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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = WTBSKDRUVZGYNAZEKHIKXPLDAEBUFXBLYL 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YLATZCXIRDKNMBVUOSHWEGFPQ
WZYXVUTSRQPONMLKIHGFEDCBA
QPFGEWHSOUVBMNKDRIXCZTALY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NZAEWHCMKVLOTSDXBQGIRFUPY
WZYXVUTSRQPONMLKIHGFEDCBA
YPUFRIGQBXDSTOLVKMCHWEAZN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MGWPIACKBLHOQUTEDZYVFSXRN
WZYXVUTSRQPONMLKIHGFEDCBA
NRXSFVYZDETUQOHLBKCAIPWGM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AECSLRFTQUWOXHPBMZIGNKDYV
WZYXVUTSRQPONMLKIHGFEDCBA
VYDKNGIZMBPHXOWUQTFRLSCEA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZRATKBUODLWQMNGFPYXSHCIEV
WZYXVUTSRQPONMLKIHGFEDCBA
VEICHSXYPFGNMQWLDOUBKTARZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OBXSPERHGLUFDKMTIWAYNQVCZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZCVQNYAWITMKDFULGHREPSXBO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EUKOGTAIQXZSLDWVYCRFMNHPB
WZYXVUTSRQPONMLKIHGFEDCBA
BPHNMFRCYVWDLSZXQIATGOKUE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IVBSAMZTUKCNOGDHLYRPXFQEW
WZYXVUTSRQPONMLKIHGFEDCBA
WEQFXPRYLHDGONCKUTZMASBVI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SOAFCVPZXHYGERBQTMDINLKUW
WZYXVUTSRQPONMLKIHGFEDCBA
WUKLNIDMTQBREGYHXZPVCFAOS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SEMCGYVTZAUPNQKXLRBFOIDHW
WZYXVUTSRQPONMLKIHGFEDCBA
WHDIOFBRLXKQNPUAZTVYGCMES
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AXDHGEWNQCSOZLMYFBRVTKPIU
WZYXVUTSRQPONMLKIHGFEDCBA
UIPKTVRBFYMLZOSCQNWEGHDXA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XECYNVZIWDOBFUQHPAKTMGLSR
WZYXVUTSRQPONMLKIHGFEDCBA
RSLGMTKAPHQUFBODWIZVNYCEX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CFASQMPVOKGLIUNRDTYBEWZHX
WZYXVUTSRQPONMLKIHGFEDCBA
XHZWEBYTDRNUILGKOVPMQSAFC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SREXGYZLVNAHCTUMBIQOPFWDK
WZYXVUTSRQPONMLKIHGFEDCBA
KDWFPOQIBMUTCHANVLZYGXERS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZFURKXIBAGMYETSQVDWNCLPHO
WZYXVUTSRQPONMLKIHGFEDCBA
OHPLCNWDVQSTEYMGABIXKRUFZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HZPCAODILUTFEXKNGMSWYBVQR
WZYXVUTSRQPONMLKIHGFEDCBA
RQVBYWSMGNKXEFTULIDOACPZH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LBPDKXNHMRGZSQEIFTUAYWCVO
WZYXVUTSRQPONMLKIHGFEDCBA
OVCWYAUTFIEQSZGRMHNXKDPBL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BTOYUQGXEKFAZNLIVHWMPDRSC
WZYXVUTSRQPONMLKIHGFEDCBA
CSRDPMWHVILNZAFKEXGQUYOTB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QOPUHYVBKSZCATGLDIFRXNMEW
WZYXVUTSRQPONMLKIHGFEDCBA
WEMNXRFIDLGTACZSKBVYHUPOQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UOWIMTACKVLFRPSGHXEBDZNQY
WZYXVUTSRQPONMLKIHGFEDCBA
YQNZDBEXHGSPRFLVKCATMIWOU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SATCDLXQKGEHMIUBVZRFPWONY
WZYXVUTSRQPONMLKIHGFEDCBA
YNOWPFRZVBUIMHEGKQXLDCTAS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QEBVNDOPYMSGIFURKZXLCWAHT
WZYXVUTSRQPONMLKIHGFEDCBA
THAWCLXZKRUFIGSMYPODNVBEQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FRMTXUHAYDNWPBVEQCLZOGISK
WZYXVUTSRQPONMLKIHGFEDCBA
KSIGOZLCQEVBPWNDYAHUXTMRF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TWSXDFBUPRMICOGHEKZLANYQV
WZYXVUTSRQPONMLKIHGFEDCBA
VQYNALZKEHGOCIMRPUBFDXSWT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UXRAKPTIHQNOVFDMWSLGZYEBC
WZYXVUTSRQPONMLKIHGFEDCBA
CBEYZGLSWMDFVONQHITPKARXU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XCVSFLOBEPNUIZDWKRQTYAMHG
WZYXVUTSRQPONMLKIHGFEDCBA
GHMAYTQRKWDZIUNPEBOLFSVCX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GOTZPLVSFMWRBAXNIQYEKUHCD
WZYXVUTSRQPONMLKIHGFEDCBA
DCHUKEYQINXABRWMFSVLPZTOG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RMXHCTPQKNEWGZDVYAUSOIFLB
WZYXVUTSRQPONMLKIHGFEDCBA
BLFIOSUAYVDZGWENKQPTCHXMR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YGOUTDLFAVKSMWEZCHNBQIPRX
WZYXVUTSRQPONMLKIHGFEDCBA
XRPIQBNHCZEWMSKVAFLDTUOGY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AIUOXHLDYFZBREGPQWTMCVSKN
WZYXVUTSRQPONMLKIHGFEDCBA
NKSVCMTWQPGERBZFYDLHXOUIA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VQGYBLZIEMFPUKNAHRTOSCWDX
WZYXVUTSRQPONMLKIHGFEDCBA
XDWCSOTRHANKUPFMEIZLBYGQV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LPTBVXZKCSMIRYODEFWHQAUGN
WZYXVUTSRQPONMLKIHGFEDCBA
NGUAQHWFEDOYRIMSCKZXVBTPL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DRUBETNSLPMGOWHFQYZIKAVXC
WZYXVUTSRQPONMLKIHGFEDCBA
CXVAKIZYQFHWOGMPLSNTEBURD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZGARKTVBNYEFMXPWISLDCQUOH
WZYXVUTSRQPONMLKIHGFEDCBA
HOUQCDLSIWPXMFEYNBVTKRAGZ

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.