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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = EOUCPXOUTGEACLECITATZELOTSZNXPZALI 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LKWRHSVOXDTQNGYZPMFECBAIU
WZYXVUTSRQPONMLKIHGFEDCBA
UIABCEFMPZYGNQTDXOVSHRWKL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RQWTNAEZBVIPOYLUMFHCDKXGS
WZYXVUTSRQPONMLKIHGFEDCBA
SGXKDCHFMULYOPIVBZEANTWQR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PONZXYLKUEBVIAWGHRTFDSCQM
WZYXVUTSRQPONMLKIHGFEDCBA
MQCSDFTRHGWAIVBEUKLYXZNOP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EUVCTWQIMPFKDSHOYBAZGNLXR
WZYXVUTSRQPONMLKIHGFEDCBA
RXLNGZABYOHSDKFPMIQWTCVUE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RAFUPNZIHBDLXOYMTGSKQCEWV
WZYXVUTSRQPONMLKIHGFEDCBA
VWECQKSGTMYOXLDBHIZNPUFAR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FYNOSVDTAWHMXQUZPCKEBGRIL
WZYXVUTSRQPONMLKIHGFEDCBA
LIRGBEKCPZUQXMHWATDVSONYF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LYVRPAZNKIFGSBHQEXOCUMWTD
WZYXVUTSRQPONMLKIHGFEDCBA
DTWMUCOXEQHBSGFIKNZAPRVYL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CAFDMYPIUHZTEOKRVQGXWSBNL
WZYXVUTSRQPONMLKIHGFEDCBA
LNBSWXGQVRKOETZHUIPYMDFAC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BNRYLTZKVAUQICMPWFSGHEDOX
WZYXVUTSRQPONMLKIHGFEDCBA
XODEHGSFWPMCIQUAVKZTLYRNB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XWKVQPZDGTOASEUNBMFCHYILR
WZYXVUTSRQPONMLKIHGFEDCBA
RLIYHCFMBNUESAOTGDZPQVKWX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MADQEUNCFLYVKBGIXHWZTRSPO
WZYXVUTSRQPONMLKIHGFEDCBA
OPSRTZWHXIGBKVYLFCNUEQDAM
 ABCDEFGHIKLMNOPQRSTUVXYZW
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WZYXVUTSRQPONMLKIHGFEDCBA
VZBESKDIFYRPONLCTGMQHAXUW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZOXUDVSAQTGIHNCLBRWPFYEMK
WZYXVUTSRQPONMLKIHGFEDCBA
KMEYFPWRBLCNHIGTQASVDUXOZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MDKPTQNFOHLGCSBAYVRUZWIEX
WZYXVUTSRQPONMLKIHGFEDCBA
XEIWZURVYABSCGLHOFNQTPKDM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ERQFITSLAGCUVMBDZOKNXHPYW
WZYXVUTSRQPONMLKIHGFEDCBA
WYPHXNKOZDBMVUCGALSTIFQRE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LTIZBEDUVKAOCPQHSFWYGXRNM
WZYXVUTSRQPONMLKIHGFEDCBA
MNRXGYWFSHQPCOAKVUDEBZITL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AEHCIXPZGOBNSUKWTRYFDLVMQ
WZYXVUTSRQPONMLKIHGFEDCBA
QMVLDFYRTWKUSNBOGZPXICHEA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SLYKBWNEFQIZCHGROTADVMXPU
WZYXVUTSRQPONMLKIHGFEDCBA
UPXMVDATORGHCZIQFENWBKYLS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BPCVXDNHWYIULOEZTAFKMRQSG
WZYXVUTSRQPONMLKIHGFEDCBA
GSQRMKFATZEOLUIYWHNDXVCPB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SPUMWQNLTGFXYKROZHBDVAEIC
WZYXVUTSRQPONMLKIHGFEDCBA
CIEAVDBHZORKYXFGTLNQWMUPS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QGYECRZSIMTABKVNPOFHUDLXW
WZYXVUTSRQPONMLKIHGFEDCBA
WXLDUHFOPNVKBATMISZRCEYGQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TWMDYSREPZGHVXNFLOCUIKBAQ
WZYXVUTSRQPONMLKIHGFEDCBA
QABKIUCOLFNXVHGZPERSYDMWT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XMBDQKYPVANSURGTWILZECHOF
WZYXVUTSRQPONMLKIHGFEDCBA
FOHCEZLIWTGRUSNAVPYKQDBMX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NKCAOEZYGBRQXFMWSDUILTHPV
WZYXVUTSRQPONMLKIHGFEDCBA
VPHTLIUDSWMFXQRBGYZEOACKN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DHFTGPERUIAXCWZKOQBSYLMVN
WZYXVUTSRQPONMLKIHGFEDCBA
NVMLYSBQOKZWCXAIUREPGTFHD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OIGUKNZRSQXCVFYAHPDLMEWBT
WZYXVUTSRQPONMLKIHGFEDCBA
TBWEMLDPHAYFVCXQSRZNKUGIO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PAOVWGIKQCTBZLSREYMNUHDFX
WZYXVUTSRQPONMLKIHGFEDCBA
XFDHUNMYERSLZBTCQKIGWVOAP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LWDIBSYCGTEOAPFKMHNUXVRZQ
WZYXVUTSRQPONMLKIHGFEDCBA
QZRVXUNHMKFPAOETGCYSBIDWL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FNUEYORXQWZGTAKMBCPLDVSHI
WZYXVUTSRQPONMLKIHGFEDCBA
IHSVDLPCBMKATGZWQXROYEUNF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EZQVPXBCOHWDYTRUNFMLKGSIA
WZYXVUTSRQPONMLKIHGFEDCBA
AISGKLMFNURTYDWHOCBXPVQZE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MUXDZSHVICNFGPYOQWKERBATL
WZYXVUTSRQPONMLKIHGFEDCBA
LTABREKWQOYPGFNCIVHSZDXUM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ARSWIULDPOBKYXTCHEMZVQGNF
WZYXVUTSRQPONMLKIHGFEDCBA
FNGQVZMEHCTXYKBOPDLUIWSRA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YRSCOZDGPBNKMUAEVLWTHFIQX
WZYXVUTSRQPONMLKIHGFEDCBA
XQIFHTWLVEAUMKNBPGDZOCSRY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WFENCOKVGPMBTUXSHAIDLRZYQ
WZYXVUTSRQPONMLKIHGFEDCBA
QYZRLDIAHSXUTBMPGVKOCNEFW

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.