Comment. There are 95x95x14250 possible permutations of (Plaintext,
Key, Modulus N) as encryption transformations in Alice’s scheme i.e. a
possibility space of 128606250.
(large possibility spaces mean nothing in cryptography of course).
The reader might like to try encrypting a few of your own characters.
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WTShaw
That's not a large keyspace as just for permutations of your set there
are 95! possibilities.
On first glance, I remember that there are a number of working
algorithms that are in the same general area that you are in. I'll
look further at your ideas but my feeling is that even though you may
be on some sort of useful track, you have not left the station...and I
think that's fair.
adacrypt
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Complements of the Season first of all.
The way this cryptography works is that it takes smooth encryption
data i.e. the set of integers and turns it into a set of ugly, hugely
disparate, discontinuities - it is then only necessary to apply an
almost benign transformation to achieve secure ciphertext - that is
the exact opposite of current conventional crypto schemes. - the main
key is the set of moduli being used as 'N' (a 14250 strong random set
of positive integers) - this and the alhphanumeric set of 95 from
ASCII are scarmbled and sliced repeatededly, but accordingly to rule
so as to achieve profound randomness but are used only once within a
message i.e. - uses the resulting keylength only once in that message.
- complete multiple modules of the base 95 set are bona fide random
key sets when the multiple is discreet. - the key space is then 95**n
whatever the discrete multiplier 'n' is - in any case the size of a
random key set in this case has no bearing on the random state -
conversely to large keyspaces being insignificant small key sets are
not impaired by being small as the other extreme .
I am working on a universal crypto scheme that reduces the whole of
Unicode encryption to a very simple algorithm that requires no more
then 4 megabytes of sourcecode - it is only a mattter of calculating
the appropriate parameters from the code point max and min values of
any language. - the target is a program for any hand held computer in
the field - please let know if you find anthing else here - regards -
Austin O' Byrne
adacrypt
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Correction : 95**n should read (95!)**n
That is unthinkably large number. - 95 ! alone is in excess of a 490-
bit number - n is 150 in the cipher under discussion.
