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

Interactive example
Plain text
 Plain text = UNIDENTIFIEDPLANESSIGHTEDINTHEEAST 
 Cryptogram = GEBKHYMVMDZLSUCDFTWARLFUCHSEBUOUHU 
FrontBack
 ABCDEFGHIKLMNOPQRSTUVXYZW
 VRCPZSQNBDXMAEUTKWIGLFOYH
WZYXVUTSRQPONMLKIHGFEDCBA
HYOFLGIWKTUEAMXDBNQSZPCRV
 ABCDEFGHIKLMNOPQRSTUVXYZW
 GKYDUVWMZNHQEASITLFXBCPOR
WZYXVUTSRQPONMLKIHGFEDCBA
ROPCBXFLTISAEQHNZMWVUDYKG
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QRVWEDGOBLKYIXUTFNCHMSAZP
WZYXVUTSRQPONMLKIHGFEDCBA
PZASMHCNFTUXIYKLBOGDEWVRQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 WVCKZTAPOBURGLXNSQYHIMFDE
WZYXVUTSRQPONMLKIHGFEDCBA
EDFMIHYQSNXLGRUBOPATZKCVW
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DOPGHQFCTSBMVYWRNXZALKUEI
WZYXVUTSRQPONMLKIHGFEDCBA
IEUKLAZXNRWYVMBSTCFQHGPOD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 MAIKFLPVZTBNYDWQGOECRXSHU
WZYXVUTSRQPONMLKIHGFEDCBA
UHSXRCEOGQWDYNBTZVPLFKIAM
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RUENDSWFZHKITBGOCVMPXYLAQ
WZYXVUTSRQPONMLKIHGFEDCBA
QALYXPMVCOGBTIKHZFWSDNEUR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 RLYGPQWHVKMNFTIUAXECBZOSD
WZYXVUTSRQPONMLKIHGFEDCBA
DSOZBCEXAUITFNMKVHWQPGYLR
 ABCDEFGHIKLMNOPQRSTUVXYZW
 THGLKMAVFNOZIUSYDCPWRBEXQ
WZYXVUTSRQPONMLKIHGFEDCBA
QXEBRWPCDYSUIZONFVAMKLGHT
 ABCDEFGHIKLMNOPQRSTUVXYZW
 HRPTGWLQDXAOYUVECNMZIFBSK
WZYXVUTSRQPONMLKIHGFEDCBA
KSBFIZMNCEVUYOAXDQLWGTPRH
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BKVDZMNPAFYWQOGLRUHETSICX
WZYXVUTSRQPONMLKIHGFEDCBA
XCISTEHURLGOQWYFAPNMZDVKB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 IVQLMHOXDSUPBFRECTZYNGAWK
WZYXVUTSRQPONMLKIHGFEDCBA
KWAGNYZTCERFBPUSDXOHMLQVI
 ABCDEFGHIKLMNOPQRSTUVXYZW
 OFHWRMILBVYPETSZKDAUXCQNG
WZYXVUTSRQPONMLKIHGFEDCBA
GNQCXUADKZSTEPYVBLIMRWHFO
 ABCDEFGHIKLMNOPQRSTUVXYZW
 QHLXYBKDINUVSEZMAOTWCPFGR
WZYXVUTSRQPONMLKIHGFEDCBA
RGFPCWTOAMZESVUNIDKBYXLHQ
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CKZAXBQGNOEPVHUIWRYDMLFTS
WZYXVUTSRQPONMLKIHGFEDCBA
STFLMDYRWIUHVPEONGQBXAZKC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 BAULNOMXIPTKDZYQWFGCESHVR
WZYXVUTSRQPONMLKIHGFEDCBA
RVHSECGFWQYZDKTPIXMONLUAB
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EHXMFWNGTVRCIPQUBAYDZLKOS
WZYXVUTSRQPONMLKIHGFEDCBA
SOKLZDYABUQPICRVTGNWFMXHE
 ABCDEFGHIKLMNOPQRSTUVXYZW
 EMKGFYOPUXRSHZIBQTLADCNVW
WZYXVUTSRQPONMLKIHGFEDCBA
WVNCDALTQBIZHSRXUPOYFGKME
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LEONMGTZSYBPHQFDCWUARXVIK
WZYXVUTSRQPONMLKIHGFEDCBA
KIVXRAUWCDFQHPBYSZTGMNOEL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UHMCRPOXABIKTFWQGSZVYDENL
WZYXVUTSRQPONMLKIHGFEDCBA
LNEDYVZSGQWFTKIBAXOPRCMHU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 DGPXHURQEVFTIAYKMCWOBSZNL
WZYXVUTSRQPONMLKIHGFEDCBA
LNZSBOWCMKYAITFVEQRUHXPGD
 ABCDEFGHIKLMNOPQRSTUVXYZW
 PMRQFIVLZOUSDGYANTEKHXWCB
WZYXVUTSRQPONMLKIHGFEDCBA
BCWXHKETNAYGDSUOZLVIFQRMP
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NUAHLOYZCPEQGSKXIBFVWDRTM
WZYXVUTSRQPONMLKIHGFEDCBA
MTRDWVFBIXKSGQEPCZYOLHAUN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 ADBCUPONRXZESVGHWQLMFKYIT
WZYXVUTSRQPONMLKIHGFEDCBA
TIYKFMLQWHGVSEZXRNOPUCBDA
 ABCDEFGHIKLMNOPQRSTUVXYZW
 TEQCXBFWDHSRPGKNAMIZUOYLV
WZYXVUTSRQPONMLKIHGFEDCBA
VLYOUZIMANKGPRSHDWFBXCQET
 ABCDEFGHIKLMNOPQRSTUVXYZW
 KFCLNSBTHGPMIQRUADEVXZOWY
WZYXVUTSRQPONMLKIHGFEDCBA
YWOZXVEDAURQIMPGHTBSNLCFK
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CWYVBQHITPRKSGOZUXDELMANF
WZYXVUTSRQPONMLKIHGFEDCBA
FNAMLEDXUZOGSKRPTIHQBVYWC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 NVFTKYXHSRLIAUDPMQEWCGOBZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZBOGCWEQMPDUAILRSHXYKTFVN
 ABCDEFGHIKLMNOPQRSTUVXYZW
 XSDEHYQBCMNWIURAKGFLTVPOZ
WZYXVUTSRQPONMLKIHGFEDCBA
ZOPVTLFGKARUIWNMCBQYHEDSX
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LMKBUZYNCDSWRTAFGXOEQIPVH
WZYXVUTSRQPONMLKIHGFEDCBA
HVPIQEOXGFATRWSDCNYZUBKML
 ABCDEFGHIKLMNOPQRSTUVXYZW
 LIGAONPYXMSUHBZKTVDQWERFC
WZYXVUTSRQPONMLKIHGFEDCBA
CFREWQDVTKZBHUSMXYPNOAGIL
 ABCDEFGHIKLMNOPQRSTUVXYZW
 UPGCNXOYBMHQWEILVAZTSFKRD
WZYXVUTSRQPONMLKIHGFEDCBA
DRKFSTZAVLIEWQHMBYOXNCGPU
 ABCDEFGHIKLMNOPQRSTUVXYZW
 CSWVNTODBRPYGKZUQHMAXFLIE
WZYXVUTSRQPONMLKIHGFEDCBA
EILFXAMHQUZKGYPRBDOTNVWSC
 ABCDEFGHIKLMNOPQRSTUVXYZW
 SZNHTCLMDGAYXFBRVWUIQOEKP
WZYXVUTSRQPONMLKIHGFEDCBA
PKEOQIUWVRBFXYAGDMLCTHNZS

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
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