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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = HPZOLGBGYPZWXRIAGMXFKFQMSBUKBFUFGC 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GDVZOYSFBCQWTAPXNIKHRMEUL
WZYXVUTSRQPONMLKIHGFEDCBA
LUEMRHKINXPATWQCBFSYOZVDG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SCOQMGYRBVFAPLDUEHNIZTWKX
WZYXVUTSRQPONMLKIHGFEDCBA
XKWTZINHEUDLPAFVBRYGMQOCS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EVHGPNWSZMCFLXIBAOUQRKTDY
WZYXVUTSRQPONMLKIHGFEDCBA
YDTKRQUOABIXLFCMZSWNPGHVE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 REFOGZTAHWQSYINLMVXCBDPUK
WZYXVUTSRQPONMLKIHGFEDCBA
KUPDBCXVMLNIYSQWHATZGOFER
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XZDKLWBPEQUAHVGIOYFSNRCMT
WZYXVUTSRQPONMLKIHGFEDCBA
TMCRNSFYOIGVHAUQEPBWLKDZX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 POQZCIVANELRGBUYXSDTWHFMK
WZYXVUTSRQPONMLKIHGFEDCBA
KMFHWTDSXYUBGRLENAVICZQOP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AKHGUXYINTMVPLESWRBZFQOCD
WZYXVUTSRQPONMLKIHGFEDCBA
DCOQFZBRWSELPVMTNIYXUGHKA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PEKXAWULGCFDZOQTYIMNSBRVH
WZYXVUTSRQPONMLKIHGFEDCBA
HVRBSNMIYTQOZDFCGLUWAXKEP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IBZFKYTNHQOGMWRPAULSCDVEX
WZYXVUTSRQPONMLKIHGFEDCBA
XEVDCSLUAPRWMGOQHNTYKFZBI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZCQHRTOSPVAMLIYDBFUWNEGKX
WZYXVUTSRQPONMLKIHGFEDCBA
XKGENWUFBDYILMAVPSOTRHQCZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RMXEZICAWLSTBKNVHDPYUOQFG
WZYXVUTSRQPONMLKIHGFEDCBA
GFQOUYPDHVNKBTSLWACIZEXMR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YVKWEAQRUTNDBOGLHZMSFICPX
WZYXVUTSRQPONMLKIHGFEDCBA
XPCIFSMZHLGOBDNTURQAEWKVY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WGKYIQUDATMBNEXHSCLPOVZFR
WZYXVUTSRQPONMLKIHGFEDCBA
RFZVOPLCSHXENBMTADUQIYKGW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LPNOZFMDSIRECXHWBKQGAVYTU
WZYXVUTSRQPONMLKIHGFEDCBA
UTYVAGQKBWHXCERISDMFZONPL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IQNAXSLKDWGMORBYCHEVTFZUP
WZYXVUTSRQPONMLKIHGFEDCBA
PUZFTVEHCYBROMGWDKLSXANQI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FBWGLVPYIQTZADEXNOMUKHCSR
WZYXVUTSRQPONMLKIHGFEDCBA
RSCHKUMONXEDAZTQIYPVLGWBF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XLMVGUBIYFRQTPWHEZKNADCSO
WZYXVUTSRQPONMLKIHGFEDCBA
OSCDANKZEHWPTQRFYIBUGVMLX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WGEAFRXPBTYVSIQCDMZOKLHNU
WZYXVUTSRQPONMLKIHGFEDCBA
UNHLKOZMDCQISVYTBPXRFAEGW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RNETFBUOIVSZMGWHCXALPDQYK
WZYXVUTSRQPONMLKIHGFEDCBA
KYQDPLAXCHWGMZSVIOUBFTENR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ELHIUAWKFSPMNBVDXRYZOCGQT
WZYXVUTSRQPONMLKIHGFEDCBA
TQGCOZYRXDVBNMPSFKWAUIHLE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QAHDWIKMRSETONYFZCUXPLGBV
WZYXVUTSRQPONMLKIHGFEDCBA
VBGLPXUCZFYNOTESRMKIWDHAQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QYLTGPIFZMECUSVHXDWBAKNOR
WZYXVUTSRQPONMLKIHGFEDCBA
RONKABWDXHVSUCEMZFIPGTLYQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CDKUNTILFBSYPWRZGVQXHAOME
WZYXVUTSRQPONMLKIHGFEDCBA
EMOAHXQVGZRWPYSBFLITNUKDC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZBAEMSGOWYXRIHVLUPTQFNCDK
WZYXVUTSRQPONMLKIHGFEDCBA
KDCNFQTPULVHIRXYWOGSMEABZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BXTSRQPVOUEHANIWLCGZDMYKF
WZYXVUTSRQPONMLKIHGFEDCBA
FKYMDZGCLWINAHEUOVPQRSTXB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UDQZKHWFBTAVNXOGCYIRLEPMS
WZYXVUTSRQPONMLKIHGFEDCBA
SMPELRIYCGOXNVATBFWHKZQDU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 INFEHZAORYVXUBWPCSDTKLQGM
WZYXVUTSRQPONMLKIHGFEDCBA
MGQLKTDSCPWBUXVYROAZHEFNI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SQZCDLMPTRXNOFEUABKGHIVWY
WZYXVUTSRQPONMLKIHGFEDCBA
YWVIHGKBAUEFONXRTPMLDCZQS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DETCNMXBKZHULVPASFRWIOGQY
WZYXVUTSRQPONMLKIHGFEDCBA
YQGOIWRFSAPVLUHZKBXMNCTED
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EKAMFLRICVXPQZUNBSYWDTHGO
WZYXVUTSRQPONMLKIHGFEDCBA
OGHTDWYSBNUZQPXVCIRLFMAKE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OLXNURSCQBGATPDIKVWFHMEZY
WZYXVUTSRQPONMLKIHGFEDCBA
YZEMHFWVKIDPTAGBQCSRUNXLO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FWAVCPKOLYHBRNTSUQGIZMXDE
WZYXVUTSRQPONMLKIHGFEDCBA
EDXMZIGQUSTNRBHYLOKPCVAWF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ATWIQEPRFLUVSDCOMGHZYXNKB
WZYXVUTSRQPONMLKIHGFEDCBA
BKNXYZHGMOCDSVULFRPEQIWTA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DLBZURYNQGEVXSAHMTCPWKFIO
WZYXVUTSRQPONMLKIHGFEDCBA
OIFKWPCTMHASXVEGQNYRUZBLD

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
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