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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = ONDEBADCMQLUSWVWYQCMQGPBCPUYXQBDTB 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZXVDSHICNWGKUFLTPAEOYBMRQ
WZYXVUTSRQPONMLKIHGFEDCBA
QRMBYOEAPTLFUKGWNCIHSDVXZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AFDZMWVIUBEHNKSORCLYPGTQX
WZYXVUTSRQPONMLKIHGFEDCBA
XQTGPYLCROSKNHEBUIVWMZDFA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VFMACZBIDWREXYTUGHLNQPSOK
WZYXVUTSRQPONMLKIHGFEDCBA
KOSPQNLHGUTYXERWDIBZCAMFV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SBYEMFWRQAUOCDPGTNZLKXIVH
WZYXVUTSRQPONMLKIHGFEDCBA
HVIXKLZNTGPDCOUAQRWFMEYBS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YHSTBOLDNRQUPFGVAWMCKXZEI
WZYXVUTSRQPONMLKIHGFEDCBA
IEZXKCMWAVGFPUQRNDLOBTSHY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HQLYDNVMEPRUATFSGWIOCZXBK
WZYXVUTSRQPONMLKIHGFEDCBA
KBXZCOIWGSFTAURPEMVNDYLQH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VQINTWUGHRLYKABCPXDFEZOSM
WZYXVUTSRQPONMLKIHGFEDCBA
MSOZEFDXPCBAKYLRHGUWTNIQV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FEBWKTUZCIRAGDOXQMNSLPHVY
WZYXVUTSRQPONMLKIHGFEDCBA
YVHPLSNMQXODGARICZUTKWBEF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LFGAHMIPOEXCWUDNRKSTYBQZV
WZYXVUTSRQPONMLKIHGFEDCBA
VZQBYTSKRNDUWCXEOPIMHAGFL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RIZVNKETQDWAMHLSCOUYPXBGF
WZYXVUTSRQPONMLKIHGFEDCBA
FGBXPYUOCSLHMAWDQTEKNVZIR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SNPULCKYBFMQOEGXDIHVZWTAR
WZYXVUTSRQPONMLKIHGFEDCBA
RATWZVHIDXGEOQMFBYKCLUPNS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OVMURYKDIESPQNTWACGFLBXZH
WZYXVUTSRQPONMLKIHGFEDCBA
HZXBLFGCAWTNQPSEIDKYRUMVO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YHFQNVCIKZWDMESRXBLPUAOGT
WZYXVUTSRQPONMLKIHGFEDCBA
TGOAUPLBXRSEMDWZKICVNQFHY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SMUAEDZNKPWFRHOQCVYIGTBXL
WZYXVUTSRQPONMLKIHGFEDCBA
LXBTGIYVCQOHRFWPKNZDEAUMS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VMDIPUABQCGTWRENSKFZXOHYL
WZYXVUTSRQPONMLKIHGFEDCBA
LYHOXZFKSNERWTGCQBAUPIDMV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MYETLCQZGXKAWNPVOFUDHISRB
WZYXVUTSRQPONMLKIHGFEDCBA
BRSIHDUFOVPNWAKXGZQCLTEYM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TKEVYUGRABHDQFMPSNOCWLZIX
WZYXVUTSRQPONMLKIHGFEDCBA
XIZLWCONSPMFQDHBARGUYVEKT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WOUVDHPMLIKFSCGXNQETZYABR
WZYXVUTSRQPONMLKIHGFEDCBA
RBAYZTEQNXGCSFKILMPHDVUOW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HDUWLEZXVSBGMPRTACNIOFYQK
WZYXVUTSRQPONMLKIHGFEDCBA
KQYFOINCATRPMGBSVXZELWUDH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ITKOZSVBMXLQUGNPFYACRWDHE
WZYXVUTSRQPONMLKIHGFEDCBA
EHDWRCAYFPNGUQLXMBVSZOKTI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NDOFBWQVKCUEYXPSHIMTZAGRL
WZYXVUTSRQPONMLKIHGFEDCBA
LRGAZTMIHSPXYEUCKVQWBFODN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LIASCKEGXNMYZDHWUOVRTPBFQ
WZYXVUTSRQPONMLKIHGFEDCBA
QFBPTRVOUWHDZYMNXGEKCSAIL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UCGAXMNFODIYKQSTVLPZREWHB
WZYXVUTSRQPONMLKIHGFEDCBA
BHWERZPLVTSQKYIDOFNMXAGCU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IXWHBCEFMGZTQDLUOAYVRPNKS
WZYXVUTSRQPONMLKIHGFEDCBA
SKNPRVYAOULDQTZGMFECBHWXI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LSOCRZKMYVNWXPEBQATIFGDHU
WZYXVUTSRQPONMLKIHGFEDCBA
UHDGFITAQBEPXWNVYMKZRCOSL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CZWRABFSPHKOUVLNIMQDXTYGE
WZYXVUTSRQPONMLKIHGFEDCBA
EGYTXDQMINLVUOKHPSFBARWZC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OBTVIDYHCQKEUASWMGRLXFPNZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZNPFXLRGMWSAUEKQCHYDIVTBO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PTEHNMXODRZGLCIASQYUBVWFK
WZYXVUTSRQPONMLKIHGFEDCBA
KFWVBUYQSAICLGZRDOXMNHETP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CAORDFHXLPKYIZBWTMNEUQSGV
WZYXVUTSRQPONMLKIHGFEDCBA
VGSQUENMTWBZIYKPLXHFDROAC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DGXBQFHSTVRYWLEMPAUNCOKIZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZIKOCNUAPMELWYRVTSHFQBXGD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LWMZBPCHNEYRIQGAKFDVSUTOX
WZYXVUTSRQPONMLKIHGFEDCBA
XOTUSVDFKAGQIRYENHCPBZMWL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DKZOSYXPHVQWUAGCTBLMFNREI
WZYXVUTSRQPONMLKIHGFEDCBA
IERNFMLBTCGAUWQVHPXYSOZKD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OVDBEMGPKUFIXYSQNTRLAZHCW
WZYXVUTSRQPONMLKIHGFEDCBA
WCHZALRTNQSYXIFUKPGMEBDVO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DMUZYKNROLVWQFEIHPBGCXTSA
WZYXVUTSRQPONMLKIHGFEDCBA
ASTXCGBPHIEFQWVLORNKYZUMD

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.