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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = FAXFILIEBUXAQHUTGDATLFVCPFHOYLWTBA 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BWRHKMGQICEOPUZYANLFDXTSV
WZYXVUTSRQPONMLKIHGFEDCBA
VSTXDFLNAYZUPOECIQGMKHRWB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NYLKRSIPFVWUAMBDTHOGQEXZC
WZYXVUTSRQPONMLKIHGFEDCBA
CZXEQGOHTDBMAUWVFPISRKLYN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PYTEDKSBXFRNQHZIGULVOMCAW
WZYXVUTSRQPONMLKIHGFEDCBA
WACMOVLUGIZHQNRFXBSKDETYP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XQNFLHYIBCPOVSGWEURMTZKAD
WZYXVUTSRQPONMLKIHGFEDCBA
DAKZTMRUEWGSVOPCBIYHLFNQX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RCZEIWAXNHMUDTYFKOVSPQBLG
WZYXVUTSRQPONMLKIHGFEDCBA
GLBQPSVOKFYTDUMHNXAWIEZCR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UHOQSZFVXKBTLAGRMDWECIPNY
WZYXVUTSRQPONMLKIHGFEDCBA
YNPICEWDMRGALTBKXVFZSQOHU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MEASVPLCDBXFNRZYQTIUGHKOW
WZYXVUTSRQPONMLKIHGFEDCBA
WOKHGUITQYZRNFXBDCLPVSAEM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LHAWUCNBEFVRQYSPOTZDKXMGI
WZYXVUTSRQPONMLKIHGFEDCBA
IGMXKDZTOPSYQRVFEBNCUWAHL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OFCTMBEVAHRGSQKYNZILUWXDP
WZYXVUTSRQPONMLKIHGFEDCBA
PDXWULIZNYKQSGRHAVEBMTCFO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZVPSBQGHUWRXCLYEADOMINTFK
WZYXVUTSRQPONMLKIHGFEDCBA
KFTNIMODAEYLCXRWUHGQBSPVZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EQSWXLYRBOTUVCKPNGZFDAIHM
WZYXVUTSRQPONMLKIHGFEDCBA
MHIADFZGNPKCVUTOBRYLXWSQE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BRPATKFICGHSEZVXUNQYDOMWL
WZYXVUTSRQPONMLKIHGFEDCBA
LWMODYQNUXVZESHGCIFKTAPRB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WXRIGTLYHMPSOVQUADZNKEFBC
WZYXVUTSRQPONMLKIHGFEDCBA
CBFEKNZDAUQVOSPMHYLTGIRXW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NMVDAIEZBQHXWGKPUYCSRTOFL
WZYXVUTSRQPONMLKIHGFEDCBA
LFOTRSCYUPKGWXHQBZEIADVMN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UBPMNYWZQCAXGVDRFSOIEHKLT
WZYXVUTSRQPONMLKIHGFEDCBA
TLKHEIOSFRDVGXACQZWYNMPBU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XUGPYDKWSVLNTHEAMFCOIBRQZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZQRBIOCFMAEHTNLVSWKDYPGUX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WEYCGHZAOQVRXTLSIBPNFUDMK
WZYXVUTSRQPONMLKIHGFEDCBA
KMDUFNPBISLTXRVQOAZHGCYEW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TYBIAVHFSMNWKOPZGDXERULQC
WZYXVUTSRQPONMLKIHGFEDCBA
CQLUREXDGZPOKWNMSFHVAIBYT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LCMTUNKRPXQGBZDOFAWVIYESH
WZYXVUTSRQPONMLKIHGFEDCBA
HSEYIVWAFODZBGQXPRKNUTMCL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IKRZBGLDTCYFPQUMEASHNWOVX
WZYXVUTSRQPONMLKIHGFEDCBA
XVOWNHSAEMUQPFYCTDLGBZRKI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AVSDNOLYFIZMTBEXWHKPUQGCR
WZYXVUTSRQPONMLKIHGFEDCBA
RCGQUPKHWXEBTMZIFYLONDSVA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RECZLWXFQASHNPKVMUIOBGTDY
WZYXVUTSRQPONMLKIHGFEDCBA
YDTGBOIUMVKPNHSAQFXWLZCER
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AHMSIPGQTEWRCDLFYUVNZKXOB
WZYXVUTSRQPONMLKIHGFEDCBA
BOXKZNVUYFLDCRWETQGPISMHA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OULBCFDMRVTEAIYKHPQNZXGSW
WZYXVUTSRQPONMLKIHGFEDCBA
WSGXZNQPHKYIAETVRMDFCBLUO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RBTPXUEOFHSKIAWCVDGZQMLNY
WZYXVUTSRQPONMLKIHGFEDCBA
YNLMQZGDVCWAIKSHFOEUXPTBR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LUHQZNEWFXTABMGKDSRIPYVOC
WZYXVUTSRQPONMLKIHGFEDCBA
COVYPIRSDKGMBATXFWENZQHUL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZLGBQANKICMXHFEODRSVUYTPW
WZYXVUTSRQPONMLKIHGFEDCBA
WPTYUVSRDOEFHXMCIKNAQBGLZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XPDVGBURIYHKFQSLWNOATZCME
WZYXVUTSRQPONMLKIHGFEDCBA
EMCZTAONWLSQFKHYIRUBGVDPX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TERKFAIYDGCLWVPUHZBSONQMX
WZYXVUTSRQPONMLKIHGFEDCBA
XMQNOSBZHUPVWLCGDYIAFKRET
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VRXALZSONEUMIQTKYWFGDCPBH
WZYXVUTSRQPONMLKIHGFEDCBA
HBPCDGFWYKTQIMUENOSZLAXRV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NZTDWSYOMXBKRPCVIQGELAFUH
WZYXVUTSRQPONMLKIHGFEDCBA
HUFALEGQIVCPRKBXMOYSWDTZN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TDZMOGWLACPVBFQEKHXINYSUR
WZYXVUTSRQPONMLKIHGFEDCBA
RUSYNIXHKEQFBVPCALWGOMZDT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YPIAFWTHVEXDGMKNUBOZQLCSR
WZYXVUTSRQPONMLKIHGFEDCBA
RSCLQZOBUNKMGDXEVHTWFAIPY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GSDYRLVFUXKQNTMPIZABCHWEO
WZYXVUTSRQPONMLKIHGFEDCBA
OEWHCBAZIPMTNQKXUFVLRYDSG

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.