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Exercises 6.5 Up Hill struggle?

1.

Construct an addition and multiplication table modulo 6. Which pairs of numbers are additive inverses? Which pairs are multiplicative inverses, and how do they relate to 6?

2.

Construct an addition and multiplication table modulo 13. Which pairs of numbers are additive inverses? Which pairs are multiplicative inverses, and how do they relate to 13?

3.

Encipher zygomorphic using an affine cipher with key \(m=7\) and \(s=12\text{.}\)

4.

Encipher quaquaversal using an affine cipher with key \(m=17\) and \(s=3\text{.}\)

5.

Decipher TWWFS NLVBY FVNBX GPNWY XWZVN BKLVM FSHFA FKWT which was enciphered using an affine cipher with key \(m=15\) and \(s=23\text{.}\)

6.

Decipher YTGXZ GHACB HQGBN XABFU ZAGXN TJJ which was enciphered using an affine cipher with key \(m=3\) and \(s=7\text{.}\)

7.

Decrypt this message which was enciphered using an affine cipher:

EHWQC CIYKH EYKVK PIXKH ZKZKQ THZIP YGPXE KDFYX CZKXT IAOZI 
TYKCX KAIRK XKFPX IYHZK CHXQE DAQMC KFVGZ ECEYY KDCKK BKXHE 
IDCED HZKCN XEDUI PHZKW ZITKS MKCHE IDIPH ZKDKH ZKXTQ DFCMY 
QHXQA IYNQD GQDFI PHZKA ITICC QTCAZ KYKCI PVQXI DYQMN KXHME 
CQXKH IIXKA KDHED HZKYE DFCIP HZKNM VTEAQ DFQXK HIIED HEYQH 
KTGAI DAKXD KFWEH ZNITE HEACQ DFPED QDAKH IVKPE HHEDU CMVJK 
AHCPI XHZEC CKXEK CIPCO KHAZK CHZKG TKFZI WKRKX EDQDE DFEXK 
AHPQC ZEIDH IQCED UMTQX QDFAI YNTKB NXIVT KYWZE AZUQR KYGPX 
EKDFQ DINNI XHMDE HGIPF KYIDC HXQHE DUHZK RQTMK IPQPX KCZWK 
QNIDQ YIDUH ZKYQD GWEHZ WZEAZ ZKWQU KFZEC TEPKT IDUVQ HHTKQ 
UQEDC HAXEY K
8.

Decrypt this message which was enciphered using an affine cipher:

ZTWFB JOJLT ZZZTW XVAJO KOJWZ MHOLJ KTHWT WKHJF HWMBZ ZHOHM 
KIBHO QBOUJ TZBLB JVCRJ ZWHAH WXBOK IBZJL BLJWV SKHKI JKSBO 
THQKI BSAJF BRITF IJOJL TZIJQ IBAQT WKIBR HOKIN XHGBO WHOZB 
ZKTLJ KTHWR JZKIJ KHMJS OBAJK BRIHL IBOBZ SBFKB QJWQJ MOTBW 
QKHRI HLIBH RBQJQ BUKHM XOJKT KVQBU VKWHR IBMBA KITLZ BAMJW 
TWMBO THOJW QKIJK JOJLT ZRJZI TZLJZ KBOIB ITLZB AMATX IKBQJ 
AJWKB OWZVL LHWBQ JKVOW PBNJW QZJTQ OBKVO WTWXK HJOJL TZTJL 
JKNHV OHOQB OZLHW ZBTXW BVOJO JLTZL BOBAN WHQQB QITZI BJQJZ 
LVFIJ ZKHZJ NGBON XHHQJ WQZTX WBQKH ITLRT KIITZ IJWQK HABJQ 
KIBRJ N
9.

Encipher order more pizza using Hill's cipher and the matrix,

\begin{align*} m=\begin{pmatrix}1 & 5 \\ 7 & 10\end{pmatrix}, \end{align*}

be sure to how your work.

Answer

VIXJZ FVIBW DUZT

10.

Encipher we need soda too using Hill's cipher and the matrix,

\begin{align*} m=\begin{pmatrix}9 & 6 \\ 13 & 7\end{pmatrix}, \end{align*}

be sure to how your work.

11.

Decipher ZEMUM KJDIK NEWSX XHM which was enciphered using Hill's cipher and the matrix,

\begin{align*} m=\begin{pmatrix}13 & 19 \\ 1 & 6\end{pmatrix}, \end{align*}

be sure to how your work.

Answer

spicy chicken wings

12.

Decipher MRUKD QFDWI DHNL which was enciphered using Hill's cipher and the matrix,

\begin{align*} m=\begin{pmatrix}7 & 17 \\ 2 & 5\end{pmatrix}, \end{align*}

be sure to how your work.

13.

Decrypt this quote about “Chuck Norris” which was enciphered using Hill's cipher: FYQAB YTAHX XYERO MQMFP NNBXN ARJFK HLSNK QVVME IFDUJ AVOUT ZYLA

Answer

“Chuck Norris threw a grenade and killed 50 zombies, then it exploded.”

14.

Decrypt this quote about “Molly Weasley” which was enciphered using Hill's cipher: CQFUM OEAZH YUMAW MYGCV GEQDD MKCEA BIKCU ZSMGN VUGC

Affine Cipher Cell:

This SAGE cell can help you check your work when you encipher and decipher with a affine cipher, but you should be able to do the basic calculations your self.

Hill's Cipher Cell:

This SAGE cell can help you check your work when you encipher and decipher with a basic Hill's cipher, but you should be able to do the basic calculations your self.