Storia della crittografiaCifrariCifrari polialfabetici
Orchema + OTP = ORION
DIANA cipher - Trithemius' Orchema, 1507

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = EHTQLAOTMDIQNTURUBVPFUQZFMKPTBYIAM 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SZHOLIYQBAUFWPNXDTMECRGKV
WZYXVUTSRQPONMLKIHGFEDCBA
VKGRCEMTDXNPWFUABQYILOHZS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DGSBUIVRPKCWHXAMOLFEZNTYQ
WZYXVUTSRQPONMLKIHGFEDCBA
QYTNZEFLOMAXHWCKPRVIUBSGD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QXIRBAVHTZCWOPMDULFNKSEYG
WZYXVUTSRQPONMLKIHGFEDCBA
GYESKNFLUDMPOWCZTHVABRIXQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IVWQMSFHBZLCUTROXPEKDGNYA
WZYXVUTSRQPONMLKIHGFEDCBA
AYNGDKEPXORTUCLZBHFSMQWVI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BMEILWRFYHTQPAUONXGDVCKSZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZSKCVDGXNOUAPQTHYFRWLIEMB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QTRBOGDCLMNKAVIPHWZSXFYEU
WZYXVUTSRQPONMLKIHGFEDCBA
UEYFXSZWHPIVAKNMLCDGOBRTQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BCVFNGUHXYTAWSMLIROZDPEKQ
WZYXVUTSRQPONMLKIHGFEDCBA
QKEPDZORILMSWATYXHUGNFVCB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OUCIFZMHTQSYGWPDRVBLENXAK
WZYXVUTSRQPONMLKIHGFEDCBA
KAXNELBVRDPWGYSQTHMZFICUO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VGTALMPDQZINHSEWKCOFYUBXR
WZYXVUTSRQPONMLKIHGFEDCBA
RXBUYFOCKWESHNIZQDPMLATGV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QYHNAKIGDMURZXBVFPEWSCLTO
WZYXVUTSRQPONMLKIHGFEDCBA
OTLCSWEPFVBXZRUMDGIKANHYQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PUZOIREGWTHFBQMLDANKCSXYV
WZYXVUTSRQPONMLKIHGFEDCBA
VYXSCKNADLMQBFHTWGERIOZUP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HMPQIZCDYTNOWVKSBURXEFAGL
WZYXVUTSRQPONMLKIHGFEDCBA
LGAFEXRUBSKVWONTYDCZIQPMH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ILZTBKAOYQVUPWNGHEFDSCRXM
WZYXVUTSRQPONMLKIHGFEDCBA
MXRCSDFEHGNWPUVQYOAKBTZLI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IWGOFAXSZPTHNDECBKYVRMQLU
WZYXVUTSRQPONMLKIHGFEDCBA
ULQMRVYKBCEDNHTPZSXAFOGWI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UXTGMSPKBDVCANERHOIQZLYWF
WZYXVUTSRQPONMLKIHGFEDCBA
FWYLZQIOHRENACVDBKPSMGTXU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MNQZOFTHABYVRIXUCWSKDGPEL
WZYXVUTSRQPONMLKIHGFEDCBA
LEPGDKSWCUXIRVYBAHTFOZQNM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EBDSUMFHWAVKXGNYCIQPZORTL
WZYXVUTSRQPONMLKIHGFEDCBA
LTROZPQICYNGXKVAWHFMUSDBE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AZRTIKYLNODXQGVSCBMFPHEWU
WZYXVUTSRQPONMLKIHGFEDCBA
UWEHPFMBCSVGQXDONLYKITRZA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RMDELIFNAZUOXCYKHVBSTWQPG
WZYXVUTSRQPONMLKIHGFEDCBA
GPQWTSBVHKYCXOUZANFILEDMR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WERHSMZDPBOYGXVFNKATILUCQ
WZYXVUTSRQPONMLKIHGFEDCBA
QCULITAKNFVXGYOBPDZMSHREW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PSHGNRFUIQKXMOEVBLWADCZYT
WZYXVUTSRQPONMLKIHGFEDCBA
TYZCDAWLBVEOMXKQIUFRNGHSP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LATMCGWUPHFERZODKNVYSIBQX
WZYXVUTSRQPONMLKIHGFEDCBA
XQBISYVNKDOZREFHPUWGCMTAL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DMOXFTHENSIURAGWKPQCZVLBY
WZYXVUTSRQPONMLKIHGFEDCBA
YBLVZCQPKWGARUISNEHTFXOMD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MXTNZBPHOKQFUVRGAICDSEYWL
WZYXVUTSRQPONMLKIHGFEDCBA
LWYESDCIAGRVUFQKOHPBZNTXM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RXHFATSZLEVNUDBIYKCPGOQMW
WZYXVUTSRQPONMLKIHGFEDCBA
WMQOGPCKYIBDUNVELZSTAFHXR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SAPDWFUXMBYGRTNZLEQVCHKOI
WZYXVUTSRQPONMLKIHGFEDCBA
IOKHCVQELZNTRGYBMXUFWDPAS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FQMXBWOCPSDUKZGLVHERYAINT
WZYXVUTSRQPONMLKIHGFEDCBA
TNIAYREHVLGZKUDSPCOWBXMQF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EIXVYUBMKZNGOQTCRLPHWAFDS
WZYXVUTSRQPONMLKIHGFEDCBA
SDFAWHPLRCTQOGNZKMBUYVXIE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CFKMIDSTAPQZOWGNRUYBLEXHV
WZYXVUTSRQPONMLKIHGFEDCBA
VHXELBYURNGWOZQPATSDIMKFC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KYTUBAXGIHPNZEOLSMWRQDCFV
WZYXVUTSRQPONMLKIHGFEDCBA
VFCDQRWMSLOEZNPHIGXABUTYK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GUIBYAMVTFZSDEHORQLWCPNXK
WZYXVUTSRQPONMLKIHGFEDCBA
KXNPCWLQROHEDSZFTVMAYBIUG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IFVNOBUHLYDPGWEQXASCMZTRK
WZYXVUTSRQPONMLKIHGFEDCBA
KRTZMCSAXQEWGPDYLHUBONVFI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SCYIQKRXEDLGWTPUVABOHMZFN
WZYXVUTSRQPONMLKIHGFEDCBA
NFZMHOBAVUPTWGLDEXRKQIYCS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TQANOGFSERIUHDYLVBMKZCPWX
WZYXVUTSRQPONMLKIHGFEDCBA
XWPCZKMBVLYDHUIRESFGONAQT

XVI - XX century: from Orchema to ORION

In the second half of the XX century the American NSA used for some time an ORION cipher, which bears a striking resemblance to Trithemius's Orchema, except that the alphabets were written horizontally and on both sides of each sheet; one with the clear alphabet and one with the encrypted one, printed exactly in register and with a sheet of carbon paper underneath, with the carbon at the top.

Encrypting procedure

The sender circled the plain letter with a pen, one line for each character, and the carbon paper automatically circled the encrypted letter on the back. Very fast system to write in cipher, the sender only had to circle the letters of the plain text, but extremely cumbersome: one sheet, i.e. two pages, was needed for only 50 letters.

Decryption procedure

To decrypt the recipient follows the reverse procedure: using the first page backwards, starting from the first line, looks for the first letter of the ciphertext and circleit . The clear letters will automatically be circled on the other side. In the end it will be enough to transcribe them to obtain the clear text.

Fortune of the ORION cipher

Did the designer of ORION know Trithemius and his Orchema? The cipher is described by a certain David Boak in a 1973 NSA document, declassified in 2015, and he never mentions Tritemius. The question obviously remains unanswered, but the basic idea is simple enough and may very well have been independently re-invented. It is suggestive any way that the initials, OR, are the same.

Moreover, Trithemius had a very vague idea of the concept of a disordered alphabet, dancing letters (this is the meaning of the Greek Oρχημα), indeed he proposes criteria that are not exactly disordered such as the one of alternating letters used in the following pages.

Boak describes this cipher as a big improvement on the DIANA cryptosystem in terms of operational speed but at the aforementioned cost of a much larger size. He also writes that the cipher was abandoned after a short time, partly because of the encumbrance, partly because of the difficulty of having a print with the two sides exactly in register.

Security of the cipher

As with all OTP ciphers, security is based on the process used to generate the random alphabets, which should be truly random, in the sense of absolutely unpredictable; which is very difficult to obtain and generally pseudorandom algorithms are used; so it is also in this example that uses the rand() function of the PhP language, which, according to the PhP manual itself, is not cryptographically secure; PhP has also more secure but slower functions, but for a demo, rand() is enough! Furthermore, the one time pad rule must be strictly respected: use the key once and only once, it is forbidden to reuse it.


Riferimenti bibliografici
Siti e pagine web
X Searching for "Trit" on the web, only returns another cipher named TRITON.
X
X Latino : In praesente Orchemate multiplex traditura alphabetum per transpositionem & saltum tam norma ordinis quam positione literarum. Quae omnia sufficiunt pro exemplo his qui locatis non possunt esse contenti, ut modum habeant & formam quasi restant inveniendi, quia sine numero possunt variari, ut frequens orchematis expansio clarè docet.

Italiano: Nella presente Orchema vanno trasformati in molti modi l'alfabeto per spostamento e il salto sia per ordinamento sia per posizione delle lettere. Le quali tutte sono sufficienti per l'esempio a quelli che non possono essere qui contenuti, sicché abbiano modo e forma che restino da trovare, perché possono essere variati senza limite, come la frequente espansione di orchema chiaramente mostra.