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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = KPWENEPAHUNECGFGTDDMKSNEEQLDGTEVRE 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AOYLHEDNRQXCISUFMTGKVBPZW
WZYXVUTSRQPONMLKIHGFEDCBA
WZPBVKGTMFUSICXQRNDEHLYOA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QLSWVHAIFNRMPBZCXDKOUGYET
WZYXVUTSRQPONMLKIHGFEDCBA
TEYGUOKDXCZBPMRNFIAHVWSLQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ARUCTHQFWPBLSKODEGXIMZYNV
WZYXVUTSRQPONMLKIHGFEDCBA
VNYZMIXGEDOKSLBPWFQHTCURA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LXOEBFHTWIPGZRDQUNCAMSKVY
WZYXVUTSRQPONMLKIHGFEDCBA
YVKSMACNUQDRZGPIWTHFBEOXL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FKVENYQHLXIRBASOPZGDCWUTM
WZYXVUTSRQPONMLKIHGFEDCBA
MTUWCDGZPOSABRIXLHQYNEVKF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WZOBGPIRKNCFEMUAVLDXYSQTH
WZYXVUTSRQPONMLKIHGFEDCBA
HTQSYXDLVAUMEFCNKRIPGBOZW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OUYKMCINSLTFXERGHWPVDQBZA
WZYXVUTSRQPONMLKIHGFEDCBA
AZBQDVPWHGREXFTLSNICMKYUO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HTERLCFGAUSIBKZQYMODWVPXN
WZYXVUTSRQPONMLKIHGFEDCBA
NXPVWDOMYQZKBISUAGFCLRETH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IKRXEHCWOULSZNQPBVMDTAFYG
WZYXVUTSRQPONMLKIHGFEDCBA
GYFATDMVBPQNZSLUOWCHEXRKI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GTBVNEDYUWCFHAQXMLSZRKIPO
WZYXVUTSRQPONMLKIHGFEDCBA
OPIKRZSLMXQAHFCWUYDENVBTG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IPEMNSUDTOXYQLKRVHZGBFAWC
WZYXVUTSRQPONMLKIHGFEDCBA
CWAFBGZHVRKLQYXOTDUSNMEPI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CQXELZOWBYKSPNHDIFUAVMTRG
WZYXVUTSRQPONMLKIHGFEDCBA
GRTMVAUFIDHNPSKYBWOZLEXQC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OZTSNDVEABPWLMCQYUGKFIHRX
WZYXVUTSRQPONMLKIHGFEDCBA
XRHIFKGUYQCMLWPBAEVDNSTZO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BESXTYIQOCGVZLUWAPKMRNFHD
WZYXVUTSRQPONMLKIHGFEDCBA
DHFNRMKPAWULZVGCOQIYTXSEB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FVOGCTKINDAMRXWQZULHSEPBY
WZYXVUTSRQPONMLKIHGFEDCBA
YBPESHLUZQWXRMADNIKTCGOVF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WHVNZARSMYUFGDPKEBCXTOQLI
WZYXVUTSRQPONMLKIHGFEDCBA
ILQOTXCBEKPDGFUYMSRAZNVHW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IHPUTLSAGEBMWXYZQDKVROCNF
WZYXVUTSRQPONMLKIHGFEDCBA
FNCORVKDQZYXWMBEGASLTUPHI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BXKWOMHVACRNTSUZPDYGQLEFI
WZYXVUTSRQPONMLKIHGFEDCBA
IFELQGYDPZUSTNRCAVHMOWKXB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ABWEYTGSFILROHUPXDMNZKCQV
WZYXVUTSRQPONMLKIHGFEDCBA
VQCKZNMDXPUHORLIFSGTYEWBA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PCFTHLUIMYEBAWNKOZVQSGDXR
WZYXVUTSRQPONMLKIHGFEDCBA
RXDGSQVZOKNWABEYMIULHTFCP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RUAVYGKWLCFTXNEQPHSOMBDZI
WZYXVUTSRQPONMLKIHGFEDCBA
IZDBMOSHPQENXTFCLWKGYVAUR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MDFTWYKSXEPCOQRUVIHGNBALZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZLABNGHIVURQOCPEXSKYWTFDM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YQCZEWKIFBLDPGATUMNRXVHOS
WZYXVUTSRQPONMLKIHGFEDCBA
SOHVXRNMUTAGPDLBFIKWEZCQY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SCUYEVRTWOZXBGDFMHNPAKLIQ
WZYXVUTSRQPONMLKIHGFEDCBA
QILKAPNHMFDGBXZOWTRVEYUCS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YGOESBZUVRWNLPKDQIFATMXHC
WZYXVUTSRQPONMLKIHGFEDCBA
CHXMTAFIQDKPLNWRVUZBSEOGY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LBOZMCVTQAKSWFNUEGHYRIPDX
WZYXVUTSRQPONMLKIHGFEDCBA
XDPIRYHGEUNFWSKAQTVCMZOBL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QWHGVMSYZOFALBRNKEPTXCUDI
WZYXVUTSRQPONMLKIHGFEDCBA
IDUCXTPEKNRBLAFOZYSMVGHWQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SVYGCRZBAHWNXTLOEMDIKQUPF
WZYXVUTSRQPONMLKIHGFEDCBA
FPUQKIDMEOLTXNWHABZRCGYVS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KNEFORYGPCLDATIMUZHQSWVXB
WZYXVUTSRQPONMLKIHGFEDCBA
BXVWSQHZUMITADLCPGYROFENK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SCOLTPXEVWNHYURAFBDQIKGMZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZMGKIQDBFARUYHNWVEXPTLOCS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OHKAEIUGYDWPZCLXTQSRMVBNF
WZYXVUTSRQPONMLKIHGFEDCBA
FNBVMRSQTXLCZPWDYGUIEAKHO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VTFBXSPDEQIMKOGRNYLZWCHUA
WZYXVUTSRQPONMLKIHGFEDCBA
AUHCWZLYNRGOKMIQEDPSXBFTV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EADGQWZKHCIYTMFOSRVLUBXPN
WZYXVUTSRQPONMLKIHGFEDCBA
NPXBULVRSOFMTYICHKZWQGDAE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LMDYWKBAPGROHXTICUENVQZFS
WZYXVUTSRQPONMLKIHGFEDCBA
SFZQVNEUCITXHORGPABKWYDML

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.