Here are some practical hints for doing the exercises
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Week 1
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RotI = { 1 -> 5 , 2 -> 11 , 3 -> 13, 4 -> 6, 5 -> 12, 6 -> 7, 7 -> 4, 
  8 -> 17, 9 -> 22, 10 -> 26, 11 -> 14, 12 -> 20, 13 -> 15, 14 -> 23, 
  15 -> 25, 16 -> 8, 17 -> 24, 18 -> 21, 19 -> 19, 20 -> 16, 21 -> 1, 
  22 -> 9, 23 -> 2, 24 -> 18, 25 -> 3, 26 -> 10 }

RotIinv = {5 -> 1, 11 -> 2, 13 -> 3, ... }

lettercodes = Range[26]

RefB = {1 -> 25, 25 -> 1, (2,18),(3,21),(4,8),(5,17),(6,19),(7,12),
        (9,16),(10,24),(11,14),(13,15),(20,26),(22,23)}

EnigmaGuts = {1 -> 8, 8 -> 1, 2 -> 11, ... }

Enigma1[x_, n_] := 
 Mod[((Replace[Mod[x + n, 26, 1], EnigmaGuts]) - n), 26, 1]

MapThread[Enigma1, {list1, list2}]


Week 2
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plain = {1,3,4,23,9,2,12,8}

cypher = {17,4,14,6,17,3,4,23,8,8,19,3,1,24,22,11,6,22,15}

Bombe[plain_, cyfrag_, k_] := 
 If[ Enigma1[plain[[1]], k] == cyfrag[[1]] && cyfrag[[1]] == plain[[1+1]] && ...
    , {"YES!!!",k}
    , {"no"} ]


Week 3
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<< FiniteFields`


Week 4
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elliptic = ContourPlot[y^2 == x^3 - 5 x + 3, {x,-3,3},{y,-4,4},Axes->True]


EllipticAdd[p_, a_, b_, c_, P_List, Q_List] := 
 Module[{lam, x3, y3, P3},
   Which[ P == {O}, R = Q,
          Q == {O}, R = P,
          P[[1]] != Q[[1]],		  
            lam = Mod[(Q[[2]] - P[[2]]) PowerMod[Q[[1]] - P[[1]], -1, p], p];
            x3 = Mod[lam^2 - a - P[[1]] - Q[[1]], p];
            y3 = Mod[-(lam (x3 - P[[1]]) + P[[2]]), p];
            R = {x3, y3},
         (P == Q) && (P != {O}),
            lam = Mod[(3*P[[1]]^2 + 2 a*P[[1]] + b)
                      PowerMod[2 P[[2]], -1, p], p];
            x3 = Mod[lam^2 - a - P[[1]] - Q[[1]], p];
            y3 = Mod[-(lam (x3 - P[[1]]) + P[[2]]), p];
            R = {x3, y3},
         (P[[1]] == Q[[1]]) && (P[[2]] != Q[[2]]),
            R = {O}
        ]; R
       ]


Z2mEllipticAdd[a_, c_, P_List, Q_List] := 
 Module[{lam, x3, y3, P3,R},
   Which[ P == {O}, R = Q,
          Q == {O}, R = P,
          ToElementCode[P[[1]]] != ToElementCode[Q[[1]]],
            lam = (Q[[2]] + P[[2]])/(Q[[1]] + P[[1]]);
            x3 = lam^2 + lam + a + P[[1]] + Q[[1]];
            y3 = lam (x3 + P[[1]]) + x3 + P[[2]];
            R = {x3, y3},
         ((ToElementCode[P[[1]]] == ToElementCode[Q[[1]]]) && 
          (ToElementCode[P[[2]]] == ToElementCode[Q[[2]]])) &&
         (P != {O}),
            lam = P[[1]] + P[[2]]/P[[1]];
            x3 = lam^2 + lam + a;
            y3 = P[[1]]^2 + (lam + 1) x3;
            R = {x3, y3},
         (ToElementCode[P[[1]]] == ToElementCode[Q[[1]]]) &&
	 (ToElementCode[P[[2]]] != ToElementCode[Q[[2]]]),
            R = {O}
        ]; R
       ]

P =.;
a = ee; c = 0;
P[0] = {x, y};
P[i_] := P[i] = Z2mEllipticAdd[a, c, P[i - 1], P[i - 1]]