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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = CBIHYCLEBSIZPNOFTTKXURHVPYWAKDYIFV 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZUEVHOPMANFDSTBGYRWCXILKQ
WZYXVUTSRQPONMLKIHGFEDCBA
QKLIXCWRYGBTSDFNAMPOHVEUZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FWZQXDOSIKAYBPVMTEGNCLRUH
WZYXVUTSRQPONMLKIHGFEDCBA
HURLCNGETMVPBYAKISODXQZWF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NTEXFGBHIUCOLZVRWQPMSAKYD
WZYXVUTSRQPONMLKIHGFEDCBA
DYKASMPQWRVZLOCUIHBGFXETN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YAQHXTSNBPVFOCKIEZRDULWGM
WZYXVUTSRQPONMLKIHGFEDCBA
MGWLUDRZEIKCOFVPBNSTXHQAY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LAHVYRSZFWQCPIBKEMDNUOTXG
WZYXVUTSRQPONMLKIHGFEDCBA
GXTOUNDMEKBIPCQWFZSRYVHAL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KFPHQSUOZMLRCGYBDWXNAIVET
WZYXVUTSRQPONMLKIHGFEDCBA
TEVIANXWDBYGCRLMZOUSQHPFK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WDXITBRZOANGSEHKQVLCUPFYM
WZYXVUTSRQPONMLKIHGFEDCBA
MYFPUCLVQKHESGNAOZRBTIXDW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 USXMCGNFEYAIQBWPRHLVOTDKZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZKDTOVLHRPWBQIAYEFNGCMXSU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IZONRBGKYVMDHULCXSTQPEFWA
WZYXVUTSRQPONMLKIHGFEDCBA
AWFEPQTSXCLUHDMVYKGBRNOZI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CGENOBVMSIAURPTKWYXLFZHQD
WZYXVUTSRQPONMLKIHGFEDCBA
DQHZFLXYWKTPRUAISMVBONEGC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GNASIRVOXDWYUKLEMCTZPBQHF
WZYXVUTSRQPONMLKIHGFEDCBA
FHQBPZTCMELKUYWDXOVRISANG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MUVZPKDCLXIBQWTRYNHFESOAG
WZYXVUTSRQPONMLKIHGFEDCBA
GAOSEFHNYRTWQBIXLCDKPZVUM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SDXNRUALOZCBFHPWQMTKIGVEY
WZYXVUTSRQPONMLKIHGFEDCBA
YEVGIKTMQWPHFBCZOLAURNXDS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VKWPTQGYMXNEUASRCZOFDLIHB
WZYXVUTSRQPONMLKIHGFEDCBA
BHILDFOZCRSAUENXMYGQTPWKV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OLYAQWUBZKTPSNEMGIHFDRVCX
WZYXVUTSRQPONMLKIHGFEDCBA
XCVRDFHIGMENSPTKZBUWQAYLO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZQEYOSKAPLRNFTMVHDICUBXGW
WZYXVUTSRQPONMLKIHGFEDCBA
WGXBUCIDHVMTFNRLPAKSOYEQZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AMEQTLPHSNZGWYXIOKUCBFVDR
WZYXVUTSRQPONMLKIHGFEDCBA
RDVFBCUKOIXYWGZNSHPLTQEMA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZYFNWAMKDCERSLHGOTBPUQXIV
WZYXVUTSRQPONMLKIHGFEDCBA
VIXQUPBTOGHLSRECDKMAWNFYZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BFSVPRTMWELZQYCUXKHGOINAD
WZYXVUTSRQPONMLKIHGFEDCBA
DANIOGHKXUCYQZLEWMTRPVSFB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WYCUZGVDXPQMIFNOSKERLBTAH
WZYXVUTSRQPONMLKIHGFEDCBA
HATBLREKSONFIMQPXDVGZUCYW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DLKYVWUSBQRHOXFGNZPTECMAI
WZYXVUTSRQPONMLKIHGFEDCBA
IAMCETPZNGFXOHRQBSUWVYKLD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NVBGHXLREIPDCMOZAUSWYTKQF
WZYXVUTSRQPONMLKIHGFEDCBA
FQKTYWSUAZOMCDPIERLXHGBVN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MNYEQSTIUWPLFGVKXZHACOBRD
WZYXVUTSRQPONMLKIHGFEDCBA
DRBOCAHZXKVGFLPWUITSQEYNM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CYSPVFAKDHZTWINUBGLOXREQM
WZYXVUTSRQPONMLKIHGFEDCBA
MQERXOLGBUNIWTZHDKAFVPSYC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IEAPDBSCVKZWLHFQMXROTNUYG
WZYXVUTSRQPONMLKIHGFEDCBA
GYUNTORXMQFHLWZKVCSBDPAEI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UMIWKXGPYTQVFONLHRZEDBSCA
WZYXVUTSRQPONMLKIHGFEDCBA
ACSBDEZRHLNOFVQTYPGXKWIMU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KAEXQSPCBRMZWDUTONGILYFHV
WZYXVUTSRQPONMLKIHGFEDCBA
VHFYLIGNOTUDWZMRBCPSQXEAK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UXBRLYCNWVDPKEQFOMASIZHGT
WZYXVUTSRQPONMLKIHGFEDCBA
TGHZISAMOFQEKPDVWNCYLRBXU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VPYTQNMKREWIFHLCSBXUZODGA
WZYXVUTSRQPONMLKIHGFEDCBA
AGDOZUXBSCLHFIWERKMNQTYPV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AWYKDZGRVBMOQXEUTNHIFPSCL
WZYXVUTSRQPONMLKIHGFEDCBA
LCSPFIHNTUEXQOMBVRGZDKYWA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TILCYNDXKPWHSRFUAVGBZMQOE
WZYXVUTSRQPONMLKIHGFEDCBA
EOQMZBGVAUFRSHWPKXDNYCLIT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IXFKHSBRCEQPLNZVMGTAUODYW
WZYXVUTSRQPONMLKIHGFEDCBA
WYDOUATGMVZNLPQECRBSHKFXI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EHWCYQNUVSBMXPLAGFKRDIOTZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZTOIDRKFGALPXMBSVUNQYCWHE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BXYGEPMNQRIDAFCZLTVWKUHOS
WZYXVUTSRQPONMLKIHGFEDCBA
SOHUKWVTLZCFADIRQNMPEGYXB

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.