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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = VBVWLCVEWZCEBOBIQOLYUOXPTQXGNGOGZS 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PMOQZYGKDHWNTLRESBIVXCUAF
WZYXVUTSRQPONMLKIHGFEDCBA
FAUCXVIBSERLTNWHDKGYZQOMP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TLCRYKFIWUGXBQDNSPEHMVZAO
WZYXVUTSRQPONMLKIHGFEDCBA
OAZVMHEPSNDQBXGUWIFKYRCLT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OGNKSTBCVXWEZHDRPAYIFMUQL
WZYXVUTSRQPONMLKIHGFEDCBA
LQUMFIYAPRDHZEWXVCBTSKNGO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DAFWNGPTSXKIZMBULHRQOECVY
WZYXVUTSRQPONMLKIHGFEDCBA
YVCEOQRHLUBMZIKXSTPGNWFAD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NRSKLFPMHQZOAUDYWIXETGVCB
WZYXVUTSRQPONMLKIHGFEDCBA
BCVGTEXIWYDUAOZQHMPFLKSRN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LHTQVADMSOYWCGKRFZPXBNUIE
WZYXVUTSRQPONMLKIHGFEDCBA
EIUNBXPZFRKGCWYOSMDAVQTHL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 FKWAHGORZCLYETSUPNVXQDBMI
WZYXVUTSRQPONMLKIHGFEDCBA
IMBDQXVNPUSTEYLCZROGHAWKF
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ZCRUVBAFEDNLPWIQKHXGYOSMT
WZYXVUTSRQPONMLKIHGFEDCBA
TMSOYGXHKQIWPLNDEFABVURCZ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NMXQIWOKSFEUGLVHYAZTCDBRP
WZYXVUTSRQPONMLKIHGFEDCBA
PRBDCTZAYHVLGUEFSKOWIQXMN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EMTVYBHKZURXIDNQLFCWAPSGO
WZYXVUTSRQPONMLKIHGFEDCBA
OGSPAWCFLQNDIXRUZKHBYVTME
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SNWVCEAOYTKZBRUXLMGPFDIQH
WZYXVUTSRQPONMLKIHGFEDCBA
HQIDFPGMLXURBZKTYOAECVWNS
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IRYEVLZHKTMOUWFNDGQBCSXPA
WZYXVUTSRQPONMLKIHGFEDCBA
APXSCBQGDNFWUOMTKHZLVEYRI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OGDYUMFLKPEVISBCAXWZHRQNT
WZYXVUTSRQPONMLKIHGFEDCBA
TNQRHZWXACBSIVEPKLFMUYDGO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PTVGSUXWYNOFZCMHEKQALRBDI
WZYXVUTSRQPONMLKIHGFEDCBA
IDBRLAQKEHMCZFONYWXUSGVTP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BMNLZSWRKFIECOGXDTVPHAYUQ
WZYXVUTSRQPONMLKIHGFEDCBA
QUYAHPVTDXGOCEIFKRWSZLNMB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VMZXTSYEFHCWIRKODPQLUGNBA
WZYXVUTSRQPONMLKIHGFEDCBA
ABNGULQPDOKRIWCHFEYSTXZMV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EXRWQPTDNOAKMGVZISCHBYLUF
WZYXVUTSRQPONMLKIHGFEDCBA
FULYBHCSIZVGMKAONDTPQWRXE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HVGCLTIENFZABKUSMOPRWDYXQ
WZYXVUTSRQPONMLKIHGFEDCBA
QXYDWRPOMSUKBAZFNEITLCGVH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IVKWRAGOFMXZSBHYULTCDPENQ
WZYXVUTSRQPONMLKIHGFEDCBA
QNEPDCTLUYHBSZXMFOGARWKVI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TDBSVMCPYEHXKRFZOANQLIUWG
WZYXVUTSRQPONMLKIHGFEDCBA
GWUILQNAOZFRKXHEYPCMVSBDT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TYBCEZUHWNAMPQIRVFDOKXGLS
WZYXVUTSRQPONMLKIHGFEDCBA
SLGXKODFVRIQPMANWHUZECBYT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VUXLQFEOHGSDAWCRZPINYTKBM
WZYXVUTSRQPONMLKIHGFEDCBA
MBKTYNIPZRCWADSGHOEFQLXUV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WITCSDZOYKFEQUMVLPXGRHBNA
WZYXVUTSRQPONMLKIHGFEDCBA
ANBHRGXPLVMUQEFKYOZDSCTIW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ANRKPQIZGOULMEHYSVFDBTWXC
WZYXVUTSRQPONMLKIHGFEDCBA
CXWTBDFVSYHEMLUOGZIQPKRNA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IUZTGRVSHDKYNECAWPMFBOXQL
WZYXVUTSRQPONMLKIHGFEDCBA
LQXOBFMPWACENYKDHSVRGTZUI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CZIWURHPQBYGXSNDEOTKVMFLA
WZYXVUTSRQPONMLKIHGFEDCBA
ALFMVKTOEDNSXGYBQPHRUWIZC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QUVINSLKBMFYXWGZRPTEDAOCH
WZYXVUTSRQPONMLKIHGFEDCBA
HCOADETPRZGWXYFMBKLSNIVUQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DAQPSZFLUOWKCMRNVHGTYEIXB
WZYXVUTSRQPONMLKIHGFEDCBA
BXIEYTGHVNRMCKWOULFZSPQAD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DFIYKABNRSCQVMHOPZTXGEUWL
WZYXVUTSRQPONMLKIHGFEDCBA
LWUEGXTZPOHMVQCSRNBAKYIFD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DQXPGBULIRTHSCWFANZOVKYEM
WZYXVUTSRQPONMLKIHGFEDCBA
MEYKVOZNAFWCSHTRILUBGPXQD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QXVBOHFEDYMIRZPGSWULTANCK
WZYXVUTSRQPONMLKIHGFEDCBA
KCNATLUWSGPZRIMYDEFHOBVXQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GAMDPHULCYWNBFSXRVOKITEQZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZQETIKOVRXSFBNWYCLUHPDMAG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RCSLKVTIEYWMOFNGDZHPQBAUX
WZYXVUTSRQPONMLKIHGFEDCBA
XUABQPHZDGNFOMWYEITVKLSCR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LRNKYBCAUPMQGZVDTFSEXHOWI
WZYXVUTSRQPONMLKIHGFEDCBA
IWOHXESFTDVZGQMPUACBYKNRL

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.