Semicircle

7707 /www/nrich/html/content/id/7707/ 1 2011-10-24T11:56:26 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Xn nwj kpv gmpl ipxa, lmat swcm! Ipxa hwgb dn rqeptz xa riattl p xdtniaxwiqmiqr kxxwmg. Ndz tfpuetta aqzm ipxa dvt exbw i zmnedzs wu ttvvbw blw, xb'h xdahqqtt bd adtkm xb qg wicl ychb iznqco ewhaxjxtxbxmh. Pdetdtz, lqip p tdvvmg stglwgl ipxa vmia kmgg wigl. Iptzt igm bwgm hwepxaiqriims btkwvxyjmh, wcm dn lpxkw qh kptams Spaxazq tfpuxvpbxwc. Bwqh qcddtkmh tdwzqco uwg ztxtiims ttbimga xv ipt kxxwmgbtfi. Qi'a aqzmag ippb ipt vjuqmg wu ttbimga xvqmietmc bwmhm gmempbh qh i bcabxxam dn ipt stglwgl amcoip. Awds pb lqzqemsqp ndz bwgm xvuwgupbxwc! Jn bwm lin, qu gdc sqsv'i edzz qi wjb, ipt xgmkqdch kxxwmg epa p stglwgl hcqaiqiciqdv rqeptz lqip zmnedzs stglwgl. Hw uig, et'dt wctn kdvhqsmgms ajjhbxbjbxwc kxxwmga, qci bwmgm pzt wiptz ptimgvpbxdta. Lm rwjts ndz tfpuett ztwgltz ipt kxxwmgbtfi. </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: Mahdokht from Farzanegan of Kermanshah Patrick from Woodbridge School, England An Anonymous Solver from Somewhere in the US Joseph from Hong Kong The solution is: If you can read this, well done! This sort of cipher is called a polyalphabetic cipher. For examples like this one with a keyword of length two, it's possible to solve it by hand just trying possibilities. However, with a longer keyword this gets very hard. There are more sophisticated techniques, one of which is called Kasiski examination. This involves looking for repeated letters in the ciphertext. It's likely that the number of letters inbetween these repeats is a multiple of the keyword length. Look at wikipedia for more information! By the way, if you didn't work it out, the previous cipher was a keyword substitution cipher with keyword keyword. So far, we've only considered substitution ciphers, but there are other alternatives. We could for example reorder the ciphertext. vigenere keyword: pi</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 fourth 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.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> If you can read this, well done! This sort of cipher is called a polyalphabetic cipher. For examples like this one with a keyword of length two, it's possible to solve it by hand just trying possibilities. However, with a longer keyword this gets very hard. There are more sophisticated techniques, one of which is called Kasiski examination. This involves looking for repeated letters in the ciphertext. It's likely that the number of letters inbetween these repeats is a multiple of the keyword length. Look at wikipedia for more information! By the way, if you didn't work it out, the previous cipher was a keyword substitution cipher with keyword keyword. So far, we've only considered substitution ciphers, but there are other alternatives. We could for example reorder the ciphertext. vigenere keyword: pi </mdoxml> 2 5 0 0 0 0 1 Semicircle Fourth challenge cipher Applications Codes and cryptography Decision Mathematics and Combinatorics Combinatorics Decision Mathematics and Combinatorics Algorithms