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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = FLLAFOCMUHQZXQTDQFKWVQTOUXGGLRIFPL 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MGKYDXQWRZSALEUPOCTFIHVNB
WZYXVUTSRQPONMLKIHGFEDCBA
BNVHIFTCOPUELASZRWQXDYKGM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KBWQNPCUYZVSLTHIOGAXFREMD
WZYXVUTSRQPONMLKIHGFEDCBA
DMERFXAGOIHTLSVZYUCPNQWBK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TCDNXPYZLKHBOEWMAUFVIRQSG
WZYXVUTSRQPONMLKIHGFEDCBA
GSQRIVFUAMWEOBHKLZYPXNDCT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NFMAVCUYEHSTDPIQWKBGOXLRZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZRLXOGBKWQIPDTSHEYUCVAMFN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BLITFAHOQGKSCDYNXRPMZWEUV
WZYXVUTSRQPONMLKIHGFEDCBA
VUEWZMPRXNYDCSKGQOHAFTILB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IKRNMFQYSEATOLCXVUZPGBHWD
WZYXVUTSRQPONMLKIHGFEDCBA
DWHBGPZUVXCLOTAESYQFMNRKI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YPHDRKNAWZMFOGVTILCXQUEBS
WZYXVUTSRQPONMLKIHGFEDCBA
SBEUQXCLITVGOFMZWANKRDHPY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KSUZODVEMWTXIRQGCAYLPNHBF
WZYXVUTSRQPONMLKIHGFEDCBA
FBHNPLYACGQRIXTWMEVDOZUSK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XACMHUVWORNSKQEILBZGYFTDP
WZYXVUTSRQPONMLKIHGFEDCBA
PDTFYGZBLIEQKSNROWVUHMCAX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IAELOFGQHUXBPVSDMNYWRCTZK
WZYXVUTSRQPONMLKIHGFEDCBA
KZTCRWYNMDSVPBXUHQGFOLEAI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZPKRQUASYGDCNOHFLIVBWXMET
WZYXVUTSRQPONMLKIHGFEDCBA
TEMXWBVILFHONCDGYSAUQRKPZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LSOZHPYWXKNRIDMVFQEABTGCU
WZYXVUTSRQPONMLKIHGFEDCBA
UCGTBAEQFVMDIRNKXWYPHZOSL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QECBLRNDFOPVIMXZWKSGATYUH
WZYXVUTSRQPONMLKIHGFEDCBA
HUYTAGSKWZXMIVPOFDNRLBCEQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XSNHBYWFACQOMTRVDIGLZEPKU
WZYXVUTSRQPONMLKIHGFEDCBA
UKPEZLGIDVRTMOQCAFWYBHNSX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TKXNCSHYFRZBPEDUVOGLIAQWM
WZYXVUTSRQPONMLKIHGFEDCBA
MWQAILGOVUDEPBZRFYHSCNXKT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BRIOAXHNTVPGDMSZKULQWCFYE
WZYXVUTSRQPONMLKIHGFEDCBA
EYFCWQLUKZSMDGPVTNHXAOIRB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VWLIQSKFAZHUETNBMXDYORCGP
WZYXVUTSRQPONMLKIHGFEDCBA
PGCROYDXMBNTEUHZAFKSQILWV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UCRDSBZQNHIGVPKXAFWTOYELM
WZYXVUTSRQPONMLKIHGFEDCBA
MLEYOTWFAXKPVGIHNQZBSDRCU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BYDIEQCHLGZNFSXPWKMTRVOUA
WZYXVUTSRQPONMLKIHGFEDCBA
AUOVRTMKWPXSFNZGLHCQEIDYB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KFUQSYPOWZNIAXRCTDGHBMELV
WZYXVUTSRQPONMLKIHGFEDCBA
VLEMBHGDTCRXAINZWOPYSQUFK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XSRKGNVOEIFCAZDBTUHQPLYWM
WZYXVUTSRQPONMLKIHGFEDCBA
MWYLPQHUTBDZACFIEOVNGKRSX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 USEBWCYQTIAKGPONXVMRZHFLD
WZYXVUTSRQPONMLKIHGFEDCBA
DLFHZRMVXNOPGKAITQYCWBESU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZBUHSICNOEMRAFPQGXTYKDVLW
WZYXVUTSRQPONMLKIHGFEDCBA
WLVDKYTXGQPFARMEONCISHUBZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KZITOWQNUYEBASPDFGHLRVMCX
WZYXVUTSRQPONMLKIHGFEDCBA
XCMVRLHGFDPSABEYUNQWOTIZK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DPHUQAERLYCMOVGNBKTZWSXFI
WZYXVUTSRQPONMLKIHGFEDCBA
IFXSWZTKBNGVOMCYLREAQUHPD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HULSBPYQXOEZRTFMWKAIVGDCN
WZYXVUTSRQPONMLKIHGFEDCBA
NCDGVIAKWMFTRZEOXQYPBSLUH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LDTKIPSCWMEQGXNZAHUYOFVBR
WZYXVUTSRQPONMLKIHGFEDCBA
RBVFOYUHAZNXGQEMWCSPIKTDL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LBACHFPNXYTMQZIWDUGVKESRO
WZYXVUTSRQPONMLKIHGFEDCBA
ORSEKVGUDWIZQMTYXNPFHCABL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VCAQIMBLODSRPWKHXUYNETGZF
WZYXVUTSRQPONMLKIHGFEDCBA
FZGTENYUXHKWPRSDOLBMIQACV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MDWKRTFUVXAGSIPYZCHQNLEBO
WZYXVUTSRQPONMLKIHGFEDCBA
OBELNQHCZYPISGAXVUFTRKWDM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ELFUIBHOCSDYXZQRVTMGNKAWP
WZYXVUTSRQPONMLKIHGFEDCBA
PWAKNGMTVRQZXYDSCOHBIUFLE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FKNXSZACEULHWTIPYBMRQDOVG
WZYXVUTSRQPONMLKIHGFEDCBA
GVODQRMBYPITWHLUECAZSXNKF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZAWFTSLCGIUDKXHBNPYERQVOM
WZYXVUTSRQPONMLKIHGFEDCBA
MOVQREYPNBHXKDUIGCLSTFWAZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TPCKDSIFUOWMZARGXVLQBNYHE
WZYXVUTSRQPONMLKIHGFEDCBA
EHYNBQLVXGRAZMWOUFISDKCPT

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.