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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = PQTMHPLAOAORRYDEEDCEBFOSVDSPZYVRYU 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GUBYTSVOEAQKFCHLIZDPMXNRW
WZYXVUTSRQPONMLKIHGFEDCBA
WRNXMPDZILHCFKQAEOVSTYBUG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VWASOBCKFYEXQRDTMNZLPGUHI
WZYXVUTSRQPONMLKIHGFEDCBA
IHUGPLZNMTDRQXEYFKCBOSAWV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EPYFWUAZTRMVQSBLXOGKNCDHI
WZYXVUTSRQPONMLKIHGFEDCBA
IHDCNKGOXLBSQVMRTZAUWFYPE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SCEMQORDKXBHYAFUTWLNZGPVI
WZYXVUTSRQPONMLKIHGFEDCBA
IVPGZNLWTUFAYHBXKDROQMECS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FXMKHNBPRQADEGTWLVYOUIZSC
WZYXVUTSRQPONMLKIHGFEDCBA
CSZIUOYVLWTGEDAQRPBNHKMXF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MSVZNDCIQOTAPERFGXHLBKYWU
WZYXVUTSRQPONMLKIHGFEDCBA
UWYKBLHXGFREPATOQICDNZVSM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZQEXIYHBSGOVKWMTPFLRANCUD
WZYXVUTSRQPONMLKIHGFEDCBA
DUCNARLFPTMWKVOGSBHYIXEQZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
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WZYXVUTSRQPONMLKIHGFEDCBA
FUCNBEOLHGMPDXQRAIVSTWYZK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WQSALOIHNGDKFUMCTPEVZXYRB
WZYXVUTSRQPONMLKIHGFEDCBA
BRYXZVEPTCMUFKDGNHIOLASQW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KRDOFHPYAQITZUBGXMNSVLCWE
WZYXVUTSRQPONMLKIHGFEDCBA
EWCLVSNMXGBUZTIQAYPHFODRK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LWQHOBTDFGMRVESIPACNKXUZY
WZYXVUTSRQPONMLKIHGFEDCBA
YZUXKNCAPISEVRMGFDTBOHQWL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PGNRFLBHAOXDEWMKQZCUTISYV
WZYXVUTSRQPONMLKIHGFEDCBA
VYSITUCZQKMWEDXOAHBLFRNGP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GTSIHPZOBNXMQCRWVLAUDFEYK
WZYXVUTSRQPONMLKIHGFEDCBA
KYEFDUALVWRCQMXNBOZPHISTG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PIRSZWVNODYEBLGQHUCMKATFX
WZYXVUTSRQPONMLKIHGFEDCBA
XFTAKMCUHQGLBEYDONVWZSRIP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DERGBWVMQNKPIAHTZSUOYFXLC
WZYXVUTSRQPONMLKIHGFEDCBA
CLXFYOUSZTHAIPKNQMVWBGRED
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ODVZGBCMSIPTEWHQKXUFANLYR
WZYXVUTSRQPONMLKIHGFEDCBA
RYLNAFUXKQHWETPISMCBGZVDO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VLIXEZHKSFQUGAORPCTNMBWDY
WZYXVUTSRQPONMLKIHGFEDCBA
YDWBMNTCPROAGUQFSKHZEXILV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CKNLZOFMVBRUIWPTQDASXHEYG
WZYXVUTSRQPONMLKIHGFEDCBA
GYEHXSADQTPWIURBVMFOZLNKC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 THPONRSZBAXLFEKIYCVUMQDWG
WZYXVUTSRQPONMLKIHGFEDCBA
GWDQMUVCYIKEFLXABZSRNOPHT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WOFDMRYTELHVBGZCAPQKXUISN
WZYXVUTSRQPONMLKIHGFEDCBA
NSIUXKQPACZGBVHLETYRMDFOW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VNDEKTBZWHIQFAURMSXOLYGCP
WZYXVUTSRQPONMLKIHGFEDCBA
PCGYLOXSMRUAFQIHWZBTKEDNV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VXHYSZPFBTNRWKODQGEUACIML
WZYXVUTSRQPONMLKIHGFEDCBA
LMICAUEGQDOKWRNTBFPZSYHXV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VIUHKFDEQBARXMSPWNOTGYLZC
WZYXVUTSRQPONMLKIHGFEDCBA
CZLYGTONWPSMXRABQEDFKHUIV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HXDPSWIAURLBYOQZMETVNFKCG
WZYXVUTSRQPONMLKIHGFEDCBA
GCKFNVTEMZQOYBLRUAIWSPDXH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LOQVETBAYRSZCUNPFMKXGIHWD
WZYXVUTSRQPONMLKIHGFEDCBA
DWHIGXKMFPNUCZSRYABTEVQOL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LITGQPUCDNKZRHXEBSFWMYAOV
WZYXVUTSRQPONMLKIHGFEDCBA
VOAYMWFSBEXHRZKNDCUPQGTIL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YLFIWPTGEBZUSCXHNRQVKAODM
WZYXVUTSRQPONMLKIHGFEDCBA
MDOAKVQRNHXCSUZBEGTPWIFLY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XNEZOUTWADYMVGSBFQPHLCRKI
WZYXVUTSRQPONMLKIHGFEDCBA
IKRCLHPQFBSGVMYDAWTUOZENX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QEAPLHMZNIRFDSKOTWCVYGXUB
WZYXVUTSRQPONMLKIHGFEDCBA
BUXGYVCWTOKSDFRINZMHLPAEQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EKGWYFPCHDROSNZVXBAMQLUIT
WZYXVUTSRQPONMLKIHGFEDCBA
TIULQMABXVZNSORDHCPFYWGKE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LFWHVCOEMNBRZIUDXGSKATPQY
WZYXVUTSRQPONMLKIHGFEDCBA
YQPTAKSGXDUIZRBNMEOCVHWFL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RVWKEPUIOBGSNLACTQDZHFYXM
WZYXVUTSRQPONMLKIHGFEDCBA
MXYFHZDQTCALNSGBOIUPEKWVR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WTKFBAXVZHDPEOILUYRGSQNMC
WZYXVUTSRQPONMLKIHGFEDCBA
CMNQSGRYULIOEPDHZVXABFKTW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RWCHOYGIKPLFNEMVQZUXABTDS
WZYXVUTSRQPONMLKIHGFEDCBA
SDTBAXUZQVMENFLPKIGYOHCWR

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.