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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = TUFYZUQHARFAKIXOCBXRADOVGLKMYKQSFT 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AVWSCZUBLKMEHOFYGXNTQDIPR
WZYXVUTSRQPONMLKIHGFEDCBA
RPIDQTNXGYFOHEMKLBUZCSWVA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DXNBSGCOHYQFURTEAZLMWKPVI
WZYXVUTSRQPONMLKIHGFEDCBA
IVPKWMLZAETRUFQYHOCGSBNXD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NLSTRXYMFZDKAQUVEWHPIGOBC
WZYXVUTSRQPONMLKIHGFEDCBA
CBOGIPHWEVUQAKDZFMYXRTSLN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HIGYCZMPQBFNWUSVAKXRDOETL
WZYXVUTSRQPONMLKIHGFEDCBA
LTEODRXKAVSUWNFBQPMZCYGIH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WOXVZUDGEAKCMTQNFBPYSIHLR
WZYXVUTSRQPONMLKIHGFEDCBA
RLHISYPBFNQTMCKAEGDUZVXOW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VCZYBFXPDSOWURETHILGQNAKM
WZYXVUTSRQPONMLKIHGFEDCBA
MKANQGLIHTERUWOSDPXFBYZCV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GYUHWADCZBIKXSLRNMQFPTOVE
WZYXVUTSRQPONMLKIHGFEDCBA
EVOTPFQMNRLSXKIBZCDAWHUYG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 URBDVNISHQTGYXFZWKOMLEACP
WZYXVUTSRQPONMLKIHGFEDCBA
PCAELMOKWZFXYGTQHSINVDBRU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KMYWDATVCUPOFIXSBGQRLHZEN
WZYXVUTSRQPONMLKIHGFEDCBA
NEZHLRQGBSXIFOPUCVTADWYMK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KUSMVZXDRTGQLEYHWFNBCOAPI
WZYXVUTSRQPONMLKIHGFEDCBA
IPAOCBNFWHYELQGTRDXZVMSUK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CEQVFUGZNRSLMYDIHAWPXKOBT
WZYXVUTSRQPONMLKIHGFEDCBA
TBOKXPWAHIDYMLSRNZGUFVQEC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TXMALQDPFZSBERNVHWGIKUOCY
WZYXVUTSRQPONMLKIHGFEDCBA
YCOUKIGWHVNREBSZFPDQLAMXT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BHYOTZFPLGADNSKMIQUWXCEVR
WZYXVUTSRQPONMLKIHGFEDCBA
RVECXWUQIMKSNDAGLPFZTOYHB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OBWAKPDSMRIHYZUEXVLNFTQGC
WZYXVUTSRQPONMLKIHGFEDCBA
CGQTFNLVXEUZYHIRMSDPKAWBO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XKNDFZRGYSPLUEVIOBCQAMTWH
WZYXVUTSRQPONMLKIHGFEDCBA
HWTMAQCBOIVEULPSYGRZFDNKX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DEXWRGVBSZIPOMNHCAKQYTFLU
WZYXVUTSRQPONMLKIHGFEDCBA
ULFTYQKACHNMOPIZSBVGRWXED
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TDHICGOKBPWMLAEQSXZYNRFUV
WZYXVUTSRQPONMLKIHGFEDCBA
VUFRNYZXSQEALMWPBKOGCIHDT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PFDTKAMQIVSOCZUNYBXWEGHRL
WZYXVUTSRQPONMLKIHGFEDCBA
LRHGEWXBYNUZCOSVIQMAKTDFP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DBLHMYVQAPZCWNKSEXTUOGRIF
WZYXVUTSRQPONMLKIHGFEDCBA
FIRGOUTXESKNWCZPAQVYMHLBD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QSGXLHWMRDVNAKPOFUIYBCZTE
WZYXVUTSRQPONMLKIHGFEDCBA
ETZCBYIUFOPKANVDRMWHLXGSQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SOGLENAYVZHCXTRBPIFDWQMUK
WZYXVUTSRQPONMLKIHGFEDCBA
KUMQWDFIPBRTXCHZVYANELGOS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ERLWPHTDSCKFGIZAQBYOXMVNU
WZYXVUTSRQPONMLKIHGFEDCBA
UNVMXOYBQAZIGFKCSDTHPWLRE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AFZMUEQLRPBWIGSNTVOYKXDHC
WZYXVUTSRQPONMLKIHGFEDCBA
CHDXKYOVTNSGIWBPRLQEUMZFA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TPXRVAQBWEUFSHOKGNYLDCIMZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZMICDLYNGKOHSFUEWBQAVRXPT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZSRGLNABIUXKMYHQTOEWDVCFP
WZYXVUTSRQPONMLKIHGFEDCBA
PFCVDWEOTQHYMKXUIBANLGRSZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TKUVIRSCLAOWDPGYMQEHBZFXN
WZYXVUTSRQPONMLKIHGFEDCBA
NXFZBHEQMYGPDWOALCSRIVUKT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZYCEAQVLMSUDKWONPIRFTGXBH
WZYXVUTSRQPONMLKIHGFEDCBA
HBXGTFRIPNOWKDUSMLVQAECYZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ANPBDYWZXFCQELGTKIMOUSVHR
WZYXVUTSRQPONMLKIHGFEDCBA
RHVSUOMIKTGLEQCFXZWYDBPNA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZASPLIRYXOWTMVNQUDKECGFHB
WZYXVUTSRQPONMLKIHGFEDCBA
BHFGCEKDUQNVMTWOXYRILPSAZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UFONKXMIQBZYSTVEPLARDWGHC
WZYXVUTSRQPONMLKIHGFEDCBA
CHGWDRALPEVTSYZBQIMXKNOFU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WCMPQGIVXYERHODLNBFKAUSZT
WZYXVUTSRQPONMLKIHGFEDCBA
TZSUAKFBNLDOHREYXVIGQPMCW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SBOIVKHYUZLCEGWDPRNAXTQFM
WZYXVUTSRQPONMLKIHGFEDCBA
MFQTXANRPDWGECLZUYHKVIOBS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WBRATISUYCNGKLDHXFPEMVQZO
WZYXVUTSRQPONMLKIHGFEDCBA
OZQVMEPFXHDLKGNCYUSITARBW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UPWKQCLSVHIBEFAMXGTDOZYNR
WZYXVUTSRQPONMLKIHGFEDCBA
RNYZODTGXMAFEBIHVSLCQKWPU

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.