Teachers' pack - National Cipher Challenge - University of ...

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OHP Slide 2 for lesson 3CiphertextLMYFU BKUUS DDYFA XWCLA OLPSF AOLMJ FASDS NSFGJ FAOELSOMYT DJLAX EMHJM BFMIB JUMIS HFSUL AXUBA FKJAM XLSKFFKXWS DJLSO FGBJM WFKIU OLFMX MTMWA OKTTG JLSXL SKFFKXWSDJ LSIZG TSXWJ LJLSX LSUMF JSDJL SIZGH FSQYS XOGLS DMMDTSDMXJ LSBAT SMHBK BSFLS BFMCT SDKFM YXDJL SLYJM ZTANAMYUXM CJMCL MCKUT MMEAX WKJLA IKXDC LMCKU XJJLA UCKUCLKJAJ LKDZS SXTAE SHMFJ SXAXJ SFIAX KZTSI MXJLU TKUJG SKFXMCMXDS FLSLK DWMXS IKDJL SOLMF YUTAX SMHIS KXAXW TSUUTSJJSF UDKXO SDZSH MFSLA USGSU ZYJJL SGCSF SXMJI SKXAX WTSUUJLSGC SFSTM KDSDC AJLJL SIMUJ NAJKT ISKXA XWAIK WAXKZ TSAHMXTGLS OMYTD HAXDA JZYJC LSFSC KUJLS BKJJS FXCLS FSCKU JLSBKJJSFX CLSFS CKUJL SBKJJ SFXHF MISXA WIKZG FMZSF JLKFF AUOccurences table:A B C D E F G H I J K L M34 12 19 23 4 41 12 10 16 50 38 46 42N O P Q R S T U V W X Y Z3 11 1 1 0 78 22 28 0 13 41 11 1136 email:cipher@soton.ac.uk
University of Southampton National Cipher Challenge Teachers’ pack OHP Slide 3 for lesson 3Use frequency analysis to guess that S enciphers for e, and J for t.This tells us that for an affine shift cipherx à ax + ba.5 +b = 19 (e à S)a.20 + b = 10 (t à J)Solving mod 26 we see that 15.a = -9 mod 26. Now 7.15 is congruent to 1 mod 26since 7.15 = 105 = 104 +1= 4.26 +1. It follows that 7.15.a = 7.-9, or a is congruent to-63.Now -63 = -52 - 11, so a is congruent to -11, or equivalently to 15 mod 26. Hence a= 15. Now from a.5 + b = 19 we get75 +b is congruent to 19, or b is congruent to –56 mod 26.Since -56 = -2.26 - 4, b is congruent to -4 mod 26 so b = 22.To check this 20.a +b = 300 + 22 = 322 = 12.26 + 10, soa.20 + b = 10 as required. So the affine shift is x à 15x+22 and the decrypt is givenby the inverse function yà 7(y-22)[It might look strange but “dividing by 15” is the same as multiplying by 7 in mod 26arithmetic.]Equivalently the decryption is achieved by the affine shifty à 7y+2.Encryption table:a b c d e f g h i j k l mI P W D K R Y F M T A H On o p q r s t u v w x y zV C J Q X E L S Z G N U B
Page 1 and 2: email:cipher@soton.ac.uk
Page 3 and 4: Points are awarded for speed and ac
Page 5 and 6: Getting helpWe offer online feedbac
Page 7 and 8: Frequently Asked QuestionsWhat does
Page 9 and 10: 9AZYXWVUTSRQPONMLKJIHGFEDCBAZYXWVUT
Page 11: Keyword substitution ciphersTo incr
Page 14 and 15: To attack cipher text that has been
Page 16 and 17: to 26. If we choose a carelessly (s
Page 18 and 19: On transposition ciphersSometimes w
Page 20 and 21: second columns have been transposed
Page 22 and 23: Handout for lesson 1.GROUP ACode: C
Page 24: Teachers’ solutions to encryption
Page 27 and 28: University of Southampton Nation
Page 35: University of Southampton Nation

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