Reply To: Extracurricular challenges
Inspired by @AndGiggle’s use of GF(25), and because this week’s challenges are too easy,
and because it is Black Friday, here are some gifts for you.
First, what is Black Friday? BF is a dark day of consumerism that you have imported from
the United States. It began here (here = the U.S.) as the day after Thanksgiving, when
our attention is freed from the gluttany of the turkey-killing day and turns toward the
gimme-presents day. You, hedonsitic consumerists [edited by Harry] imported BF but
not the day of thanks. In Norway, I even saw signs that said “Black Friday all week long”
(Black Friday hele uke); like Thanksgiving never existed. Someone in the forum was
wondering about my level of evilness. So consider these challenges a pay-back for stealing
our darkest but most holy of holidays.
These challenges take the Caesar and Vigenère ciphers and replace addition in Z/26Z with
multiplication in GF(27). The moduli for two of them are given; for the other two not.
Elements (which are polynomials) of GF(27) are mapped to integers by evaluating them at
x = 3, which is the modulus of Z/3Z, the underlying field from which the coefficients of
the polynomials are drawn. Letters of the alphabet are mapped to nonzero integers only:
A=1, B=2, …, Z=26. If any of this sounds strange or confusing to you, consider it an
opportunity to go out and learn something. Evil, remember?
Challenge GF(27)_1:
cipher: Caesar
modulus: x^3 + 2x + 1
ciphertext: DBJPFYYLVFJAVBPPBSPFSFXBSPXBAAKJALJZBJPSBLPKJAMKGJFPPFXBDFZFRJMBLSPBZLJZJFP
PFVBLOBLGBSKNLRKPMFCPGLHKJALJFPMBSBYYFSPKPFVZMKGKNFCVZXBLSLJTPSKLVBQNBIPPMBRSBPNMBZJBDD
FYDBBKJAMKGNFGBXLNHLMBVIVBDDXSFHBJZFRJGLJPSTKJACDBVBDDVTPFXBAKJVKYBLALKJRMBJPFFFVZYFSLN
MLJAB
md5(PLAINTEXT): 934c48d3e7d78ab2d392bf56206d0d6f
Challenge GF(27)_2:
cipher: Caesar
modulus: ?
ciphertext: WAYEAREITTORBQFTSVFBRUSQNXTYARMTITTOVOTREURIQVWNQITNWROBVOTREURIQVWXRNUXUXY
OBYEARVOWTBIUWAQETFREWDQNBEQSATNEYITJROXUFYSTDNTWKATBFUROBDNTWKATBFUYRXETOWTOKTBWQTOBYW
md5(PLAINTEXT): a7e49656ab26a750d41354484f40f7be
Challenge GF(27)_3:
cipher: Vigenère
modulus: x^3 + 2x^2 + x + 1
ciphertext: WLUPFZIIAZTRTGFZIRNYDYBDMLXYLCIJSSRLFJPNOTIHXYFWUEBZXLRABZXNMQJZSNHJNWOOIJM
SQNUEUYWLNYFESBFKFREGTNUSQCOSXWRGNNYVGLCRBROBDIBJTBTJBEVDAXDYDDXEBZXDNDBYQZIIRSOMCKCVXB
JUSQYRDCTQTBCKGLSETUJATTOYAMQHSHFZYGMUUHRKAPQDOPEXDVYLPRBUFIYUMMNLWGFFOBWLUPOMASAPFDRVT
FTMLSSGFZEYBHLTAYMZSNESDOSEDCRHFZEGTVMXICBVKGTJIHQMTNTROQTJNHDDWYTGRNOPFYIRBKCRYGMNBVYL
UPIXOERQRMRGMAFZFRLEFSBNOUZNUTIIRSLZIIRYGDSGBZTWAVANXBENYVZGSLFERLFHTFTKATXMDGCJXR
md5(PLAINTEXT): d1b993390d150a2bc53f1a86a8e78c24
Challenge GF(27)_4:
cipher: Vigenère
modulus: ?
ciphertext: HNULERILEELIVWQMHDHFFOSSTLHETTOLMFFXSAQIBUATLVYVXNEENTFIHOCNOPVJTXGIPOHNRQE
XLRCNNIGFAFXUIPOVLDONTILEPZDRDTEQTTFLTOTNEHJOLXUYMUHCOQOKNUSPTYVEATOLCSXAEXGLSXOHRLRGXD
FXUEAYGHHUSFFLEEOTJOFSBORFIYOEKDGJNEENOPEIIJTTFLTSNRDMDLAZLIPUURGDERYWAPNOAALIQMSGALIJT
LSNATETCNEQNPMUCJQRHGANUURPONIDDIRLDSAQEROCSVFNUCOZXZAEROXDTCQTTEGUACVWJDMPELSVLVRPEIJF
GITOCTDTEETLFWFTGMNVETCETCQRFWAMRRWQFDUEJPFNUKANETDHUIUYGIXRGILATPFRSEGHPFINTLEPGAFGHEP
AECKFIUNAPOYARLRQDZPGLSSGUPHUSGFHFGEANEQNPFHFTLHNPEKDUNJMVJGUDAOTIGHDGEUHDFNUZNRLVBRLDH
CGHHUEIYSEYLEPYTAYZNRYTCHMFCEXIJZLGXASRMRFDATXKDCDAPHETFFOTOLMKXGIPZSZDRTRQECDHSBQIHLAO
BQYFFGHHAAAIURNKL
md5(PLAINTEXT): 3bbc3f50b2f401b39e5b27a809f6dae5