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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = DDCSUDTEIROCPXXOKRBMLTVGTVQAUSHXKQ 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BEUIOAQZWTCXKSVRNGMDPFYLH
WZYXVUTSRQPONMLKIHGFEDCBA
HLYFPDMGNRVSKXCTWZQAOIUEB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PRYISZKVQOFTDEUAGNHBMCWXL
WZYXVUTSRQPONMLKIHGFEDCBA
LXWCMBHNGAUEDTFOQVKZSIYRP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WPZSMFHECTXBGUVRDNILKAYQO
WZYXVUTSRQPONMLKIHGFEDCBA
OQYAKLINDRVUGBXTCEHFMSZPW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YOUSHNTWLIKVRPAGQCMEZFDXB
WZYXVUTSRQPONMLKIHGFEDCBA
BXDFZEMCQGAPRVKILWTNHSUOY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WXZRUMOHGISYBPKNDELVCTFAQ
WZYXVUTSRQPONMLKIHGFEDCBA
QAFTCVLEDNKPBYSIGHOMURZXW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CNGTAWRYZKSMDFVLXQOPEBUIH
WZYXVUTSRQPONMLKIHGFEDCBA
HIUBEPOQXLVFDMSKZYRWATGNC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WBQPNGUAOKCREZMSVDTYXFLIH
WZYXVUTSRQPONMLKIHGFEDCBA
HILFXYTDVSMZERCKOAUGNPQBW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PBYNUOLXEDKMZIAHRSQGCWFTV
WZYXVUTSRQPONMLKIHGFEDCBA
VTFWCGQSRHAIZMKDEXLOUNYBP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WZRUPIHSFYLVGEANQMKCOXDBT
WZYXVUTSRQPONMLKIHGFEDCBA
TBDXOCKMQNAEGVLYFSHIPURZW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AGHDLYCKRZWXMSIFENUQOPBVT
WZYXVUTSRQPONMLKIHGFEDCBA
TVBPOQUNEFISMXWZRKCYLDHGA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NIRCOZETDHABPLUMKVXWYSFGQ
WZYXVUTSRQPONMLKIHGFEDCBA
QGFSYWXVKMULPBAHDTEZOCRIN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TFACWVOINRXKYMLDPQHZBUESG
WZYXVUTSRQPONMLKIHGFEDCBA
GSEUBZHQPDLMYKXRNIOVWCAFT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AONFQGZUEWTBMDPHYXCLRIVSK
WZYXVUTSRQPONMLKIHGFEDCBA
KSVIRLCXYHPDMBTWEUZGQFNOA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VCQYTEZIPBXUANFWKGMORLHSD
WZYXVUTSRQPONMLKIHGFEDCBA
DSHLROMGKWFNAUXBPIZETYQCV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XBYUCPQFHOWKMGDSEATZIRLNV
WZYXVUTSRQPONMLKIHGFEDCBA
VNLRIZTAESDGMKWOHFQPCUYBX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TAVEQNBSLZUDOWHFYRMGXIKPC
WZYXVUTSRQPONMLKIHGFEDCBA
CPKIXGMRYFHWODUZLSBNQEVAT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GAPNKTFLQMBCRXSIUVWHZDOYE
WZYXVUTSRQPONMLKIHGFEDCBA
EYODZHWVUISXRCBMQLFTKNPAG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 POZALXFMITVBWEQKDRUYCGNSH
WZYXVUTSRQPONMLKIHGFEDCBA
HSNGCYURDKQEWBVTIMFXLAZOP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XPCFHUVTRYENAQWSKBOMLDZGI
WZYXVUTSRQPONMLKIHGFEDCBA
IGZDLMOBKSWQANEYRTVUHFCPX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UHFEWKAQMIXDBSZVTOYNLRCPG
WZYXVUTSRQPONMLKIHGFEDCBA
GPCRLNYOTVZSBDXIMQAKWEFHU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VEURKYLQCPSITFZWABDOXNHGM
WZYXVUTSRQPONMLKIHGFEDCBA
MGHNXODBAWZFTISPCQLYKRUEV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EZQHNFCTAVDYKUBWOMRSIPXGL
WZYXVUTSRQPONMLKIHGFEDCBA
LGXPISRMOWBUKYDVATCFNHQZE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PGNDTKISWRCEXYFQZAVOBUHML
WZYXVUTSRQPONMLKIHGFEDCBA
LMHUBOVAZQFYXECRWSIKTDNGP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BYCXGRNMFSEPAVOTWQKUZDLHI
WZYXVUTSRQPONMLKIHGFEDCBA
IHLDZUKQWTOVAPESFMNRGXCYB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NCVTRGUOHSXAEFIZLYWDKPBMQ
WZYXVUTSRQPONMLKIHGFEDCBA
QMBPKDWYLZIFEAXSHOUGRTVCN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZWDQYCEBVURGOKMIFPNLXHTSA
WZYXVUTSRQPONMLKIHGFEDCBA
ASTHXLNPFIMKOGRUVBECYQDWZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WXUCZTAVBPSFQYDNOHIERMGKL
WZYXVUTSRQPONMLKIHGFEDCBA
LKGMREIHONDYQFSPBVATZCUXW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SETMVWKQXLPRINUCGZAHBYDFO
WZYXVUTSRQPONMLKIHGFEDCBA
OFDYBHAZGCUNIRPLXQKWVMTES
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MDBVPKOUCWQELHZYXRNIGTAFS
WZYXVUTSRQPONMLKIHGFEDCBA
SFATGINRXYZHLEQWCUOKPVBDM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OLYVSDGZEBMQPFUNTXWARKICH
WZYXVUTSRQPONMLKIHGFEDCBA
HCIKRAWXTNUFPQMBEZGDSVYLO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NZKOHLBVGYQPDMUEXFTACRWSI
WZYXVUTSRQPONMLKIHGFEDCBA
ISWRCATFXEUMDPQYGVBLHOKZN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XTFVGSHDEYOPWIZRQKACBMLUN
WZYXVUTSRQPONMLKIHGFEDCBA
NULMBCAKQRZIWPOYEDHSGVFTX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GRMCQUWIZTNSBVYXEKPHFLDOA
WZYXVUTSRQPONMLKIHGFEDCBA
AODLFHPKEXYVBSNTZIWUQCMRG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VEBATGKMRNWLIOHDZCQXFSPYU
WZYXVUTSRQPONMLKIHGFEDCBA
UYPSFXQCZDHOILWNRMKGTABEV

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.