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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = AZDFZUDILMTUNELVPALBVNOFVTCRGYZMHV 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XQWRTBOZDKUFNCMVYGSAHIEPL
WZYXVUTSRQPONMLKIHGFEDCBA
LPEIHASGYVMCNFUKDZOBTRWQX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RTLQKVMBXEYUZPWFICAONSHDG
WZYXVUTSRQPONMLKIHGFEDCBA
GDHSNOACIFWPZUYEXBMVKQLTR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VKHBGSTWDMNZXLQCIPAEROYUF
WZYXVUTSRQPONMLKIHGFEDCBA
FUYOREAPICQLXZNMDWTSGBHKV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OLMFQKBZUDEPYCSHTRGANVXWI
WZYXVUTSRQPONMLKIHGFEDCBA
IWXVNAGRTHSCYPEDUZBKQFMLO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OGYIZLVKXCUFESANWPHBDRTQM
WZYXVUTSRQPONMLKIHGFEDCBA
MQTRDBHPWNASEFUCXKVLZIYGO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TYECQPRZLAVWUFSBGHKXIONMD
WZYXVUTSRQPONMLKIHGFEDCBA
DMNOIXKHGBSFUWVALZRPQCEYT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CVSULNOHTRWGFYXEPQDZKBAMI
WZYXVUTSRQPONMLKIHGFEDCBA
IMABKZDQPEXYFGWRTHONLUSVC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BAOCUQFPIWDXNLSHMZTGYVRKE
WZYXVUTSRQPONMLKIHGFEDCBA
EKRVYGTZMHSLNXDWIPFQUCOAB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZKRAFLDGXEYOMPTHQSVWBCINU
WZYXVUTSRQPONMLKIHGFEDCBA
UNICBWVSQHTPMOYEXGDLFARKZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NWOLSVHBMIFYQKUTECAZXGPDR
WZYXVUTSRQPONMLKIHGFEDCBA
RDPGXZACETUKQYFIMBHVSLOWN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FQCNTUZPGKIBXLREVMYAHOSDW
WZYXVUTSRQPONMLKIHGFEDCBA
WDSOHAYMVERLXBIKGPZUTNCQF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LIVUXYAMWKDQHSZRCBONPTEFG
WZYXVUTSRQPONMLKIHGFEDCBA
GFETPNOBCRZSHQDKWMAYXUVIL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LMBWXPIFKECHGSNVUZARYTQDO
WZYXVUTSRQPONMLKIHGFEDCBA
ODQTYRAZUVNSGHCEKFIPXWBML
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HTKPZWYGAXEOLMVQNCSBIRUDF
WZYXVUTSRQPONMLKIHGFEDCBA
FDURIBSCNQVMLOEXAGYWZPKTH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LKQDMCOEPWANZISYTBHFGXVRU
WZYXVUTSRQPONMLKIHGFEDCBA
URVXGFHBTYSIZNAWPEOCMDQKL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YUHTFWEPNIARVCDSGOXMBZKLQ
WZYXVUTSRQPONMLKIHGFEDCBA
QLKZBMXOGSDCVRAINPEWFTHUY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KECDPYALHVRGBMXONSITUWQFZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZFQWUTISNOXMBGRVHLAYPDCEK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FDOMHSXNUZWPYETQVALBRCIGK
WZYXVUTSRQPONMLKIHGFEDCBA
KGICRBLAVQTEYPWZUNXSHMODF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TVHIZBOCPWKEUXYQRLMDFGANS
WZYXVUTSRQPONMLKIHGFEDCBA
SNAGFDMLRQYXUEKWPCOBZIHVT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EGNPMVHIBTFDKOYCXWZRUQLAS
WZYXVUTSRQPONMLKIHGFEDCBA
SALQURZWXCYOKDFTBIHVMPNGE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OUYPEDVKQHZIRBMFLTNXGSCAW
WZYXVUTSRQPONMLKIHGFEDCBA
WACSGXNTLFMBRIZHQKVDEPYUO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZHKGTVXNRLSYDBMPAWEFOQICU
WZYXVUTSRQPONMLKIHGFEDCBA
UCIQOFEWAPMBDYSLRNXVTGKHZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GRSQBIPLVZDNUTEFKCOXYAMWH
WZYXVUTSRQPONMLKIHGFEDCBA
HWMAYXOCKFETUNDZVLPIBQSRG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TBZHFYOVPEWXRINQKCLDMSGUA
WZYXVUTSRQPONMLKIHGFEDCBA
AUGSMDLCKQNIRXWEPVOYFHZBT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EIHVZROWPUCMKADSYFLGTBXQN
WZYXVUTSRQPONMLKIHGFEDCBA
NQXBTGLFYSDAKMCUPWORZVHIE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AMGRCNXKTQFLDHWZOSIPVYEUB
WZYXVUTSRQPONMLKIHGFEDCBA
BUEYVPISOZWHDLFQTKXNCRGMA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VPMQOBSAHGDXCNLUYZTWKIFER
WZYXVUTSRQPONMLKIHGFEDCBA
REFIKWTZYULNCXDGHASBOQMPV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XWAIUKEMVSBYLCGQDZROHNFPT
WZYXVUTSRQPONMLKIHGFEDCBA
TPFNHORZDQGCLYBSVMEKUIAWX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EZYNFALGBUCOXPKTQHIRSWMDV
WZYXVUTSRQPONMLKIHGFEDCBA
VDMWSRIHQTKPXOCUBGLAFNYZE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DTALYGPVECBIQKMNOXHZWUFRS
WZYXVUTSRQPONMLKIHGFEDCBA
SRFUWZHXONMKQIBCEVPGYLATD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QOXEZLHRMTKUDFWGIAVPCBYSN
WZYXVUTSRQPONMLKIHGFEDCBA
NSYBCPVAIGWFDUKTMRHLZEXOQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MYDQAFGRBNPSVECOXZTHUILWK
WZYXVUTSRQPONMLKIHGFEDCBA
KWLIUHTZXOCEVSPNBRGFAQDYM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YFASGIDCOUETWRQLKHBPNXMVZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZVMXNPBHKLQRWTEUOCDIGSAFY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CYHMUEKAGBLQIPWZRSVFNDTXO
WZYXVUTSRQPONMLKIHGFEDCBA
OXTDNFVSRZWPIQLBGAKEUMHYC

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.