Teoria algor\303\255tmica dos n\303\272meros e criptografia<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o1 </Font><Equation executable="false" style="Heading 1" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRicvJSdmYW1pbHlHUTBUaW1lc35OZXd+Um9tYW5GJy8lJXNpemVHUSMxMkYnLyUlYm9sZEdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation><Font encoding="UTF-8"> [\303\215ndice de Coincid\303\252ncia]</Font></Text-field>Nesta pergunta, voc\303\252 calcula o \303\255ndice de coincid\303\252ncia de uma sequ\303\252ncia. Dada uma string 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 de comprimento t de s\303\255mbolos de um alfabeto 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 por n s\303\255mbolos. Deixe 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 o n\303\272mero de ocorr\303\252ncias do i-\303\251simo s\303\255mbolo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEiaUYnRjJGNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUZA na corda LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JlEiU0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LlEiLkYnRjIvRjZRJ25vcm1hbEYnLyUmZmVuY2VHRjQvJSpzZXBhcmF0b3JHRjQvJSlzdHJldGNoeUdGNC8lKnN5bW1ldHJpY0dGNC8lKGxhcmdlb3BHRjQvJS5tb3ZhYmxlbGltaXRzR0Y0LyUnYWNjZW50R0Y0LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGTi1GOTYuUSJ+RidGMkY8Rj5GQEZCRkRGRkZIRkpGTEZPRlFGUUYyRjw=O \303\255ndice de coincid\303\252ncia \303\251 igual a 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 A incid\303\252ncia da ocorr\303\252ncia pode ser usada para determinar se um c\303\263digo \303\251 um c\303\263digo de substitui\303\247\303\243o monoalfab\303\251tica ou um c\303\263digo de substitui\303\247\303\243o polialfab\303\251tico. Suponha que o ingl\303\252s seja o idioma do texto simples. Em uma cifra de substitui\303\247\303\243o monoalfab\303\251tica, as frequ\303\252ncias LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEiaUYnRjJGNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUZA deve ser aproximadamente igual \303\240s frequ\303\252ncias de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiYUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEiaUYnRjJGNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUZA em Ingl\303\252s . Em uma cifra de substitui\303\247\303\243o polialfab\303\251tica ideal, as frequ\303\252ncias LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEiaUYnRjJGNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUZA deve ser aproximadamente igual a LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkmbWZyYWNHRiQ2KC1JI21uR0YkNiVRIjFGJy8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1GIzYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnRjIvRjZRJ2l0YWxpY0YnRjJGNS8lLmxpbmV0aGlja25lc3NHRjEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGRy8lKWJldmVsbGVkR0Y0RjJGNQ==, i.e.cada letra ocorre com igual probabilidade.restart;with(StringTools):with(Statistics):Nesta quest\303\243o, assumimos quealphabet := Iota("a".."z");As probabilidades das letras no alfabeto que ocorrem no texto t\303\255pico em ingl\303\252s s\303\243o dadas na lista FE. O i-\303\251simo elemento da FE \303\251 a probabilidade da i-\303\251sima letra do alfabeto. A distribui\303\247\303\243o de probabilidade pode ser visualizada com o gr\303\241fico de barras produzido pelo ColumnGraph.FE := [0.8167000000e-1, 0.1492000000e-1, 0.2782000000e-1, 0.4253000000e-1, .1270200000, 0.2228000000e-1, 0.2015000000e-1, 0.6094000000e-1, 0.6966000000e-1, 0.1530000000e-2, 0.7720000000e-2, 0.4025000000e-1, 0.2406000000e-1, 0.6749000000e-1, 0.7507000000e-1, 0.1929000000e-1, 0.9500000000e-3, 0.5987000000e-1, 0.6327000000e-1, 0.9056000000e-1, 0.2758000000e-1, 0.9780000000e-2, 0.2360000000e-1, 0.1500000000e-2, 0.1974000000e-1, 0.7400000000e-3];ColumnGraph(FE);a) Calcule o \303\215ndice de Coincid\303\252ncia para letras em ingl\303\252s usando as probabilidades padr\303\243o. Calcule tamb\303\251m o \303\215ndice de Coincid\303\252ncia, assumindo que cada letra do alfabeto ocorra com a mesma frequ\303\252ncia.LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYuLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUkjbWlHRiQ2JVEjRkVGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGKy1GLDYtUSI9RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjI3Nzc3NzhlbUYnL0ZFRlNGKy1JJm1mcmFjR0YkNigtRiM2KS1GRzYlUSRTVU1GJ0ZKRk0tSShtZmVuY2VkR0YkNiYtRiM2Ki1GRzYlUSJpRidGSkZNRitGT0YrLUkjbW5HRiQ2JFEiMUYnRi9GKy8lK2V4ZWN1dGFibGVHRjRGL0YvLyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRistRmhuNiQtRiM2Ky1GRzYlUSJmRidGSkZNLUZobjYmLUYjNiVGXG9GY29GL0YvRmVvRmhvRistRiw2LVEnJnNkb3Q7RidGL0YyRjVGN0Y5RjtGPUY/RkFGREYrLUZobjYkLUYjNilGX3BGYnBGKy1GLDYtUSomdW1pbnVzMDtGJ0YvRjJGNUY3RjlGO0Y9Rj8vRkJRLDAuMjIyMjIyMmVtRicvRkVGYXFGX29GY29GL0YvRitGY29GL0YvRitGY29GLy1GIzYmRistRmhuNiQtRiM2KC1GRzYlUSJuRidGSkZNRitGZnAtRmhuNiQtRiM2J0ZpcS1GLDYtUSgmbWludXM7RidGL0YyRjVGN0Y5RjtGPUY/RmBxRmJxRl9vRkpGTUYvRkpGTUYvRkpGTS8lLmxpbmV0aGlja25lc3NHRmJvLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRmdyLyUpYmV2ZWxsZWRHRjQtRkc2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdGQy8lJmRlcHRoR0Zkcy8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GYHM2JkZic0Zlc0Zncy9GanNRJWF1dG9GJ0Zcc0Zjb0Yvb) Calcule o \303\215ndice de Coincid\303\252ncia para os dois c\303\263digos seguintes. Primeiro, voc\303\252 deve calcular uma lista de frequ\303\252ncias das letras nos dois c\303\263digos e, em seguida, calcular o \303\215ndice de Coincid\303\252ncia. Qual deles \303\251 mais prov\303\241vel que seja um c\303\263digo de substitui\303\247\303\243o monoalfab\303\251tico?
Voc\303\252 pode usar o comando CountCharacterOccurrences do pacote StringTools para contar as frequ\303\252ncias de caracteres. Voc\303\252 pode usar o comando add para calcular o \303\215ndice de Coincid\303\252ncia.cstr1 := "dqgbhwvdlgohjudqgwkhvroxwlrqlvebqrphdqvvrgliilfxowdvbrxpljkwehohdgwrlpdjlqhiurpwkhiluvwkdvwblqvshfwlrqriwkhfkdudfwhuvwkhvhfkdudfwhuvdvdqbrqhpljkwuhdglobjxhvvirupdflskhuwkdwlvwrvdbwkhbfrqyhbdphdqlqjexwwkhqiurpzkdwlvnqrzqrinlgglfrxogqrwvxssrvhklpfdsdeohrifrqvwuxfwlqjdqbriwkhpruhdevwuxvhfubswrjudskvlpdghxspbplqgdwrqfhwkdwwklvzdvridvlpsohvshflhvvxfkkrzhyhudvzrxogdsshduwrwkhfuxghlqwhoohfwriwkhvdlorudevroxwhoblqvroxeohzlwkrxwwkhnhb";Length(cstr1);cstr2 := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyinky";Length(cstr2);cstrl1 = SUM[i = 1]*f[i]*(f[i]-1)/(429*(429-1));<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 2 [Vigenere Cypher]</Font></Text-field> Lembre-se de que o c\303\263digo Vigenere \303\251 um c\303\263digo de substitui\303\247\303\243o polialfab\303\251tica, que aplica o deslocamento de C\303\251sar, com diferentes turnos, \303\240s letras do texto sem formata\303\247\303\243o. Qual turno \303\251 usado, \303\251 determinado por uma tecla. Deixe 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 ser a chave e deixar LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEiaUYnRjJGNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSJ+RidGNUZALyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWUY1RkA=seja o valor num\303\251rico da letra LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEia0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEiaUYnRjJGNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRidGNUZA na chave, a primeira letra do texto \303\251 alterada por 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 segunda letra by 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 ..., e LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn-th carta de LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtRi82JlEidEYnRjJGNUY4RjUvRjlRJ25vcm1hbEYnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSIuRidGNUZALyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWUY1RkA= Ap\303\263s o primeiro LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnRjIvRjZRJ25vcm1hbEYn letras os turnos come\303\247am de novo LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYlUSIxRidGNS9GOVEnbm9ybWFsRidGNUZBLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYuUSIuRidGNUZBLyUmZmVuY2VHRjcvJSpzZXBhcmF0b3JHRjcvJSlzdHJldGNoeUdGNy8lKnN5bW1ldHJpY0dGNy8lKGxhcmdlb3BHRjcvJS5tb3ZhYmxlbGltaXRzR0Y3LyUnYWNjZW50R0Y3LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGWkY1RkE=Implemente as fun\303\247\303\265es Maple EncryptVigenere e DecryptVigenere para criptografar e descriptografar seq\303\274\303\252ncias de caracteres usando o cifra Vigenere. Essas fun\303\247\303\265es devem receber uma string que \303\251 a chave e o alfabeto. Usaremos o alfabeto ingl\303\252s padr\303\243o e as strings de entrada ter\303\243o pontua\303\247\303\243o e espa\303\247os removidos e as letras mai\303\272sculas ser\303\243o substitu\303\255das pelas letras min\303\272sculas correspondentes.
Voc\303\252 pode implementar suas fun\303\247\303\265es modificando a fun\303\247\303\243o Caesar.
Experimente suas fun\303\247\303\265es na string lstr abaixo.
restart;with(StringTools):Letter2Number := proc(str,Convert)
local i, L; L := []; for i from StringTools:-Length(str) by -1 to 1 do L := [Convert[str[i]],op(L)]; end do; return L;end;Number2Letter := proc(L,alphabet) local i, str; str := ""; for i from 1 to nops(L) do str := cat(alphabet[L[i]+1],str); end do; return StringTools:-Reverse(str);end;alphabet := Iota("a".."z");Convert := table();for i from 1 to Length(alphabet) do Convert[alphabet[i]] := i-1;end do:Ceasar := proc(str,key,alphabet) local i, n, L, C, Convert, cypher; Convert := table(); n := StringTools:-Length(alphabet); for i from 1 to n do Convert[alphabet[i]] := i-1; end do; L := Letter2Number(str,Convert); C := []; for i from 1 to nops(L) do C := [op(C),L[i]+key mod n]; end do; cypher := Number2Letter(C,alphabet); return cypher;end;EncryptVigenere := proc(str,key,alphabet)end;DecryptVigenere := proc(str,key,alphabet)end;lstr := "once upon a time you dressed so fine you through the bums a dime in your prime didnt you";lstr := StringTools:-Remove(IsSpace,lstr);<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 3 [Cripan\303\241lise de Vigenere Cypher]</Font></Text-field>Nesta pergunta, voc\303\252 recebe um c\303\263digo que foi obtido usando um c\303\263digo Vigenere, cuidado com a pergunta 2, e \303\251 solicitado que o decifre. A abordagem b\303\241sica est\303\241 descrita no folheto de "The Code", de Simon Singh: 1) Determine o comprimento da chave procurando subsequ\303\252ncias repetidas; 2) use a an\303\241lise de frequ\303\252ncia nas subsequ\303\252ncias obtidas selecionando s\303\255mbolos do c\303\263digo em m\303\272ltiplos do comprimento da chave. . Os detalhes dessas etapas ser\303\243o descritos abaixo. Voc\303\252 ser\303\241 solicitado a escrever v\303\241rios procedimentos de bordo que auxiliam nesse processo.restart;with(StringTools):cstr := "eqjyvxvgiuphmrrrgzhvwrrukmrtijfbtodidtsjsgofwmfalkeveolqlmhkfhrerhwuidejonvjuumklhliiwwnajxbonjthitzsqufklhihrvditvvvzhvwhihrvditvvvgsrrbunvqlmhkvhgdzpbmuvwvloiqdiiglhxtyewosksvgyklhecfrykyrqhgnzrjhukxkknwvrswyewosbrrcnfjnodumfuuchqutjysvojikomtesgbcirlcfrvzrlgwonxeqeowxkkmfvhgbjxuasvguepksjxaglvomrhhapdcponuewuntiwnakxkosnevufrwlspcivvetmhyslgknoniykrrwzuuchdvpveuzoklhirlhhonkioretxrltyivgicsugbjsoatvpbonjsoabcizotysxztyinky";n := Length(cstr);a) Determine o comprimento da chave. Pesquise substrings repetidos de comprimento 4, 5, 6. Fa\303\247a a varredura da cifra, selecionando cada substring poss\303\255vel de comprimento l = 4,5,6 e procure se a substring selecionada ocorre mais tarde na cifra. Voc\303\252 pode usar o SearchText do pacote StringTools para procurar a substring no restante do c\303\263digo. Se voc\303\252 encontrar uma substring repetida, imprima a substring e o espa\303\247o entre as ocorr\303\252ncias da substring. Encontre o maior divisor comum das lacunas.
N\303\243o esque\303\247a que voc\303\252 pode acessar substrings usando a nota\303\247\303\243o de intervalo. POR EXEMPLO.cstr[1..4]; cstr[200..210]; cstr[400..n];b) Construa subseq\303\274\303\252ncias do c\303\263digo, selecionando caracteres em m\303\272ltiplos do comprimento da chave. I.E. Se k \303\251 o comprimento da chave, construa subsequ\303\252ncias: c1 = cstr[1],cstr[1+k],...,cstr[1+n/k],...,ck = cstr[k],cstr[2*k],...,cstr[floor(n/k)*k]. Dica do Maple: use seq e cat para formar essas strings.c) Calcule as frequ\303\252ncias de caracteres nas substrings formadas a partir de (b). Voc\303\252 deve construir uma lista F = [f1 / n, ..., ft / n], em que fi \303\251 o n\303\272mero de ocorr\303\252ncias do s\303\255mbolo i na string e n \303\251 o n\303\272mero de s\303\255mbolos na string, e t \303\251 o n\303\272mero de s\303\255mbolos no alfabeto. N\303\243o esque\303\247a que voc\303\252 pode usar evalf () para obter uma aproxima\303\247\303\243o de ponto flutuante das fra\303\247\303\265es fi / n, e voc\303\252 pode usar CountCharacterOccurrences () do pacote StringTools para obter o n\303\272mero de ocorr\303\252ncias do i-\303\251simo s\303\255mbolo. Para o alfabeto, use a, ..., z. Veja a pergunta 1.alphabet := Iota("a".."z");d) Determine os turnos Ceasar para as 5 subsequ\303\252ncias de (c) e, portanto, determine a chave. Isso \303\251 feito comparando as frequ\303\252ncias calculadas em (c) com as probabilidades de letras em ingl\303\252s padr\303\243o fornecidas na lista FE.
Voc\303\252 deve escrever uma fun\303\247\303\243o FindShift (F1, F2) que recebe como entrada F1 = as frequ\303\252ncias padr\303\243o e F2 = as frequ\303\252ncias deslocadas. A fun\303\247\303\243o FindShift (F1, F2) encontra os turnos s que minimizam o erro entre as duas listas de frequ\303\252ncias. I.E. Para cada turno poss\303\255vel
s = 0,1, ..., 25 = nops (F1), calcule a soma dos quadrados da diferen\303\247a F1 [i] -F2 [i + s mod 26]. Encontre o valor de s que minimiza essa soma. Essa ser\303\241 a mudan\303\247a mais prov\303\241vel.
Observe que na soma acima, voc\303\252 precisar\303\241 corrigir a indexa\303\247\303\243o devido ao fato de o Maple indexar listas e matrizes iniciando em 1 em vez de 0.
Use a fun\303\247\303\243o FindShift para encontrar a chave usada para criar o cyper cstr.FE := [0.8167000000e-1, 0.1492000000e-1, 0.2782000000e-1, 0.4253000000e-1, .1270200000, 0.2228000000e-1, 0.2015000000e-1, 0.6094000000e-1, 0.6966000000e-1, 0.1530000000e-2, 0.7720000000e-2, 0.4025000000e-1, 0.2406000000e-1, 0.6749000000e-1, 0.7507000000e-1, 0.1929000000e-1, 0.9500000000e-3, 0.5987000000e-1, 0.6327000000e-1, 0.9056000000e-1, 0.2758000000e-1, 0.9780000000e-2, 0.2360000000e-1, 0.1500000000e-2, 0.1974000000e-1, 0.7400000000e-3];FindShift := proc(F1,F2)end;e) Decifre cstr usando a chave encontrada em (d) e sua rotina DecryptVigenere da pergunta 2. Observe que o texto criptografado ter\303\241 espa\303\247os em branco removidos.<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 4 [Aritm\303\251tica modular e GCDs]</Font></Text-field>restart;a) Use o algoritmo euclidiano estendido (o comando maple igcdex) para encontrar o inverso de 5 em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEoJiM4NDg0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYlUSMyN0YnRjUvRjlRJ25vcm1hbEYnRjVGQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlEiLkYnRjVGQS8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlpGNUZB Verifique seu resultado.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b)Use a identidade de Euler para calcular o inverso de 5 em LUklbXN1Ykc2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2JlErJmludGVnZXJzO0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUklbXJvd0dGJDYlLUkjbW5HRiQ2JVEjMjdGJ0YyL0Y2USdub3JtYWxGJ0YyRj8vJS9zdWJzY3JpcHRzaGlmdEdRIjBGJw==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbW5HRiQ2JFEiNUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy1JI21vR0YkNi1RIn5GJ0YvLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkctRjM2L1EkbW9kRicvJSVib2xkR1EldHJ1ZUYnL0YwUSVib2xkRicvJStmb250d2VpZ2h0R0ZRRjZGOUY7Rj1GP0ZBRkNGRUZIRjItRiw2JFEjMjdGJ0YvLyUrZXhlY3V0YWJsZUdGOEYvc)Encontre todos os elementos que possuem invers\303\265es em LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEoJiM4NDg0O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYlUSMyN0YnRjUvRjlRJ25vcm1hbEYnRjVGQS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUkjbW9HRiQ2LlEiLkYnRjVGQS8lJmZlbmNlR0Y3LyUqc2VwYXJhdG9yR0Y3LyUpc3RyZXRjaHlHRjcvJSpzeW1tZXRyaWNHRjcvJShsYXJnZW9wR0Y3LyUubW92YWJsZWxpbWl0c0dGNy8lJ2FjY2VudEdGNy8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlpGNUZB e mostrar sua inversa. Quantos existem?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d) Exerc\303\255cio 3.19 do texto. Dica - compare as etapas no algoritmo euclidiano para calcular o gcd (a, b) com as etapas ao calcular 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 e use indu\303\247\303\243o.gcd 5LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Quest\303\243o 5 [N\303\272meros Primos e sua Distribui\303\247\303\243o]</Font></Text-field>restart;a) Pergunta 2.1 do texto. Prove que existem infinitos primos que s\303\243o um menos que um m\303\272ltiplo de quatro (ou seja, da forma 4 * n - 1. Dica: Siga a prova de Euclides de que existem infinitos primos e mostre que qualquer n\303\272mero inteiro da forma 4 * n - 1 deve ser divis\303\255vel por um primo da mesma forma.
b) Quest\303\243o 2.13 do texto. Esta quest\303\243o requer que voc\303\252 primeiro escolha 100 n\303\272meros consecutivos de sete d\303\255gitos e os fatore usando a divis\303\243o de teste (voc\303\252 pode simplesmente usar o comando ifactor do Maple. Qual \303\251 a distribui\303\247\303\243o dos tamanhos dos n\303\272meros primos que dividem seus n\303\272meros inteiros? Quantos dos n\303\272meros inteiros n t\303\252m um primo fator maior que 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 Descreva a distribui\303\247\303\243o, m\303\251dia e desvio padr\303\243o do logaritmo do maior fator primo dividido pelo logaritmo de n
.maple.ifactor(4,n,-1);LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=maple.ifactor(3/4,n,1/2,1/3);