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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = MLLPPIRKQALGPDEQPXLAMUOOBQYRWPQWQL 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LDCXFEKRZPGSTQNBIVAMHOYWU
WZYXVUTSRQPONMLKIHGFEDCBA
UWYOHMAVIBNQTSGPZRKEFXCDL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GOSVXDFWHAEMLTKZYUNPIQRBC
WZYXVUTSRQPONMLKIHGFEDCBA
CBRQIPNUYZKTLMEAHWFDXVSOG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WFUNDVSQLOMRXIZTHCBGPAEYK
WZYXVUTSRQPONMLKIHGFEDCBA
KYEAPGBCHTZIXRMOLQSVDNUFW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VBHPDCQLYEOTZGINXWFKUASMR
WZYXVUTSRQPONMLKIHGFEDCBA
RMSAUKFWXNIGZTOEYLQCDPHBV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IZLQPAMSGBVHRCFXTWOYDENKU
WZYXVUTSRQPONMLKIHGFEDCBA
UKNEDYOWTXFCRHVBGSMAPQLZI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YXMVDTEBGUQFIKOHAZWCLRSPN
WZYXVUTSRQPONMLKIHGFEDCBA
NPSRLCWZAHOKIFQUGBETDVMXY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PCHFDSEAIWKZLNGBYQROXUTVM
WZYXVUTSRQPONMLKIHGFEDCBA
MVTUXORQYBGNLZKWIAESDFHCP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NVWETDUXKZYBCAHFILMPOQRSG
WZYXVUTSRQPONMLKIHGFEDCBA
GSRQOPMLIFHACBYZKXUDTEWVN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SNDAHQOBRVYULTEMXFPZIKWGC
WZYXVUTSRQPONMLKIHGFEDCBA
CGWKIZPFXMETLUYVRBOQHADNS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HYGSOXKBANIRWLDTEZFVCUPMQ
WZYXVUTSRQPONMLKIHGFEDCBA
QMPUCVFZETDLWRINABKXOSGYH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HUCELBPINGYKSZFAMXDTOVWRQ
WZYXVUTSRQPONMLKIHGFEDCBA
QRWVOTDXMAFZSKYGNIPBLECUH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RATGKCPEHVOIFYSMUZBQDLWXN
WZYXVUTSRQPONMLKIHGFEDCBA
NXWLDQBZUMSYFIOVHEPCKGTAR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HZTAXRQVKYEMIGPCUWFNLOBDS
WZYXVUTSRQPONMLKIHGFEDCBA
SDBOLNFWUCPGIMEYKVQRXATZH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TMVKIYRGQUDHLBXFENZSWPCOA
WZYXVUTSRQPONMLKIHGFEDCBA
AOCPWSZNEFXBLHDUQGRYIKVMT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EOBLZVDMRQXKHCFGPTSNIWYUA
WZYXVUTSRQPONMLKIHGFEDCBA
AUYWINSTPGFCHKXQRMDVZLBOE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LPUZMBDWEOXYQGNFCASIHTRVK
WZYXVUTSRQPONMLKIHGFEDCBA
KVRTHISACFNGQYXOEWDBMZUPL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CWFVPYHDRGQTKOXULSIZBNAEM
WZYXVUTSRQPONMLKIHGFEDCBA
MEANBZISLUXOKTQGRDHYPVFWC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HQBWIGCLOYVMEADRTXUKSPZNF
WZYXVUTSRQPONMLKIHGFEDCBA
FNZPSKUXTRDAEMVYOLCGIWBQH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QYXOGFZVHUDNWKATILBMPRSCE
WZYXVUTSRQPONMLKIHGFEDCBA
ECSRPMBLITAKWNDUHVZFGOXYQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FCWZQDPOAHXKEURBGLITNYVSM
WZYXVUTSRQPONMLKIHGFEDCBA
MSVYNTILGBRUEKXHAOPDQZWCF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GIRFTWMVZLNBACEKYPOUDQXHS
WZYXVUTSRQPONMLKIHGFEDCBA
SHXQDUOPYKECABNLZVMWTFRIG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IRKFMNPUBVHCEGAXYLTZOWSQD
WZYXVUTSRQPONMLKIHGFEDCBA
DQSWOZTLYXAGECHVBUPNMFKRI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NZTHFERXPYDALWCGMIOSKVBQU
WZYXVUTSRQPONMLKIHGFEDCBA
UQBVKSOIMGCWLADYPXREFHTZN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WUNROXELPKTVCQHAZIGYMFBSD
WZYXVUTSRQPONMLKIHGFEDCBA
DSBFMYGIZAHQCVTKPLEXORNUW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VEYBQNALCUDZWOPKIMSFXTRGH
WZYXVUTSRQPONMLKIHGFEDCBA
HGRTXFSMIKPOWZDUCLANQBYEV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XBYDWTVEQZPGUFHOCIRNMAKLS
WZYXVUTSRQPONMLKIHGFEDCBA
SLKAMNRICOHFUGPZQEVTWDYBX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DATEMWZNXBLSYOKVGQUHRIPCF
WZYXVUTSRQPONMLKIHGFEDCBA
FCPIRHUQGVKOYSLBXNZWMETAD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MXQOANSBGVKFUWDTIZRYELCHP
WZYXVUTSRQPONMLKIHGFEDCBA
PHCLEYRZITDWUFKVGBSNAOQXM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UZGMBRYWFLXSCADVNIPKOHTEQ
WZYXVUTSRQPONMLKIHGFEDCBA
QETHOKPINVDACSXLFWYRBMGZU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UQYBPLXNSGRIDOTMKHZFEWAVC
WZYXVUTSRQPONMLKIHGFEDCBA
CVAWEFZHKMTODIRGSNXLPBYQU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NHXGQBCIWEYOZMFKDSRULATVP
WZYXVUTSRQPONMLKIHGFEDCBA
PVTALURSDKFMZOYEWICBQGXHN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WMUAIFORCVHEYPDBNSZXQKGLT
WZYXVUTSRQPONMLKIHGFEDCBA
TLGKQXZSNBDPYEHVCROFIAUMW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XSAFPCGDYINEUBLROQMWTKHVZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZVHKTWMQORLBUENIYDGCPFASX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FYRHGNDAPMTQSVKXBOLEZCUIW
WZYXVUTSRQPONMLKIHGFEDCBA
WIUCZELOBXKVSQTMPADNGHRYF

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.