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B Coder + Decoder de Hill0_MAS.bak
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B Coder + Decoder de Hill0_MAS.bak
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<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="18" minor="0"/>
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<Group view="presentation" hide-input="false" hide-output="true" inline-output="false" labelreference="L1" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L2" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">restart; with(linalg):
CrypteHill := proc(M::matrix,L::vector)
local letters, itable, matrice, pgcd, texte, blocksize, numblocks, pmatrix, cmatrix, ct,i,ptext;
letters := array ( 0..25,[A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z]);
itable := table();
for i from 0 to 25 do
itable[ letters[i] ] := i:
od:
matrice:=M;
pgcd:=gcd(det(matrice) mod 26, 26);
print(pgcd);
if pgcd = 1 then
texte := L;
for i from 1 to vectdim(texte) do
texte[i] := itable[ texte[i] ]:
od:
blocksize := rowdim(matrice);
numblocks := vectdim(texte)/blocksize;
pmatrix := matrix(numblocks, blocksize,texte);
cmatrix := map(m-> m mod 26, evalm(pmatrix &*matrice));
ct := convert (cmatrix, vector);
for i from 1 to vectdim(ct)do
ct[i] := letters[ct[i]];
od;
fi;
print(ct);
for i from 1 to vectdim (ct) do
ct[i] := itable[ct[i]]:
od:
cmatrix := matrix(numblocks,blocksize,ct);
cmatrix := map(m-> m mod 26, evalm(pmatrix &* matrice));
ct := convert (cmatrix, vector);
for i from 1 to vectdim(ct) do
ct[i] := letters[ ct[i] ]:
od:
for i from 1 to vectdim(ct) do
ct[i] :=itable[ ct[i] ];
od;
cmatrix:= matrix(numblocks, blocksize, ct);
pmatrix := map(m -> m mod 26, evalm(cmatrix &* matrice^(-1)));
ptext := convert(pmatrix, vector);
for i from 1 to vectdim(ptext) do
ptext[i] := letters[ ptext[i] ];
od;
print(ptext);
end proc;</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">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</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L71" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal">M := matrix(3,3,[1,3,3,5,3,2,7,2,5]);
L :=vector([V,I,F]);
CrypteHill(M,L);</Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2JVEiTUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIzo9RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiYtRiM2Ji1JJ210YWJsZUdGJDY3LUkkbXRyR0YkNigtSSRtdGRHRiQ2KC1JI21uR0YkNiRRIjFGJ0Y5LyUpcm93YWxpZ25HUSFGJy8lLGNvbHVtbmFsaWduR0Zdby8lK2dyb3VwYWxpZ25HRl1vLyUocm93c3BhbkdGam4vJStjb2x1bW5zcGFuR0Zqbi1GZW42KC1GaG42JFEiM0YnRjlGW29GXm9GYG9GYm9GZG9GZm9GW29GXm9GYG8tRlg2KC1GZW42KC1GaG42JFEiNUYnRjlGW29GXm9GYG9GYm9GZG9GZm8tRmVuNigtRmhuNiRRIjJGJ0Y5RltvRl5vRmBvRmJvRmRvRltvRl5vRmBvLUZYNigtRmVuNigtRmhuNiRRIjdGJ0Y5RltvRl5vRmBvRmJvRmRvRmJwRl1wRltvRl5vRmBvLyUmYWxpZ25HUSVheGlzRicvRlxvUSliYXNlbGluZUYnL0Zfb1EmcmlnaHRGJy9GYW9RJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0YxLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGW3IvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSYwLjhlbUYnLyUpcm93bGluZXNHUSVub25lRicvJSxjb2x1bW5saW5lc0dGZnIvJSZmcmFtZUdGZnIvJS1mcmFtZXNwYWNpbmdHUSwwLjRlbX4wLjVleEYnLyUqZXF1YWxyb3dzR0Y9LyUtZXF1YWxjb2x1bW5zR0Y9LyUtZGlzcGxheXN0eWxlR0Y9LyUlc2lkZUdGZHEvJTBtaW5sYWJlbHNwYWNpbmdHRmNyLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lKXJlYWRvbmx5R0Y9RjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0Zoc0ZbdEY5">PTYiNiQ7IiIiIiIkRiVFXFtsKjYkRiZGJkYmNiRGJiIiI0YnNiRGJ0YrRis2JEYmRidGJzYkRitGK0YnNiRGK0YmIiImNiRGJ0YnRjA2JEYrRidGKzYkRidGJiIiKA==</Equation></Text-field>
</Output>
<Output>
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