Newsgroups: sci.crypt
From: straits@netcom.com (Stewart C. Strait)
Subject: PUZZLE or exercise with phi-test

The cryptosystem used below can be broken with unknown plaintext using the phi test together with techniques familiar from the Vigenere cipher.

Every ciphertext letter is the mod-26 sum of the corresponding plaintext letter plus some subset of the key letters. As in the Vigenere cipher, A=0, B=1, C=2, ..., Z=25.
If the plaintext is n letters long, 2^(j-1) < n <= 2^j, there must be exactly j+1 key letters. (Additional key letters would not be used anyway.)

Let the plaintext, ciphertext, and key be respectively p[0],p[1], ...; c[0],c[1], ...; and k[0],k[1], ... .

Then c[i]=p[i]+k[0]+ (sum over all p such that (2^p) & i is nonzero) of k[p+1].

Another description:

1. Caesar encrypt every letter with the first key letter.
2. Encrypt every other letter with the next key letter.
3. Encrypt every other pair of letters, both with the next key letter.
4. Encrypt every other group of 4 letters, all with the next key letter.
5. Keep doubling the group length and using another key letter until the whole text would be one group.

Example:

Plaintext:  This is quite a weak system.  Key: YPMIWX

Plaintext:   THIS ISQU ITEA WEAK SYST EM
Keys used:   YYYY YYYY YYYY YYYY YYYY YY
              P P  P P  P P  P P  P P  P
               MM   MM   MM   MM   MM
                  IIII      IIII      II
                       WWWW WWWW
                                 XXXX XX
             ---------------------------
Ciphertext:  RUSR ONIB CCKV YVON NIZP HE

The ciphertext is the mod-26 sum of the columns, using A=0, B=1, ... .

Note that the cipher is not periodic. You may find it convenient to call this the 'VIGROTOR' system, since it could be produced by a rotor-like machine with two-position rotors, where each rotor does a different Caesar substitution in the two positions.
Real rotor machines are not so weak.

The puzzle itself:

Plaintext is public domain, English, and may begin or end in mid-word.

straits.3.002; VIGROTOR; 1024 Ciphertext letters.
ACGUR UMWKH HIARZ RWNTW SRNFG LLMVB LDNQG FCPYB ZICUR YUDKG MDDQJ XKSMN
YYIYG NDCSS OZRVZ AIBKZ NUKZZ DLIOP GDVYH LAUNN NYSJB FJMRI SJQZR HAZUK
JGUTP LLRTE LEBDH VKZXB LIIJY RILER WKWCE KCYQT MLLXX KUIGU GNVAD HPKEH
RMHUU GOCNC AKZEE FOUET UTWDE GKYXB FKRUX FUHVO QFBWT VBWRT EEAFO OOZVL
FSASS AAFYN ZJGZH UTWSE RUREI LUYYD BSLII JAIYU OROBM CVRSO QXUYC FFTCW
MGMKP VDMNS IOGHP CYCFM CDKES PGTAA JYYIJ OZAHN ZAMJG TKPVK TVAOC HUCYJ
BGRZR IUZCK KKKIQ TNGKL ZJFOL BYRCD TWPQW KQBWJ RACDX MIZTC UYPSP PYPLO
YKQAU HGBPY ZCFLJ ZLVEE IIREE XPAYQ VOVMU DGXRJ GTIEL UMCWY QUOKQ GDQVX
EZSRG RPTUH MOWFX AGWLD MEWQY FHKEL UXQSI EYWFS OWVUJ USIDN WWIAW XCLCJ
NQIKQ LIRLU UVZYS WREJN STMAO XNFJE ASLEZ YWZKY OJROU VQSZG HYULZ ICGCL
JZZYN OIPCY ACYZB PPBBW HIPCM PLDWP HJVDJ YILBK LHNWQ PJFKT PFZCK WFCXE
MGXJJ PKNHZ XXNOM ORMSK WDEAR DVTSL SPUBF KKZLM OSJTK NFQNE QZHQW ZQDCP
UAWCO OEHFH IDZIA ZXOIP DVNBC KAWAH MDSAG TNVCA ABLIU KUBYH OLCXU LLOOW
EYGIV NLWCH KSISO AVPZA QPNIK NIVSV MZGQQ VTIQX DFLHS RAHPB LQWVP LBEWH
JKJSL SHYDA KXRMI ZQHVE YCYHA QIKEI WSEUP CJLRM QPCNN RMZKM SBVYT JOTYQ
MNEYO DOFNZ JLUJF ROAGR IBHAL ADWRA ZOASY AGBKL YRJSD MHVHA DUYKO NVWKN
XEJBY ODKEB RKGPD RBQMH JBTIL GSFDR PUIXC HMYNQ TZUHZ GCOIV RYPHY FNOVD
DSOA

If I end up posting a lot of these I'll probably use rec.puzzles instead of sci.crypt and just give a brief announcement in sci.crypt. (Unless there is a consensus that they belong here.)

Stewart C. Strait
straits@netcom.com

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