7709 /www/nrich/html/content/id/7709/ 1 2011-10-24T13:36:21 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>KVJZVZGDKYRZFLNRYEZJITYVVVCGECVJZKKFWYVKYTTYNKUVJVZWIGIYFRRVVUFJ NVFTVIKFNJJINVKNREEFHFYUVVVRZGYYJWFLLSZJMRJECVVVRFWIVRJFVGZUCEDI TCIJESZWIRWKXUZVRCFVTCEVKINYVZEKVFNIZPKEYKVVKETYJNJVVYYTZWLERXRV RVRKJVZIJIJRUFEPIUERFCJPZFVKZEPNJSUZWGTGJDRIWNFZYPTEVVRKEJMRWYLCZ RFJEUJZKFZEVZWCWKCKXPVFRDXJITZTKILYCFKECVVGVYEFFRDVZLYTNJEFEFUDW EECJUVFRGVJKIRDJJJVYVKDPVIZIUELVGKKNTNDJTVKVVPKMFYKYZFLKZTZJITV </p> <div> </div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>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.</p> <p> </p> <p>Successful solvers of this part were</p> <p>Patrick from Woodbridge School, England<br></br> An Anonymous Solver from Somewhere in the US<br></br> Joseph from Hong Kong</p> <p> </p> <p>The solution is:<br></br> <br></br> This was a Caesar shift of seventeen followed by a transposition of rows and columns. This of course retains the letter frequencies of English, which probably helped you decipher this. In this case, the two methods of encryption commute, however this isn&#39;t always the case. Apart from some special cases, if we use a vigenere cipher and then a transposition, we will get a different result depending on which order we do them in. Can you find any cases for which these will commute?</p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>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&#39;t try this in the classroom!</p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><p>This is the sixth of our <a href="https://nrich.maths.org/7081">challenge ciphers</a>.</p> <p>We recommend that you attempt them in order, as the solution of each challenge gives a small (and necessary!) hint for the next challenge.</p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <p>This was a Caesar shift of seventeen followed by a transposition of rows and columns. This of course retains the letter frequencies of English, which probably helped you decipher this. In this case, the two methods of encryption commute, however this isn&#39;t always the case. Apart from some special cases, if we use a vigenere cipher and then a transposition, we will get a different result depending on which order we do them in. Can you find any cases for which these will commute?</p> </mdoxml> 2 5 0 0 0 0 1 Jluuis or even Asutguus? Sixth challenge cipher Decision Mathematics and Combinatorics Combinatorics Decision Mathematics and Combinatorics Algorithms Applications Codes and cryptography