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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = CCIABORNHBYTYMWDIPHMFZPAEVOXNBFYNM 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SPBMVNEQYURKOGIWXZDCLAHTF
WZYXVUTSRQPONMLKIHGFEDCBA
FTHALCDZXWIGOKRUYQENVMBPS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZHLSQVIEYXAMCPGUFTNODKRBW
WZYXVUTSRQPONMLKIHGFEDCBA
WBRKDONTFUGPCMAXYEIVQSLHZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SZAHRVFBIWPDLXYGTMKOQCUNE
WZYXVUTSRQPONMLKIHGFEDCBA
ENUCQOKMTGYXLDPWIBFVRHAZS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NYFAGDUHEBXWLVKMQORPIZCTS
WZYXVUTSRQPONMLKIHGFEDCBA
STCZIPROQMKVLWXBEHUDGAFYN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TNIPBDCWKEHQXMSYGRAFVOULZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZLUOVFARGYSMXQHEKWCDBPINT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZLSEFXWQDNUHOTPMABKIVGRCY
WZYXVUTSRQPONMLKIHGFEDCBA
YCRGVIKBAMPTOHUNDQWXFESLZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UBVKFSIQMOYGLPNWEXRCHDAZT
WZYXVUTSRQPONMLKIHGFEDCBA
TZADHCRXEWNPLGYOMQISFKVBU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QHEGPTASNLYFVMUDKWRZIOBCX
WZYXVUTSRQPONMLKIHGFEDCBA
XCBOIZRWKDUMVFYLNSATPGEHQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MTORGHESNPCDUYVWQZKAIXFLB
WZYXVUTSRQPONMLKIHGFEDCBA
BLFXIAKZQWVYUDCPNSEHGROTM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KZFREOCWBUIMAXYPDHGVTLQSN
WZYXVUTSRQPONMLKIHGFEDCBA
NSQLTVGHDPYXAMIUBWCOERFZK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TIPEYCQVKGAZMWXDHNFBOULRS
WZYXVUTSRQPONMLKIHGFEDCBA
SRLUOBFNHDXWMZAGKVQCYEPIT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EIZTCQNMFUHKLBXSDVAGYORPW
WZYXVUTSRQPONMLKIHGFEDCBA
WPROYGAVDSXBLKHUFMNQCTZIE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PIFXVCWEASKRGUYZBHLMTQNOD
WZYXVUTSRQPONMLKIHGFEDCBA
DONQTMLHBZYUGRKSAEWCVXFIP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OFDWHQPSXIMZGRABYTKULCVNE
WZYXVUTSRQPONMLKIHGFEDCBA
ENVCLUKTYBARGZMIXSPQHWDFO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WSIKGHYPMXUALNVRZQBFTCEOD
WZYXVUTSRQPONMLKIHGFEDCBA
DOECTFBQZRVNLAUXMPYHGKISW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EBTZVFYNPHXUDLIAKMQSGORCW
WZYXVUTSRQPONMLKIHGFEDCBA
WCROGSQMKAILDUXHPNYFVZTBE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EXORIWUKQTDYNSHZLCBAPGFMV
WZYXVUTSRQPONMLKIHGFEDCBA
VMFGPABCLZHSNYDTQKUWIROXE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AIBRLMVFZNQYGCSDKPUEWTXHO
WZYXVUTSRQPONMLKIHGFEDCBA
OHXTWEUPKDSCGYQNZFVMLRBIA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UBDEGYFOZTVKPAIWQHLRSCXMN
WZYXVUTSRQPONMLKIHGFEDCBA
NMXCSRLHQWIAPKVTZOFYGEDBU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZFPROKISMNXGTDELAVWBYUQCH
WZYXVUTSRQPONMLKIHGFEDCBA
HCQUYBWVALEDTGXNMSIKORPFZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KVLGBMFIZXYHEQUSNDPROWTAC
WZYXVUTSRQPONMLKIHGFEDCBA
CATWORPDNSUQEHYXZIFMBGLVK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VCTODWYZIFARLKQGHBPUXMENS
WZYXVUTSRQPONMLKIHGFEDCBA
SNEMXUPBHGQKLRAFIZYWDOTCV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VRQMZLGAHYDFUCSBIOPNEWXKT
WZYXVUTSRQPONMLKIHGFEDCBA
TKXWENPOIBSCUFDYHAGLZMQRV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NZRSALMUDBQTHVWFXECYPGIKO
WZYXVUTSRQPONMLKIHGFEDCBA
OKIGPYCEXFWVHTQBDUMLASRZN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NILEMUTHKOGZYBAXVRDPSFCWQ
WZYXVUTSRQPONMLKIHGFEDCBA
QWCFSPDRVXABYZGOKHTUMELIN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FXSGCLUNVWYKPETAOQZMIRDBH
WZYXVUTSRQPONMLKIHGFEDCBA
HBDRIMZQOATEPKYWVNULCGSXF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AFPIDERWXUCKOQBNSMHYLGVTZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZTVGLYHMSNBQOKCUXWREDIPFA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DYZRIWSMLBPONQHFUTXCKEVAG
WZYXVUTSRQPONMLKIHGFEDCBA
GAVEKCXTUFHQNOPBLMSWIRZYD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MQTVSXWNRLAPGIEHCZBUKFODY
WZYXVUTSRQPONMLKIHGFEDCBA
YDOFKUBZCHEIGPALRNWXSVTQM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TXSLBGZQARKYOCNHDMVPUEWIF
WZYXVUTSRQPONMLKIHGFEDCBA
FIWEUPVMDHNCOYKRAQZGBLSXT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QAUDFEYBXLGIKVHWMCSOTZNPR
WZYXVUTSRQPONMLKIHGFEDCBA
RPNZTOSCMWHVKIGLXBYEFDUAQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YSZQGEIKANOCHRBUTFXMLWPDV
WZYXVUTSRQPONMLKIHGFEDCBA
VDPWLMXFTUBRHCONAKIEGQZSY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YBHFDWEVXTICKPGRANZQMSLOU
WZYXVUTSRQPONMLKIHGFEDCBA
UOLSMQZNARGPKCITXVEWDFHBY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PXCFGNDKULOTQHSIRYMAWBEVZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZVEBWAMYRISHQTOLUKDNGFCXP

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.