Reply To: Extracurricular challenges

Here is the first of 2 hill ciphertexts, inspired by madness’ suggestion of a constant vector addition.

For both ciphers, if there were fewer letters in the keyword than the matrix size and (for example) the keyword ended with X, I would have filled the remaining matrix entries with Y, Z, ., _, A, B, and so on until the matrix was full. I filled the matrix in the standard way, left-to-right, top-to-bottom, without discarding duplicate letters.

First cipher: upsidedown-2025-1

This cipher uses a 3×3 matrix (mod 28), generated by a keyword, with a constant vector (size 3) added to each block AFTER encryption. Alphabet: ABCDEFGHIJKLMNOPQRSTUVWXYZ._ (the underscore is used as a space character in the plaintext)

DXZZGMXHP.HVMGIAOIYTFYWAJOUGLDSLTAOOPHLRHXYRMZ_TFCMAGGYAZOPJFIQBPXSLTKRGZLB
FWEPPRHZMYFFSJYVP_MDHCSKQFITE_ZVBYF.DYIRUDMZPJEJFWEOIJBMSUCFRHXWRAHEIAGNMNG
NRCHFRIMAHBGZTXMDTMVA_MAYOEIAVWGUI.GYF.H_ZTD_AEDYWAUCFZT_YQ_AHPAGUCQAECORF.
QQOAGUNUPB_KQ_FGAUXZANJGTBBEJ.BTOXLO_NFMTF_DDAGGMHHDWATDDQ_FIHZ.__HJK_AWADL
JJOAQBDNJEDQB.A_POYTFECGYYYHUALJWZLBZKAQWEQ_FIMMBTOQWULXSMGIFDDKRGMCSAGMKGY
UCDSQU.SAMDRTBGBTOLJWP_KQFQ_TCLJSRPIYF..WRVNGIPHUOGDNDGKFBHLQHPP.ABTOR.KH_S
YZITWECGLIVSDMAYMF.SFIHLS.ILAEJJMXVGAGNIHZGLDIHLKRGYUFARWPDWECEBTODAMA.E_CV
YMLCBSPDWECEBTONWOMF_VETIXZVBGTXCWGUAGGUFSYSKAGMW.GXJ.YKVB.SIB.DMAAHPEDQX.E
EQ_ZQU.SAMDRTBGBTOLJWQGLYMFAOWDGY_Z_GAUTPW_RC_VVDHJNE.ECEMYNYTVWROAGAGMNXVD
FJAPGXQ_TKRGBTOUOPQBTYHXWROAGAUOWJOUYSJR__XEMIPHUQMZTXUXFNBQDRWYVDKKIQ.YULL
LJSZOIEDQB.AGMNXVDMOYJWAMNUNHONRXQ_TNVSLC.UQMBNKX.EQQOAIMZTXR__CAMUXFPOHW.G
R_BFEJMSBPW_Q_TAOWFNGAGACQAECORF.QQOAGUNUPB_KYFFODBMALEVWAGAAQQLT_AQLAOIAJP
GWKC.STLXARILKDUCF.LFAGGUFEJBFTXKJJ.EZNLEMIXLP.MTPWLHPJQIYIVABVCWGMWEWIHQU_
.IURWFHIYPB_I.GYF._BOPCQECESAZFLXUXTNVSLJWZKO_OBZDHERQLABL_TSKAAGUZERMBS.WK
ASZMQCF.MQQOQCAFEXQFQ_TCTBBYF..WRVNGIPHUMVYLLUMAHRXEOMX_JOXVAMTTDDKRGDSIXJ.
QQBUYITBBYTFYGBIPHODPWROAGAPWHAXHUBMXMKUOKXBTECED_W_KRECEIKQAOWG.HYF.XONUXT
UDHWBFQENHOLECEYMRGTSYTFAWTQSIIPHTSVMZ_JJ.IIXUCFRVCPDWQQOUQMPFORUDQGTMOYMRL
FXKDFHW.YBTOIPHUXTUDHWBFAGGADBXX.AUGYTFAWFPWBYMFBCJOGAMRZTLWTDRK_PGWKHRWI.S
_VSIPHDZGWKSAOIAUGYTFFNGMGIUCFFRKZQAEO.DVQTKRCPLWROAGAXBLGWKVET

I have a program that solves this (ciphertext-only) in about two minutes. I can give cribs if needed.

The addition of a constant vector is more or less the same thing as composing a Vigenere cipher on top of the Hill cipher. So if you make the matrix the identity matrix this gives just a Vigenere. When the matrix (and thus the addition vector) is one dimensional you get an affine shift cipher, so this system is really very general and definitely worth studying! Harry