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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = SHWZETHCCYRCQPTEQXQISQSQMMUGDMGCFP 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VHOIMRZLAGQCUPWKXTBSYFDNE
WZYXVUTSRQPONMLKIHGFEDCBA
ENDFYSBTXKWPUCQGALZRMIOHV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GMRECOWLAKYSHNUTZVFIQXBPD
WZYXVUTSRQPONMLKIHGFEDCBA
DPBXQIFVZTUNHSYKALWOCERMG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AOPEDKNSWTULRCMZYBGHVXFQI
WZYXVUTSRQPONMLKIHGFEDCBA
IQFXVHGBYZMCRLUTWSNKDEPOA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SGWZVXYHKCMQOAREPDUNLTIFB
WZYXVUTSRQPONMLKIHGFEDCBA
BFITLNUDPERAOQMCKHYXVZWGS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CQZHEDAOGWLBYTPIKNVMFRXSU
WZYXVUTSRQPONMLKIHGFEDCBA
USXRFMVNKIPTYBLWGOADEHZQC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UZVNRYOGXWIATSCQEDPMKBFLH
WZYXVUTSRQPONMLKIHGFEDCBA
HLFBKMPDEQCSTAIWXGOYRNVZU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IZYGDVBCRQUOKFNLTPHXSEWMA
WZYXVUTSRQPONMLKIHGFEDCBA
AMWESXHPTLNFKOUQRCBVDGYZI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZNHBLEMKCUQWVPSOGFXRYADIT
WZYXVUTSRQPONMLKIHGFEDCBA
TIDAYRXFGOSPVWQUCKMELBHNZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WAUZVCXKIYRMHDOEPNTFGLQBS
WZYXVUTSRQPONMLKIHGFEDCBA
SBQLGFTNPEODHMRYIKXCVZUAW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EIONSAMUYKQZGWDHVTPXCRFLB
WZYXVUTSRQPONMLKIHGFEDCBA
BLFRCXPTVHDWGZQKYUMASNOIE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UEGLRPQWBCSDNIZYVXFTAMKOH
WZYXVUTSRQPONMLKIHGFEDCBA
HOKMATFXVYZINDSCBWQPRLGEU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OIDCKZYNEHBUXFTWRVMSQGPLA
WZYXVUTSRQPONMLKIHGFEDCBA
ALPGQSMVRWTFXUBHENYZKCDIO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SZHGXPVDRWLOUYQBAKCFIETMN
WZYXVUTSRQPONMLKIHGFEDCBA
NMTEIFCKABQYUOLWRDVPXGHZS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YEZSWOKVXQPIMUDLGTFCRHBAN
WZYXVUTSRQPONMLKIHGFEDCBA
NABHRCFTGLDUMIPQXVKOWSZEY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TUVOCHMGFEKZRDYNWLAXQPISB
WZYXVUTSRQPONMLKIHGFEDCBA
BSIPQXALWNYDRZKEFGMHCOVUT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YMXKVQDRLTSUEBANHWFOZIGCP
WZYXVUTSRQPONMLKIHGFEDCBA
PCGIZOFWHNABEUSTLRDQVKXMY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PZHAQNYCKIWDOTRGMLUSFBXEV
WZYXVUTSRQPONMLKIHGFEDCBA
VEXBFSULMGRTODWIKCYNQAHZP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PFZDMQTIYSWKOBVACXNRHUELG
WZYXVUTSRQPONMLKIHGFEDCBA
GLEUHRNXCAVBOKWSYITQMDZFP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VIPUSYGWRLHFDTEAXQNZMKOCB
WZYXVUTSRQPONMLKIHGFEDCBA
BCOKMZNQXAETDFHLRWGYSUPIV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UDFABSXLIREHWGZPONVKTYCQM
WZYXVUTSRQPONMLKIHGFEDCBA
MQCYTKVNOPZGWHERILXSBAFDU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WEFZTMSXPRYGNHLCKUBOQVADI
WZYXVUTSRQPONMLKIHGFEDCBA
IDAVQOBUKCLHNGYRPXSMTZFEW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KXINHYOQBMGREFDAPUVTLWCSZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZSCWLTVUPADFERGMBQOYHNIXK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QTWRXLBPYKCUANVHDISFOZGEM
WZYXVUTSRQPONMLKIHGFEDCBA
MEGZOFSIDHVNAUCKYPBLXRWTQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EOKGQRYHPNCBUZAFWVISTMLDX
WZYXVUTSRQPONMLKIHGFEDCBA
XDLMTSIVWFAZUBCNPHYRQGKOE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YVEMDQRSAZGOUKCIPFWLHBTNX
WZYXVUTSRQPONMLKIHGFEDCBA
XNTBHLWFPICKUOGZASRQDMEVY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WTZNXHKRMYUDLOCISQEBAPVFG
WZYXVUTSRQPONMLKIHGFEDCBA
GFVPABEQSICOLDUYMRKHXNZTW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MOSYPWVGXHEFUATRBCLNIZKDQ
WZYXVUTSRQPONMLKIHGFEDCBA
QDKZINLCBRTAUFEHXGVWPYSOM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TFZRLMCWDYOBVXAHIKGPNESQU
WZYXVUTSRQPONMLKIHGFEDCBA
UQSENPGKIHAXVBOYDWCMLRZFT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZRMHXUBDSTNEYLIVCKQAOFGWP
WZYXVUTSRQPONMLKIHGFEDCBA
PWGFOAQKCVILYENTSDBUXHMRZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RCHWMUYDIGAENFXKTBLPQZSVO
WZYXVUTSRQPONMLKIHGFEDCBA
OVSZQPLBTKXFNEAGIDYUMWHCR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LMTUGZIKDNYAHWFQXOVBECSPR
WZYXVUTSRQPONMLKIHGFEDCBA
RPSCEBVOXQFWHAYNDKIZGUTML
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CSDMQVYANPHKBXRLTUOIWFGEZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZEGFWIOUTLRXBKHPNAYVQMDSC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TQIOZMRPNBEHWDXSKFUCYAVLG
WZYXVUTSRQPONMLKIHGFEDCBA
GLVAYCUFKSXDWHEBNPRMZOIQT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ONAEZIYQSLMDCFVHKGPUBWRTX
WZYXVUTSRQPONMLKIHGFEDCBA
XTRWBUPGKHVFCDMLSQYIZEANO

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.