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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = FIDLVXWWIXLSXZHABRWKWWAYSRVMIYROYH 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BKNLGXZYARDHMUCVPOTFIQSEW
WZYXVUTSRQPONMLKIHGFEDCBA
WESQIFTOPVCUMHDRAYZXGLNKB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QWVZYTAGHKNCIMDBROLPSEXUF
WZYXVUTSRQPONMLKIHGFEDCBA
FUXESPLORBDMICNKHGATYZVWQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CGKQILEMDFNAOURXHTWVYZBPS
WZYXVUTSRQPONMLKIHGFEDCBA
SPBZYVWTHXRUOANFDMELIQKGC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PONLMQSVXCAEHIGTUFYDZKBRW
WZYXVUTSRQPONMLKIHGFEDCBA
WRBKZDYFUTGIHEACXVSQMLNOP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YTHBVQPKEDWSROLXNMCAFUZGI
WZYXVUTSRQPONMLKIHGFEDCBA
IGZUFACMNXLORSWDEKPQVBHTY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZATGECFWMIVBXLKDNYSUPQOHR
WZYXVUTSRQPONMLKIHGFEDCBA
RHOQPUSYNDKLXBVIMWFCEGTAZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TEQMOBKRXSVYUNDAIFWPHZCGL
WZYXVUTSRQPONMLKIHGFEDCBA
LGCZHPWFIADNUYVSXRKBOMQET
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YXLNBHFGWSTADMURCQOVZKIEP
WZYXVUTSRQPONMLKIHGFEDCBA
PEIKZVOQCRUMDATSWGFHBNLXY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EPOFWIBXTRZCVGAQDHUMYNLSK
WZYXVUTSRQPONMLKIHGFEDCBA
KSLNYMUHDQAGVCZRTXBIWFOPE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GLTQNFVBXWADEZURYSMCHIKOP
WZYXVUTSRQPONMLKIHGFEDCBA
POKIHCMSYRUZEDAWXBVFNQTLG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MWOXLQCYGTIPNHFRKSUDEBVAZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZAVBEDUSKRFHNPITGYCQLXOWM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NMDSQECPUABKHWVZLIRXTYGFO
WZYXVUTSRQPONMLKIHGFEDCBA
OFGYTXRILZVWHKBAUPCEQSDMN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YSZGDVTOALFEPUXMRCQNWIBHK
WZYXVUTSRQPONMLKIHGFEDCBA
KHBIWNQCRMXUPEFLAOTVDGZSY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WUCIBSGVQNZLHPMTXOEKFYDRA
WZYXVUTSRQPONMLKIHGFEDCBA
ARDYFKEOXTMPHLZNQVGSBICUW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HPIMSLKORVQEWDZNCGXYUFTBA
WZYXVUTSRQPONMLKIHGFEDCBA
ABTFUYXGCNZDWEQVROKLSMIPH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KEVYXMDLTPBGAQUSFCZNHIWOR
WZYXVUTSRQPONMLKIHGFEDCBA
ROWIHNZCFSUQAGBPTLDMXYVEK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PLSGBQUFKRCZXNTIOYEDVAMWH
WZYXVUTSRQPONMLKIHGFEDCBA
HWMAVDEYOITNXZCRKFUQBGSLP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UTDMGEBSYKVNACZQHROXIWLFP
WZYXVUTSRQPONMLKIHGFEDCBA
PFLWIXORHQZCANVKYSBEGMDTU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PYLZQGSIMCTREHNOBWUDXFKVA
WZYXVUTSRQPONMLKIHGFEDCBA
AVKFXDUWBONHERTCMISGQZLYP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BYQLDZACKWRSPEGVTUFIMONHX
WZYXVUTSRQPONMLKIHGFEDCBA
XHNOMIFUTVGEPSRWKCAZDLQYB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ODSZRLWNBKTYIQFHGAEPMCUVX
WZYXVUTSRQPONMLKIHGFEDCBA
XVUCMPEAGHFQIYTKBNWLRZSDO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IMUSVCFWTDPGBHLQZKARXOYNE
WZYXVUTSRQPONMLKIHGFEDCBA
ENYOXRAKZQLHBGPDTWFCVSUMI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IZSNWTVHMODQUCKYRPABELFGX
WZYXVUTSRQPONMLKIHGFEDCBA
XGFLEBAPRYKCUQDOMHVTWNSZI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QDKOYBXUTISNFECZMVPLGRHAW
WZYXVUTSRQPONMLKIHGFEDCBA
WAHRGLPVMZCEFNSITUXBYOKDQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RFNSTHEYQVPUMKIADBLOGCWXZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZXWCGOLBDAIKMUPVQYEHTSNFR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PMKCSEVYRLOWTHNGBIAUZDXFQ
WZYXVUTSRQPONMLKIHGFEDCBA
QFXDZUAIBGNHTWOLRYVESCKMP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LHQINKZYUBPWVGOEARXFCMSTD
WZYXVUTSRQPONMLKIHGFEDCBA
DTSMCFXRAEOGVWPBUYZKNIQHL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GNVEOHRXYWDFUCZTPSMBKAILQ
WZYXVUTSRQPONMLKIHGFEDCBA
QLIAKBMSPTZCUFDWYXRHOEVNG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QGREXHMIATYKFSCLWNBDPOZUV
WZYXVUTSRQPONMLKIHGFEDCBA
VUZOPDBNWLCSFKYTAIMHXERGQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AVDGYIXEZBWHOLKFCRPTSQNMU
WZYXVUTSRQPONMLKIHGFEDCBA
UMNQSTPRCFKLOHWBZEXIYGDVA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SKVNRUOIYTFBPHAQLDEZMGWXC
WZYXVUTSRQPONMLKIHGFEDCBA
CXWGMZEDLQAHPBFTYIOURNVKS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OQFDSZXBTKULWEHRNIGAPCVYM
WZYXVUTSRQPONMLKIHGFEDCBA
MYVCPAGINRHEWLUKTBXZSDFQO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HDRCBKTUOXLNSIEAGYFQWZVMP
WZYXVUTSRQPONMLKIHGFEDCBA
PMVZWQFYGAEISNLXOUTKBCRDH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BAKRVSYZGCDOQTEMFPHNXIULW
WZYXVUTSRQPONMLKIHGFEDCBA
WLUIXNHPFMETQODCGZYSVRKAB

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.