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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = DAZAPWFUDDWQFWAZWOTURALDBHNUEMEMBP 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VFWBGQKERSAZOLMCINXDUYHPT
WZYXVUTSRQPONMLKIHGFEDCBA
TPHYUDXNICMLOZASREKQGBWFV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HWNULIQSGTYZACORDMFPXEVBK
WZYXVUTSRQPONMLKIHGFEDCBA
KBVEXPFMDROCAZYTGSQILUNWH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WYABGOIFZDSMTLUNHRPKECVXQ
WZYXVUTSRQPONMLKIHGFEDCBA
QXVCEKPRHNULTMSDZFIOGBAYW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DXVAFWBGZCLPMQONHYISTRUEK
WZYXVUTSRQPONMLKIHGFEDCBA
KEURTSIYHNOQMPLCZGBWFAVXD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ESKUPZYLTXNQWMOVADFHIRGCB
WZYXVUTSRQPONMLKIHGFEDCBA
BCGRIHFDAVOMWQNXTLYZPUKSE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IGRDQVKHCBZEWMXYUPSOFTNLA
WZYXVUTSRQPONMLKIHGFEDCBA
ALNTFOSPUYXMWEZBCHKVQDRGI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HMWCBZNIRQXKYEOADSFPTVLGU
WZYXVUTSRQPONMLKIHGFEDCBA
UGLVTPFSDAOEYKXQRINZBCWMH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BOSVEXCPUGQTNWHFZMDAKLIYR
WZYXVUTSRQPONMLKIHGFEDCBA
RYILKADMZFHWNTQGUPCXEVSOB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RIHAODCWVXFQZTLEMGUNPBKSY
WZYXVUTSRQPONMLKIHGFEDCBA
YSKBPNUGMELTZQFXVWCDOAHIR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LMPRGYFSDICKOBENQXHATVZUW
WZYXVUTSRQPONMLKIHGFEDCBA
WUZVTAHXQNEBOKCIDSFYGRPML
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XTEDWMOLAGUYNKCVQIFSPRBHZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZHBRPSFIQVCKNYUGALOMWDETX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CMEQTHNPOULWDZYISXVABKRFG
WZYXVUTSRQPONMLKIHGFEDCBA
GFRKBAVXSIYZDWLUOPNHTQEMC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KAPMHIQVOCNXSWFDRELTGZBUY
WZYXVUTSRQPONMLKIHGFEDCBA
YUBZGTLERDFWSXNCOVQIHMPAK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GCNZQMISAUWHFTXKDPYBVEOLR
WZYXVUTSRQPONMLKIHGFEDCBA
RLOEVBYPDKXTFHWUASIMQZNCG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 AKHDOWMRNIEYTVXLSCQGBFUZP
WZYXVUTSRQPONMLKIHGFEDCBA
PZUFBGQCSLXVTYEINRMWODHKA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TOAISNHBXMPVZCFEGDYWULRKQ
WZYXVUTSRQPONMLKIHGFEDCBA
QKRLUWYDGEFCZVPMXBHNSIAOT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CIYSWULOVREHBGDQTZMPANXFK
WZYXVUTSRQPONMLKIHGFEDCBA
KFXNAPMZTQDGBHERVOLUWSYIC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZFUPLRTVNISHYDEQMOXWKBCGA
WZYXVUTSRQPONMLKIHGFEDCBA
AGCBKWXOMQEDYHSINVTRLPUFZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LWQIEDKOZYXRSPFCMTAUBVHNG
WZYXVUTSRQPONMLKIHGFEDCBA
GNHVBUATMCFPSRXYZOKDEIQWL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GPDYKCLIUTQZBAXEWOSRVFHNM
WZYXVUTSRQPONMLKIHGFEDCBA
MNHFVRSOWEXABZQTUILCKYDPG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WPZIGQRVTLCXUKMNAHOBFYDES
WZYXVUTSRQPONMLKIHGFEDCBA
SEDYFBOHANMKUXCLTVRQGIZPW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RXOVKSUAPEHGZDCMLBNWTYQFI
WZYXVUTSRQPONMLKIHGFEDCBA
IFQYTWNBLMCDZGHEPAUSKVOXR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ARKBTZSNMOWEHCXPIFLUGYVDQ
WZYXVUTSRQPONMLKIHGFEDCBA
QDVYGULFIPXCHEWOMNSZTBKRA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 YWZTDNURXSIQKAGCBMLEOFPVH
WZYXVUTSRQPONMLKIHGFEDCBA
HVPFOELMBCGAKQISXRUNDTZWY
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CZFBIKWGLVNURETPSQDXAMYOH
WZYXVUTSRQPONMLKIHGFEDCBA
HOYMAXDQSPTERUNVLGWKIBFZC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XASIRDLPHNZQMCYFOUWTGKEBV
WZYXVUTSRQPONMLKIHGFEDCBA
VBEKGTWUOFYCMQZNHPLDRISAX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CFZXTQSVIBMLNDUWYGKAHPORE
WZYXVUTSRQPONMLKIHGFEDCBA
EROPHAKGYWUDNLMBIVSQTXZFC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FMGRQZTVYNLKEIWHXDUACSBPO
WZYXVUTSRQPONMLKIHGFEDCBA
OPBSCAUDXHWIEKLNYVTZQRGMF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CVAQTSYEWLRXFMPODHBNIUKZG
WZYXVUTSRQPONMLKIHGFEDCBA
GZKUINBHDOPMFXRLWEYSTQAVC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NYGOMQRFPDAHCIKUWBVSZLTEX
WZYXVUTSRQPONMLKIHGFEDCBA
XETLZSVBWUKICHADPFRQMOGYN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DMCREPFAXTOKIYZNVGQBLHSUW
WZYXVUTSRQPONMLKIHGFEDCBA
WUSHLBQGVNZYIKOTXAFPERCMD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MHFBPXGZYUALWCIQORTKNEDVS
WZYXVUTSRQPONMLKIHGFEDCBA
SVDENKTROQICWLAUYZGXPBFHM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HWYGLSTRXUDPACOZEBQIKMVNF
WZYXVUTSRQPONMLKIHGFEDCBA
FNVMKIQBEZOCAPDUXRTSLGYWH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BGQIVNRUKZDCSYAOEXPHLTMFW
WZYXVUTSRQPONMLKIHGFEDCBA
WFMTLHPXEOAYSCDZKURNVIQGB

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.