MATHEMATISCHES INSTITUT DER UNIVERSIT ¨AT M ¨UNCHEN
Prof. Otto Forster
WS 2002/2003 November 28, 2002
Crypto Contest / Preisaufgabe
for the students of the course Cryptography, WS 2002/03
The problem is to decrypt the following cipher text
AWRCV QKDWW BBSIF IDSBL GAYVU XBQOD CWLQE GDBPO RUHMH SYEQP HFQCW KCRPC MUIHX FEHES NQKLO RRLKX GAGUP OQSVK ZNWLM WJKHG GUWRM BQWTI XWNKK MNMET CTDTP RYFZF IDYKG TQYFB FPRBT JPBGK OWTYC SZCLA CVMWX ARBSO DAGSR ZPTBK YSNPP LLGKR PXRJZ MKFHY GAKIJ GAYGK ATOMW ZIZVJ RTKCX NEFQH OGXAC WRHEL SVBFJ BXQAJ SSBUJ AOJRZ XQLJY NIHUY AUVOU PAQIN DEVPI VZIEN TONZY GRSLU KYYWU ZTVNU OUCTJ KWGMK TIUMK BOTDQ DAESD OMCLX IJHHT KWUDS SPVAA FGAFD VTKUT AHSTD BFBQC MVERX FCTAM NYVKM LNHPB JULWL OQZXN RDUWU LFKRT PLGJT EAFEW PKMMQ ODSOZ JZOBY KCANV AMXUQ JFMSR WTPJB JJXYN XYHGZ BQGEI GZZES QEKKJ IBJBY SZPAL WQRLS TUYRA MQQDH SYHPG HOOSV KXXZT MECKH TCATR ECZFJ JJJCV GBIWT CASYO SPMUR OQLFZ BLXAX WDSQK MFXVI BAGAC JBAAU IMVQX LHCKQ MHUNA FEXWI YFJPG BDKCI ABLNA GJNSW IFYNU JJWBU YYTAQ IPPLR NQZPY DNLFG HVAKJ HIIYX ENVYL KKOCK APFXZ NFZZJ EHFIK WSIXF XDLRF SVIMB RYUKJ NIFLQ AOSCW TXWNV FUKQX LOTCP UWRAB UPAHZ OWQXQ YPVLR GEGGF DKIUU XXUWN IQAWQ JEDKP BKLMR VEXTI QXCPZ LURVR JANSA TVWRS IFYNN JSBLK AJQBJ LZLBX RSKDG ONJZW AKKHN LLIBI BYQQA KIYHZ UOPRX VZGBP TXYDE LLNKV WULSK AESRD YZHAQ NWPUE QSVRY DAKXP VQWWK AJUMY GIRNP XKXNI EJHGM WZBLO BTUEG PCJMJ WSKIU NQGZJ PQTTA SQTST UMSCY FTFWT IJSNL YXCUW IMQLZ IGHJA VRXGC UOVXF WDUNL YQSNK GQMZI FNAQR ZYCOK PFUWF SETGR IHYAO NZQRO ETRUX BXTHQ LENQT JYZBQ LLGJA USFRQ HIJAA WRRGU PSOBC QVTPB CHHJB FEGVJ HCOPA ADDOP WUFZE ITYED CGEZY UGJXZ BLQXU ODKLJ YJHQZ THUZK
which resulted from an English plaintext, written in the alphabet {A,B, . . . ,Z} ∼= Z26 without spaces and punctuation marks. The text was encrypted using a composition of three different cipher systems
C =R◦P ◦T.
(1)T is a transposition cipher depending on a secret permutationσof{1,2,3,4,5}and works as follows: The text is divided into blocks of 25 letters. These letters are written as the five rows (xi1xi2. . . xi5),i= 1,2, . . . ,5, of a 5×5-matrix. The transformed block is the sequence of columns (x1σ(j)x2σ(j). . . x5σ(j)),j = 1,2, . . . ,5, in the permuted order.
(If the last block is shorter than 25 letters, only the upper part of the matrix is filled, and the columns become shorter.)
(2) P is a monoalphabetic substitution using a secret permutationπ :Z26 →Z26. p.t.o.
(3) The third transformation R is done by a rotor machine consisting of three rotors with hardwired permutations π1, π2, π3 : Z26 → Z26, which are taken from the set {πa, πb, πc}in an unknown order, with
πa: EKMFLGDQVZNTOWYHXUSPAIBRCJ πb: AJDKSIRUXBLHWTMCQGZNPYFVOE πc: BDFHJLCPRTXVZNYEIWGAKMUSQO
This notation means πa(A) = E, πa(B) = K, πa(C) = M, etc. (The same permutations were also used in the Enigma.) The rotors had secret initial positions (s1, s2, s3)∈Z326. The i-th letter of the input text to R (starting with i = 0) is transformed by the permutation
(ρ−k3(i)π3ρk3(i))◦(ρ−k2(i)π2ρk2(i))◦(ρ−k1(i)π1ρk1(i)) :Z26→Z26, where ρ:Z26→Z26 is the shift ρ(x) :=x+ 1 (mod 26) and the integers
k1(i), k2(i), k3(i)∈ {0,1,2, . . . ,25} are defined by the relation
s1+s2·26 +s3·262+i=k1(i) +k2(i)·26 +k3(i)·262 (mod 263).
Solutions, together with a short explanation of the method used, should be sent by Email as soon as possible, but not later than Feb. 4, 2003, 9:00 a.m. to
forster@mathematik.uni-muenchen.de
Winner is who first returns the correct solution. The winner (or the winning team) receives 32 extra marks and a modest prize.
To save you typing, a data file containing the cipher text and the permutationsπa, πb, πc
can be downloaded from the homepage of the course
http://www.mathematik.uni-muenchen.de/~forster/vorlA2w_cry.html You might also be interested to have a look at the previous crypto contests 3 and 6 years ago.
Wishing you a successful decoding
Otto Forster
