There is a man on the giant island called Great Britain who is brave. His essays
on his weak crypto remind me of the thought experiments of Einstein. He also
used a spanning nomenclature to describe three dimensional spaces. He
used rulers and rods to measure space and he rejected the aether. So
also adacrypt has a spanner for mechanical seeming thought experiments
which he generously shares on sci.cry in the presence of DasFox
and his team of automatons. The rectilinear grid of integers within
which the 14250 character weak crypto key operates may be analogous to a crystal
lattice. A vulnerability therefore exists where X-Ray crystallography
uses Bragg diffraction to expose the structure and content of
Spancrypt_1. This is more than a metaphor to expect the X-Rays of math
and Boole to someday break adacrypt's construct. Although his
perseverance and verbosity are admirable, his assailants are legion.
Keep up the good work there on the island of Great Britain. You are an
asset beyond palladium! Your spanners may replace rulers and rods, but
relativistic cryptography is subject to length dilation as Einstein
has calculated only with the help of Minkowski and Lorentz. Who will
step forward to be adacrypt’s Minkowski?
He says:
"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
power of computer systems. This article is promoting the technology
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
adversary who does not have access to the keys in Alice and Bob’s
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
the ciphertext that is made deliberately sporadic, it hides the
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
cryptanalyst could use. The salient thing about this cryptography is
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.
The download on free offer from my website at http://www.scalarcryptography.co.uk
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
very easily, off the top of your head so to speak.
The cipher on download offer also contains a no-frills second version
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
> I'm pleased that you are au fait with it all - please help out by
> disseminating it on "Popular Cryptography Magazine" - regards -
> adacrypt "
Yes, the Spring Issue is covering your teachings. Einstein also was,
according to his teacher Minkowski, "A slow dog", mathematically. That
did not matter. The energy of Einstein and adacrypt prevailed as a
team of mathematicians self-assembled around the seminal thought
experiments. Minkowski was an expert at number theory :
"Minkowski explored the arithmetic of quadratic forms, especially
concerning n variables, and his research into that topic led him to
consider certain geometric properties in a space of n dimensions. In
1896, he presented his geometry of numbers, a geometrical method that
solved problems in number theory."
http://en.wikipedia.org/wiki/Hermann_Minkowski
Where are the Minkowskis and Levi-Civitas of 2011 when adacrypt needs
you? Step up and do the heavy lifting to deliver this weak crypto.
The legend continues, even to this day, Tuesday, March 22, 2011. Adacrypt continues to post new insights on sci.cry while a band of itinerant critics harangue him without mercy. Safe on his giant island, seemingly aloof to the tragedies in Fukushima and Iraq, adacrypt has prevailed.
adacrypt wrote:
> > > "The mathematician who introduced me to cryptography
> > > is or was, interested in cryptography also. In passing, he turned
> > > down the presidency of an Arab country east of Suez once upon a time,
> > > I think the price of bullet-proof vests may have put him off."
Globemaker asked,
> Dear adacrypt, are you referring to Dr. Ahmed Chalabi, a mathematician
> from Iraq?
> http://www.sourcewatch.org/index.php?title=Ahmed_Chalabi
"Yes indeed - I had no idea that he was such a publicly known figure
although I had guessed at the degree of involvement with the US.
Mrs Chalabi is a delightful cook of Lebanese cuisine and the family
are really nice people - regards" - adacrypt.
> Great, there have been rumors about adacrypt and Chalabi, but it is
> good to see you verify it in the open. Please tell us more: how did
> you first meet him? Did he put an ad in the London newspaper seeking a
> science officer or progammer to be hired?
"Nope.
I worked in the building where he has a family flat and I became aware
that he was a mathematician. I approached him one day and introduced
him to my factoring theorem and invited him to have a read and to
comment on it. Having read my stuff he came back later and said to me
did I know anything about cryptography (my background is marine
engineering => running oil tankers, drill ships. shipbuilding, power
stations world wide etc. At that stage I didn't want to continue in
high pressure positions of employment and decide to settle ashore in a
building services & maintenance security role in a London block of
flats).
I was not a close friend of Ahmed Chalabi but I shared some
interesting problems by way of mathematical challenges that he
occasionally put to me. I have a high regard for him and his family
although I haven' seen anything of any of them for nearly ten years
now. I have heard some innuendo in the press and frankly I ignore
this - given the volatile situation in his home country I would not
believe anything I hear - I have worked in some Arab countries and
know their ways a little so I say that if you can make a fast buck
faster than the rest then that is par for the course by their own
standards.
Ahmad is still fiercely loyal to the US - I can vouch for that.
About the cryptography, I wrote my first vector cipher within a few
days of being introduced to cryptography by Ahmad Chalabi and I have
spent the past 12 years approximately defending it against detractors
in sci crypt who haven't a hope in hell of ever understanding it.
I get the impression that I may have been under surveillance because
of my having known Ahmad and his role in the Iraq campaign. If so
then it was completely unnecessary - I have a great regard for the
whole family but cannot say that I am close to them. Ahmad always
came across to me as being fiercely loyal to Uncle Sam" - adacrypt
............................
Gööd work with incredible value is revealed next ! Here is the math of adacrypt, spelled in Cyrillic or Greek, for your entertainment from January 6, 2011 due to jbriggs444 :
ηττπ://ωωω.δερκειλερ.cομ/Νεωσγρουπσ/σcι.cρξπτ/2011-01/μσγ00071.ητμλ
Фром: Шбриггс444 <Шбриггс444@ххххххххх>
Дате: Тчу, 6 Јан 2011 06:42:58 -0800 (ПСТ)
Он Деш 30 2010, 8:55 пм, гор...@ххххххххххххххххх (Гордон Бурдитт)
ыроте:
Оч. И сее И'ще беен ыастинг мз тиме трзинг то маке сенсе оф тчис. И'лл
траде зоу зоур алгоритчм фор тче десигн оф а перпетуал мотион машчине
И'ще гот.
И ыастед а гоод бит оф мз тиме ас ыелл. Ит ис ан амажинг ыеб оф
обфусшатион лазеред он а трищиал анд брокен алгоритчм.
Ычат фоллоыс ис ан аналзсис оф Адашрзптс алгоритчм анд а рендеринг оф
ит
инто а феы линес оф де-обфусшатед псеудошоде.
Тче кез инсигчт то тче тчинг ис буриед ин тче счорт форм десшриптион:
"
Еншрзптион.
[(Х + Кез) + (Х + Плаинтехт)] (Модуло Н) = а ресидуе >= 0
Шипчертехт = ресидуе – Н
Дешрзптион.
Дешрзптион Кез ≡ ресидуе + Н
Плаинтехт (ас мессагетехт интегер) = Шипчертехт + 2Н – 2Х – Кез.
"
Тчис ис шчараштер бз шчараштер аддитион, субтраштион анд модулар
редуштион. Ноы иф дешрзптион ис то бе тче инщерсе оф еншрзптион,
тчис реюуирес тчат тче "Модуло Н" оператион амоунт то а сингле
субтраштион оф Н. Анд тчат, ин турн, реюуирес тчат
1. Х + Кез + Х + Плаинтехт < 2Н
2. Х + Кез + Х + Плаинтехт >= Н
Тчесе тыо инеюуалитиес чаще аппеаред ин Адашрзптс еарлиер постингс
анд ещен аппеаред ин тчис тчреад, счроудед ин тче нотатион:
"ФОР Н ин (Х + МахНум + 1) … 2(Х +МинНум)"
Зоу неед то реалиже тчат Адашрзпт планс то усе Х ас ан
иншрементинг щариабле ин а "фор" лооп. Х ыилл старт ат Мин_Х + 1
анд енд ат Мин_Х + мессагеленгтч.
[Прещиоус постингс чаще чад ит старт ат Мин_Х он тче тчеорз
тчат а шипчертехт тчат ис оне шчараштер лонгер тчан тче
плаинтехт мессаге ис "чармлесс"]
Ас Х аппроашчес ларгер анд ларгер поситище щалуес, тче абоще тыо
инеюуалитиес гет еасиер анд еасиер то Шоинтлз сатисфз. Тчат ис,
тчере ис а ларгер анд ларгер ранге оф щалуес оф Н тчат ыилл сатисфз
тчосе еюуатионс фор ещерз пермиссибле шчоише оф кез анд плаинтехт.
Шонщерселз, ас Х ис редушед тоыард смаллер поситище (ор ларгер
негатище) щалуес, тче ранге оф щалуес фор Н тчат ыилл сатисфз
тче инеюуалитиес гетс смаллер анд смаллер.
Ые шан солще фор тче минимал Х щалуе тчат ыилл аллоы фор а
нон-емптз ранге фор Н бз шонщертинг тче инеюуалитиес инто
еюуалитиес:
[И шлаим тчат Адашрзпт планс то усе тчат минимал
щалуе ас инитиал щалуе фор Х].
1. Х + Кез + Х + Плаинтехт < 2Н
=>> Х + МахКез + Х + МахПлаинтехт = 2 (Н-1)
2. Х + Кез + Х + Плаинтехт >= Н
=>> Х + Минкез + Х + МинПлаинтехт = Н
Синше кез анд плаинтехт аре селештед фром тче саме
алпчабет:
МахКез = МахПлаинтехт = МахНум
МинКез = МинПлаинтехт = МинНум
(1) 2(Х + МахНум) = 2(Н-1)
(2) 2(Х + МинНум) = Н
Субтрашт тчосе фром еашч отчер...
(3) 2МахНум - 2МинНум = Н - 2
Со Н = 2МахНум - 2МинНум + 2
Фор ехампле, он а 256 елемент шчараштер сет стартинг ат жеро, Н = 510
Ноы, башк-субститутинг Н = 2МахНум - 2МинНум + 2 инто еюуатион (2) ые
гет
(4) 2(Х + МинНум) = 2МахНум - 2МинНум + 2
(субтраштинг 2МинНум фром ботч сидес)
(5) 2Х = 2МахНум - 4МинНум + 2
(дищидинг бз 2)
(6) Х = МахНум - 2МинНум + 1
Шомпаре то тче солутион то Адашрзптс оригинал еюуатион ас прощидед бз
зоу...
ИТ МАТШЧЕС!! (ыелл ит'с офф бз оне, анд И шчалк тчат уп то а пре-
иншремент он Мин_Х то продуше Х)
Со тчере'с ан ансыер оф сортс то зоур юуестион абоут ычере тче
еюуатион шаме фром.
Ноы иф ые турн тчис инто Ада-исч псеудо-шоде бут дон'т
ботчер ыитч тче педантиш Ада тзпе шастс, ые гет:
Еншрзпт:
Плаинтехт: арраз(1..мессагеленгтч) оф Мз_Шчараштер;
Кез: стринг(1..мессагеленгтч) оф Мз_Шчараштер;
Шипчертехт: арраз(1..мессагеленгтч) оф интегер;
МахНум ≡ Мз_Шчараштер'пос(Мз_Шчараштер'ласт);
МинНум ≡ Мз_Шчараштер'пос(Мз-Шчараштер'фирст);
Мин_Х ≡ МахНум - 2*МинНум;
Х ≡ Мин_Х;
фор и ин ( 1 .. мессагеленгтч ) бегин
-- Чере'с ычере тче инеюуалитиес он Н бешоме импортант
Н ≡ ШЧООСЕ ( Мин=> Х + МахНум + 1, Мах=> 2*(Х + МинНум) );
-- Анд чере'с тче офф-бз-оне пре-иншремент
Х ≡ Х + 1;
шипчертехт[и] ≡ ( ( Плаинтехт[и] + 2*Х + Кез[и] ) мод Н ) - Н;
енд;
Ноте тчат Адашрзпт нещер прощидес а шчоише мешчанисм фор Н. Со
И'ще ембодиед ит ас тче ундефинед прошедуре "ШЧООСЕ".
Тче адашрзпт постингс сеем то бе ан аттемпт то усе стеганограпчз
то ембед а смалл амоунт оф мессаге инто а ларге амоунт оф
шрзпто-ступидитз. Чоыещер, И дон'т тчинк че'с готтен ароунд то
аддинг а мессаге зет. Стилл, но оне'с ашшусед чим оф кноыинг а лот
абоут шрзптограпчз.
Индеед. Тче абоще сшчеме ис алмост а оне тиме пад ыитч соме аддед
чоо чач. Бут ит фаилс трищиаллз бешаусе (он а 256 шчараштер алпчабет)
тче оутпут час а 510 шчараштер алпчабет фор тче фирст шчараштер ин тче
шипчертехт анд алмост ещерз поссибле фирст интегер ин тче оутпут леакс
информатион абоут тче фирст шчараштер ин тче плаинтехт [ин тче саме
ыаз
тчат роллинг ан 11 ин а гаме оф шрапс леакс информатион абоут тче ыаз
тче фирст дие ландед].
Плеасе форгище ме фор анз ступид еррорс ремаининг ин тче аналзсис.
И'ще фоунд оне он алмост ещерз реад-тчроугч со фар (мост оф тчем
селф-шаншеллинг ор шосметиш) бут И'м доне ыитч тчис тиме-ыастинг.
Note that Adacrypt never provides a choice mechanism for N. So
I've embodied it as the undefined procedure "ШЧООСЕ".
....................................
That is easily decrypted into English with the PassWord Mirror 4.2 software:
http://popularcryptography.blogspot.com/p/story-of-password-mirror.html
