Vital?

7706 /www/nrich/html/content/id/7706/ 1 2011-10-24T11:54:52 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <div>QAOGKPQHOPPKDOUKPOIYNXLQOWSPBIDKIKRRBIOYBLAONKQJMEQJZYQJBBOHJTB IDJIIBIOGOQQONPOKYAQBHOQAOLNJEGOHUBQACSPQSPBIDJIOYBLAONQJOIYNXLQ KGGQAOGOQQONPBIKHOPPKDOBPQAKQUOHKBIQKBIQAORNOMSOIYXJRGOQQONPB IQAOLGKBIQOVQPJUONOKEGOQJSPORNOMSOIYXKIKGXPBPQJAOGLWOYBLAONBQU OYJSGWBIPQOKWSPOWBRRONOIQKGLAKEOQPRJNWBRRONOIQLKNQPJRKHOPPKDO RJNOVKHLGOUOYJSGWOIYNXLQQAOJWWGOQQONPUBQAJIOYBLAONKIWQAOOTOIG OQQONPUBQAKIJQAONQABPBPYKGGOWKTBDOIONOYBLAONUBQAFOXUJNWGOIDQA QUJDJJWGSYF</div> <div> </div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Have you managed to solve the entire <a href="http://nrich.maths.org/7081">Stage 5 Cipher Challenge</a>? Solutions are now closed, but perhaps you want to take up the full challenge. Successful solvers of this part were Josip from Australia Joseph from Hong Kong (and probably also Patrick from Woodbridge School and maybe others - I accidentally forgot to leave the submit a solution tab open!) Josip give the following nice advice Ok, so I recently started going some cryptography in my spare time after entering a YouTube competition. After a few hours, I finally caught on the way to step-by step solve the puzzles. For this particular puzzle, I got the hint to use frequency analysis from the previous puzzle. Instead of taking a trip down the tedious path and going through and looking at the repetition of each letter and word pattern, I used this handy little website. http://www.richkni.co.uk/php/crypta/freq.php To compliment me with switching letters back and forth, I used http://25yearsofprogramming.com/fun/ciphers.htm which also contains a "FA", but makes it much easier to replace letters and see immediate results. (I always compare frequency in the text to frequency in theory and try to match them.) The following is an example I use to step my way to more efficiently cracking the code; efficiency is everything. This gave me the vital letter frequency, as well as 2,3,4,5 and 6 letter repetitions! I immediately looked at the 3 letter repetition section to notice "qao". I automatically assumed this to be the word "the", as it is many times. Now that I have those three letters, I apply this to the six letter section in hope to get something out. The "goqqon" word gets my attention because it contains two pairs of like letters. Also because we know that o=e, it significantly helps. Now, I thought to myself in the context of the previous two puzzles, 'what could _eXXe_' be? (with XX being a double letter). It didn't take long for me to think of 'letter'!! I also noticed that it was able to be plurals, so I added an 's'. From here, things got slightly easier. With the help of frequency analysis, I tried to strip the less common letters and replace them with more popular ones, and sometimes with luck. Research in word patterns I thought benefited me hugely, and so I recommend them too; http://scottbryce.com/cryptograms/stats.htm. I started strongly from around the centre of the puzzle, with "ALL THE LETTERS IN A MESSAGE IS THAT" and then slowly edged my way to find smaller words in between that made things clearer. As I write my 'confirmed' (used) letters down on paper, I have a remaining list which can still be rearranged anywhere without affecting the already made words. This is really good for times when you are stuck, (as I was). You can simply change a few letters and hopefully see a pattern that makes you think. Sometimes you can try to fill in the sentence with your own words also. e.g "THIS IS CALLED A _____ _____". I knew from the context that the puzzle was referring to another cipher (which also gave away the word 'cipher') but quickly researched a few cipher names to reveal a nice fit of 'vigenere'. The other tricky part was arranging the less common letters. However, sometimes the surrounding letters gives it away, such as "freQuency". Also, when you have words already made, spacing them helps significantly. The solution is: The last message was encrypted using an affine cipher, 'a' to 'q', 'b' to 'z', 'c' to 'i', i.e. moving on nine letters each time. The problem with just using one cipher to encrypt all the letters in a message is that we maintain the frequency of letters in the plaintext, so we're able to use frequency analysis to help decipher it. We could instead use different alphabets for different parts of a message. For example we could encrypt the odd letters with one cipher and the even letters with another. This is called a Vigenere cipher with keyword length two. Good luck! keyword cipher: abcdefghijklmnopqrstuvwxyz KEYWORDABCFGHIJLMNPQSTUVXZ </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">This challenge cipher forms part of a very difficult <a href="http://nrich.maths.org/7081">sequence of ciphers</a> suitable for keen groups or individuals, maths clubs and very optional homework challenges. Don't try this in the classroom!</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">This is the third of our <a href="https://nrich.maths.org/7081">challenge ciphers</a>. We recommend that you attempt them in order, as the solution of each challenge gives a small (and necessary!) hint for the next challenge. <table border="0" cellpadding="0" cellspacing="0" style="width: 459pt; border-collapse: collapse" width="621"> <colgroup> <col span="27" style="width: 17pt" width="23"></col></colgroup> <tbody> <tr height="20" style="height: 15pt"> <td class="xl65" height="20" style="border-bottom: windowtext 0.5pt solid; border-left: windowtext 0.5pt solid; background-color: transparent; width: 17pt; height: 15pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23"> </td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">O</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">Q</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">B</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">I</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">K</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">P</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">N</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">J</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">A</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">G</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">Y</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">L</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">W</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">R</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">U</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">S</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">D</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">H</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">X</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">E</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">M</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">T</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">F</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">V</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">C</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; width: 17pt; border-top: windowtext 0.5pt solid; border-right: windowtext 0.5pt solid" width="23">Z</td> </tr> <tr height="20" style="height: 15pt"> <td class="xl65" height="20" style="border-bottom: windowtext 0.5pt solid; border-left: windowtext 0.5pt solid; background-color: transparent; height: 15pt; border-top: black; border-right: windowtext 0.5pt solid">f</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">72</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">48</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">31</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">29</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">28</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">27</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">25</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">24</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">23</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">21</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">16</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">14</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">13</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">12</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">11</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">10</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">9</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">8</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">7</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">4</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">3</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">3</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">2</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">2</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">1</td> <td class="xl66" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">1</td> </tr> <tr height="20" style="height: 15pt"> <td class="xl65" height="20" style="border-bottom: windowtext 0.5pt solid; border-left: windowtext 0.5pt solid; background-color: transparent; height: 15pt; border-top: black; border-right: windowtext 0.5pt solid">%</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">16</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">11</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">7</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">7</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">6</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">6</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">6</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">5</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">5</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">5</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">4</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">3</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">3</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">3</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">2</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">2</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">2</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">2</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">2</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">1</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">1</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">1</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">0</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">0</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">0</td> <td align="right" class="xl65" style="border-bottom: windowtext 0.5pt solid; border-left: black; background-color: transparent; border-top: black; border-right: windowtext 0.5pt solid">0</td> </tr> </tbody> </table> <table border="0" cellpadding="0" cellspacing="0" style="width: 395px" width="395"> <colgroup> <col></col> <col span="2"></col> <col></col> <col></col></colgroup> <tbody> <tr height="20"> <td height="20" style="width: 76px; height: 20px">OYBLAON</td> <td align="right" style="width: 64px">5</td> <td style="width: 64px"> </td> <td style="width: 127px">ORNOMSOIYX</td> <td align="right" style="width: 64px">2</td> </tr> <tr height="20"> <td height="20" style="height: 20px">GOQQONP</td> <td align="right">4</td> <td> </td> <td>GOQQONPUBQA</td> <td align="right">2</td> </tr> <tr height="20"> <td height="20" style="height: 20px">HOPPKDO</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">IOYBLAO</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">OIYNXLQ</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> </tr> </tbody> </table> <table border="0" cellpadding="0" cellspacing="0" style="width: 564px" width="565"> <colgroup> <col span="2"></col> <col></col> <col span="2"></col> <col></col> <col span="2"></col> <col></col> <col span="2"></col></colgroup> <tbody> <tr height="20"> <td colspan="2" height="20" style="width: 128px; height: 20px">Top Digraphs</td> <td style="width: 23px"> </td> <td colspan="2" style="width: 128px">Top Tri-graphs</td> <td style="width: 15px"> </td> <td style="width: 64px"> </td> <td style="width: 64px"> </td> <td style="width: 15px"> </td> <td style="width: 64px"> </td> <td style="width: 64px"> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">ON</td> <td align="right">15</td> <td> </td> <td>QAO</td> <td align="right">8</td> <td> </td> <td>BLAO</td> <td align="right">5</td> <td> </td> <td>OQQONP</td> <td align="right">5</td> </tr> <tr height="20"> <td height="20" style="height: 20px">QA</td> <td align="right">15</td> <td> </td> <td>AON</td> <td align="right">6</td> <td> </td> <td>LAON</td> <td align="right">5</td> <td> </td> <td>OYBLAO</td> <td align="right">5</td> </tr> <tr height="20"> <td height="20" style="height: 20px">AO</td> <td align="right">14</td> <td> </td> <td>BLA</td> <td align="right">5</td> <td> </td> <td>OQQO</td> <td align="right">5</td> <td> </td> <td>YBLAON</td> <td align="right">5</td> </tr> <tr height="20"> <td height="20" style="height: 20px">OI</td> <td align="right">10</td> <td> </td> <td>GOQ</td> <td align="right">5</td> <td> </td> <td>OYBL</td> <td align="right">5</td> <td> </td> <td>GOQQON</td> <td align="right">4</td> </tr> <tr height="20"> <td height="20" style="height: 20px">BI</td> <td align="right">9</td> <td> </td> <td>LAO</td> <td align="right">5</td> <td> </td> <td>QONP</td> <td align="right">5</td> <td> </td> <td>HOPPKD</td> <td align="right">3</td> </tr> <tr height="20"> <td height="20" style="height: 20px">GO</td> <td align="right">9</td> <td> </td> <td>OIY</td> <td align="right">5</td> <td> </td> <td>QQON</td> <td align="right">5</td> <td> </td> <td>IOYBLA</td> <td align="right">3</td> </tr> <tr height="20"> <td height="20" style="height: 20px">OQ</td> <td align="right">8</td> <td> </td> <td>ONP</td> <td align="right">5</td> <td> </td> <td>YBLA</td> <td align="right">5</td> <td> </td> <td>IYNXLQ</td> <td align="right">3</td> </tr> <tr height="20"> <td height="20" style="height: 20px">QO</td> <td align="right">8</td> <td> </td> <td>OQQ</td> <td align="right">5</td> <td> </td> <td> </td> <td> </td> <td> </td> <td>OIYNXL</td> <td align="right">3</td> </tr> <tr height="20"> <td height="20" style="height: 20px">NO</td> <td align="right">7</td> <td> </td> <td>OYB</td> <td align="right">5</td> <td> </td> <td> </td> <td> </td> <td> </td> <td>OPPKDO</td> <td align="right">3</td> </tr> <tr height="20"> <td height="20" style="height: 20px">OY</td> <td align="right">7</td> <td> </td> <td>QON</td> <td align="right">5</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">IQ</td> <td align="right">6</td> <td> </td> <td>YBL</td> <td align="right">5</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">LA</td> <td align="right">6</td> <td> </td> <td>BQA</td> <td align="right">4</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">PB</td> <td align="right">6</td> <td> </td> <td>ONO</td> <td align="right">4</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">QJ</td> <td align="right">6</td> <td> </td> <td>UBQ</td> <td align="right">4</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">QQ</td> <td align="right">6</td> <td> </td> <td>AOG</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">BL</td> <td align="right">5</td> <td> </td> <td>BIQ</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">BQ</td> <td align="right">5</td> <td> </td> <td>HOP</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">IO</td> <td align="right">5</td> <td> </td> <td>IOY</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">IY</td> <td align="right">5</td> <td> </td> <td>IYN</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">NP</td> <td align="right">5</td> <td> </td> <td>KBI</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">PQ</td> <td align="right">5</td> <td> </td> <td>KDO</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px">SP</td> <td align="right">5</td> <td> </td> <td>NXL</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px"> </td> <td> </td> <td> </td> <td>OPP</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px"> </td> <td> </td> <td> </td> <td>PBI</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px"> </td> <td> </td> <td> </td> <td>PKD</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px"> </td> <td> </td> <td> </td> <td>PPK</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px"> </td> <td> </td> <td> </td> <td>XLQ</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> <tr height="20"> <td height="20" style="height: 20px"> </td> <td> </td> <td> </td> <td>YNX</td> <td align="right">3</td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> <td> </td> </tr> </tbody> </table> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> The last message was encrypted using an affine cipher, 'a' to 'q', 'b' to 'z', 'c' to 'i', i.e. moving on nine letters each time. The problem with just using one cipher to encrypt all the letters in a message is that we maintain the frequency of letters in the plaintext, so we're able to use frequency analysis to help decipher it. We could instead use different alphabets for different parts of a message. For example we could encrypt the odd letters with one cipher and the even letters with another. This is called a Vigenere cipher with keyword length two. Good luck! <div>keyword cipher:</div> <pre> abcdefghijklmnopqrstuvwxyz KEYWORDABCFGHIJLMNPQSTUVXZ </pre> </mdoxml> 2 5 0 0 0 0 1 Vital? Third challenge cipher Decision Mathematics and Combinatorics Combinatorics Decision Mathematics and Combinatorics Algorithms Applications Codes and cryptography