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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = YNYNXDGEOUUDFKRXAMPGTXUVGYURZGFFTR 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XOCRZSBAUEGHQMWFKNIYLVDPT
WZYXVUTSRQPONMLKIHGFEDCBA
TPDVLYINKFWMQHGEUABSZRCOX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OHFVUKRIMEGCNLWQSBAZDTPYX
WZYXVUTSRQPONMLKIHGFEDCBA
XYPTDZABSQWLNCGEMIRKUVFHO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ATKEZRSGYMBHDNUOVWQCXILFP
WZYXVUTSRQPONMLKIHGFEDCBA
PFLIXCQWVOUNDHBMYGSRZEKTA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ICTNQEOKRUGDLSBZPHAWFVXYM
WZYXVUTSRQPONMLKIHGFEDCBA
MYXVFWAHPZBSLDGURKOEQNTCI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RVNCXWKYPULTGZFADMIQOEBHS
WZYXVUTSRQPONMLKIHGFEDCBA
SHBEOQIMDAFZGTLUPYKWXCNVR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FCUXABOYQPSMDRHWGILETNKVZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZVKNTELIGWHRDMSPQYOBAXUCF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AYFIZONCKLDMVWXPRQGETHSUB
WZYXVUTSRQPONMLKIHGFEDCBA
BUSHTEGQRPXWVMDLKCNOZIFYA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NLCVQWUKEBMTPOAZRHXIFDGYS
WZYXVUTSRQPONMLKIHGFEDCBA
SYGDFIXHRZAOPTMBEKUWQVCLN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LRYVNOHWPCMQADXBKSTEUIGFZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZFGIUETSKBXDAQMCPWHONVYRL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ELMKGWVYUQNHAOBFCTIDSRXPZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZPXRSDITCFBOAHNQUYVWGKMLE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SROGUYLCHXKFQIBMZPEDVTANW
WZYXVUTSRQPONMLKIHGFEDCBA
WNATVDEPZMBIQFKXHCLYUGORS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MVCDYEUPRBIQOLZKXFGHNSAWT
WZYXVUTSRQPONMLKIHGFEDCBA
TWASNHGFXKZLOQIBRPUEYDCVM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GOLQVEARIDPNZBFCSYUXTHWMK
WZYXVUTSRQPONMLKIHGFEDCBA
KMWHTXUYSCFBZNPDIRAEVQLOG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YETXBPDOASKHUWNVICRLGZQFM
WZYXVUTSRQPONMLKIHGFEDCBA
MFQZGLRCIVNWUHKSAODPBXTEY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RSOHMXETPBVDGKFAYNZUCQILW
WZYXVUTSRQPONMLKIHGFEDCBA
WLIQCUZNYAFKGDVBPTEXMHOSR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RMGNOVCDIPUEXKYZBWAQHFLTS
WZYXVUTSRQPONMLKIHGFEDCBA
STLFHQAWBZYKXEUPIDCVONGMR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BXOGAWVNHLZCPEMDURTIKSQFY
WZYXVUTSRQPONMLKIHGFEDCBA
YFQSKITRUDMEPCZLHNVWAGOXB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZOUGHSICFQDKPVNYRMEXWBLTA
WZYXVUTSRQPONMLKIHGFEDCBA
ATLBWXEMRYNVPKDQFCISHGUOZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UYRDFLCTGMAWSHINOPXBZQVKE
WZYXVUTSRQPONMLKIHGFEDCBA
EKVQZBXPONIHSWAMGTCLFDRYU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MPKBCRYWGAFTEZXNDUILHSQVO
WZYXVUTSRQPONMLKIHGFEDCBA
OVQSHLIUDNXZETFAGWYRCBKPM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PNZGCWTQIVRYMLDOUXKHSBFEA
WZYXVUTSRQPONMLKIHGFEDCBA
AEFBSHKXUODLMYRVIQTWCGZNP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WTBNHKDXIMZFEQSALRVYPGUOC
WZYXVUTSRQPONMLKIHGFEDCBA
COUGPYVRLASQEFZMIXDKHNBTW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OPNHFBICEYMSWGXQDKUVTRALZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZLARTVUKDQXGWSMYECIBFHNPO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WDUSVAHLPQORZNXMBGTEFCKIY
WZYXVUTSRQPONMLKIHGFEDCBA
YIKCFETGBMXNZROQPLHAVSUDW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EDNGPYFSTZMRCXIVLWQBUKHAO
WZYXVUTSRQPONMLKIHGFEDCBA
OAHKUBQWLVIXCRMZTSFYPGNDE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RMOCXIGAYPNTSDHUQBZKFVELW
WZYXVUTSRQPONMLKIHGFEDCBA
WLEVFKZBQUHDSTNPYAGIXCOMR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GCBRKMIXZNSHUQDFEYWLATVOP
WZYXVUTSRQPONMLKIHGFEDCBA
POVTALWYEFDQUHSNZXIMKRBCG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HNAIVPQYOEDWMZUTLCRFGXKBS
WZYXVUTSRQPONMLKIHGFEDCBA
SBKXGFRCLTUZMWDEOYQPVIANH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SGIOMTYZQCRDULVWNKEPFBHXA
WZYXVUTSRQPONMLKIHGFEDCBA
AXHBFPEKNWVLUDRCQZYTMOIGS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RBVCGPUMYHZNDTFKOLAEQWXSI
WZYXVUTSRQPONMLKIHGFEDCBA
ISXWQEALOKFTDNZHYMUPGCVBR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NMTXFQLGKPOAHWYSVEURIBCDZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZDCBIRUEVSYWHAOPKGLQFXTMN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FIBWGOPTDLZVUHEMXKRSANQYC
WZYXVUTSRQPONMLKIHGFEDCBA
CYQNASRKXMEHUVZLDTPOGWBIF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IFDPLHVSKXZUEOWNMTCRAYGBQ
WZYXVUTSRQPONMLKIHGFEDCBA
QBGYARCTMNWOEUZXKSVHLPDFI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LKXBWYMECZPISFTNAQROHGDUV
WZYXVUTSRQPONMLKIHGFEDCBA
VUDGHORQANTFSIPZCEMYWBXKL

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.