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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = NZWRDLYKCIECFUFFPSBCWTGDSUVPGFGIQT 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZXWRSYGEQUMITOBLHVFNKDAPC
WZYXVUTSRQPONMLKIHGFEDCBA
CPADKNFVHLBOTIMUQEGYSRWXZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IXUTRVQNSKFPZLHOCAMBDGYEW
WZYXVUTSRQPONMLKIHGFEDCBA
WEYGDBMACOHLZPFKSNQVRTUXI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HTLNKDVFWQAUIRPYBGXOZESMC
WZYXVUTSRQPONMLKIHGFEDCBA
CMSEZOXGBYPRIUAQWFVDKNLTH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ABNREHZXSKIVFPUTOMCGDWLQY
WZYXVUTSRQPONMLKIHGFEDCBA
YQLWDGCMOTUPFVIKSXZHERNBA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YGEVDKXFSNLAMHTUPQWBIROZC
WZYXVUTSRQPONMLKIHGFEDCBA
CZORIBWQPUTHMALNSFXKDVEGY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UBVANOZSRQWCLETDKXIPHFGYM
WZYXVUTSRQPONMLKIHGFEDCBA
MYGFHPIXKDTELCWQRSZONAVBU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FIVXEPQHLRUZMNOCKTYGDWABS
WZYXVUTSRQPONMLKIHGFEDCBA
SBAWDGYTKCONMZURLHQPEXVIF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 URMWQOEAKBGCTPLHINYXZDFVS
WZYXVUTSRQPONMLKIHGFEDCBA
SVFDZXYNIHLPTCGBKAEOQWMRU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XWSYECQVNPMFZLOUTIHDARKBG
WZYXVUTSRQPONMLKIHGFEDCBA
GBKRADHITUOLZFMPNVQCEYSWX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OGUVXQPTIMALFWDBRKZECYHSN
WZYXVUTSRQPONMLKIHGFEDCBA
NSHYCEZKRBDWFLAMITPQXVUGO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PXMHEFYOWSIQGCAZDTLBVNUKR
WZYXVUTSRQPONMLKIHGFEDCBA
RKUNVBLTDZACGQISWOYFEHMXP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WKFCEVSALBMPYUOQGDZIHXRTN
WZYXVUTSRQPONMLKIHGFEDCBA
NTRXHIZDGQOUYPMBLASVECFKW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SPOKYXHEBMLZDNFCUTARGVWIQ
WZYXVUTSRQPONMLKIHGFEDCBA
QIWVGRATUCFNDZLMBEHXYKOPS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ANQPGXFZKSUEBCLROIVWMYTDH
WZYXVUTSRQPONMLKIHGFEDCBA
HDTYMWVIORLCBEUSKZFXGPQNA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FKRZQGWBVNISTEALCMODXYPUH
WZYXVUTSRQPONMLKIHGFEDCBA
HUPYXDOMCLAETSINVBWGQZRKF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LIOCPMHYBGRKFUEXAZSNWVDQT
WZYXVUTSRQPONMLKIHGFEDCBA
TQDVWNSZAXEUFKRGBYHMPCOIL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KTFYPVHZGLMSUERAXCIODBQNW
WZYXVUTSRQPONMLKIHGFEDCBA
WNQBDOICXAREUSMLGZHVPYFTK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UAMDFVNYWIOTQKCBXSZGPRELH
WZYXVUTSRQPONMLKIHGFEDCBA
HLERPGZSXBCKQTOIWYNVFDMAU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QDLCIAYMPWOGNKFVXBSHEURTZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZTRUEHSBXVFKNGOWPMYAICLDQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LTIOPSBUCFAEGNVDZYQKHRMXW
WZYXVUTSRQPONMLKIHGFEDCBA
WXMRHKQYZDVNGEAFCUBSPOITL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LGHRKTWBCOSVPFYXIZUNEAMDQ
WZYXVUTSRQPONMLKIHGFEDCBA
QDMAENUZIXYFPVSOCBWTKRHGL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YKXANQLTZBDPCGSOVIFEMWRHU
WZYXVUTSRQPONMLKIHGFEDCBA
UHRWMEFIVOSGCPDBZTLQNAXKY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FUYVBLSMHTWZEPRDQIGACXONK
WZYXVUTSRQPONMLKIHGFEDCBA
KNOXCAGIQDRPEZWTHMSLBVYUF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YXWIDTOVQKZCELMAHNFBPSURG
WZYXVUTSRQPONMLKIHGFEDCBA
GRUSPBFNHAMLECZKQVOTDIWXY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WXRSLQOHTAMKPGECINFZYDBUV
WZYXVUTSRQPONMLKIHGFEDCBA
VUBDYZFNICEGPKMATHOQLSRXW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LQCKHWIEUBTOVDFXRSNAGYPMZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZMPYGANSRXFDVOTBUEIWHKCQL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LMFTUXCIZORYVSKWHAPNDGBQE
WZYXVUTSRQPONMLKIHGFEDCBA
EQBGDNPAHWKSVYROZICXUTFML
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KWNYLIGVQARMCBOTUFPSZEDXH
WZYXVUTSRQPONMLKIHGFEDCBA
HXDEZSPFUTOBCMRAQVGILYNWK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XFSDEROGHNTQYMCZBUWIAPVKL
WZYXVUTSRQPONMLKIHGFEDCBA
LKVPAIWUBZCMYQTNHGOREDSFX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MGRQFXNLOTUCDZHSKWIABPEYV
WZYXVUTSRQPONMLKIHGFEDCBA
VYEPBAIWKSHZDCUTOLNXFQRGM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IYWEGDROUHVPTFBMALSZQKNXC
WZYXVUTSRQPONMLKIHGFEDCBA
CXNKQZSLAMBFTPVHUORDGEWYI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IUCOQLYNKBVRTFHAEWXMDPSGZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZGSPDMXWEAHFTRVBKNYLQOCUI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IBESTZAMCPDOLRWNHQGVYKXUF
WZYXVUTSRQPONMLKIHGFEDCBA
FUXKYVGQHNWRLODPCMAZTSEBI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HZIUKECNMVBLXQGOSYTARDPFW
WZYXVUTSRQPONMLKIHGFEDCBA
WFPDRATYSOGQXLBVMNCEKUIZH

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.