lecture6.html

lecture6.mw

> # a little bit of cryptography:

> with(StringTools):

> Map( Capitalize, "This is a test." );

> Map( LowerCase, %);

> convert("Test string", 'bytes');

> convert([65,66,67], 'bytes');

> convert("abcdefghijklmnopqrstuvwxyz", 'bytes');

> convert("ABCDEFGHIJKLMNOPQRSTUVWXYZ", 'bytes');

> # irem(a, b) gives the remainder r of a upon division by b,
# i.e. the r in a = q * b + r with 0 <= r < b.
# For example,

> irem(17,5);

> # but

> irem(-1,5);

> # the Caesar cipher is the following:
# it takes the plaintext and shifts the letters
# alphabetically by some fixed amount
# For instance, a shift by 3 amounts to
# a -> d
# b -> e
# c -> f
# ...
# w -> z
# x -> a
# y -> b
# z -> d
#
# So, abc becomes def, for instance.
# to decipher, oneft back the other direction by the same amount.

> # now we implement the Caesar cipher,
# which is shifting the letters of the alphabet by some fixed amount

> caesar := proc(s::string, shift::integer)
local S, l, i, c;
S := convert(s,'bytes');
l := nops(S);
for i to l do
   c := S[i];
   if c >= 97 and c <= 122 then
     c := c - 97 + shift;
     c := irem(c, 26);
     if c < 0 then c := c + 26; end;
     S[i] := 97 + c;
   end;
end;
return convert(S,'bytes');
end;

> # encryption:

> caesar("abcdefghijklmnopqrstuvwxyz", 3);

> # decryption using the negative shift

> caesar(%, -3);

> caesar("abcdefghijklmnopqrstuvwxyz", 26);

> vigenere_cipher := proc(s::string, k::string)
local S, l, K, kl, i, j, c, d;
S := convert(s,'bytes');
l := nops(S);
K := convert(k,'bytes');
kl := nops(K);
for i to l do
   j := irem(i, kl) + 1;
   c := S[i];
   d := K[j];
   if c >= 97 and c <= 122 then
     c := c - 97;
     c := c + d;
     c := irem(c, 26);
     if c < 0 then c := c + 26; end;
     S[i] := 97 + c;
   end;
end;
return convert(S,'bytes');
end:

> p := "Shake and quiver, little tree, Throw gold and silver down to me";

> c := vigenere_cipher(p, "verysecret");

> vigenere_decipher := proc(s::string, k::string)
local S, l, K, kl, i, j, c, d;
S := convert(s,'bytes');
l := nops(S);
K := convert(k,'bytes');
kl := nops(K);
for i to l do
   j := irem(i, kl) + 1;
   c := S[i];
   d := K[j];
   if c >= 97 and c <= 122 then
     c := c - 97;
     c := c - d;
     while c < 0 do
       c := c + 26;
       end;
     c := irem(c, 26);
     S[i] := 97 + c;
   end;
end;
return convert(S,'bytes');
end:

> vigenere_decipher(c, "verysecret");

> p := "I have seen too much not to know that the impression of a woman may be more valuable than the conclusion of an analytical reasoner.";

> vigenere_cipher(p, "arthurdoyle");

Error, (in vigenere_cipher) assigning to a long list, please use Arrays

> S := convert(p,'bytes');

> S[1] := 100;

Error, assigning to a long list, please use Arrays

> T := Array(S);

> T[1];

> vigenere_cipher := proc(s::string, k::string)
local S, T, L, l, K, kl, i, j, c, d;
S := convert(s,'bytes');
T := Array(S);
l := nops(S);
K := convert(k,'bytes');
kl := nops(K);
for i to l do
   j := irem(i, kl) + 1;
   c := T[i];
   d := K[j];
   if c >= 97 and c <= 122 then
     c := c - 97;
     c := c + d;
     c := irem(c, 26);
     if c < 0 then c := c + 26; end;
     T[i] := 97 + c;
   end;
end;
L := [];
for i to l do
   L := [op(L),T[i]];
end;
return convert(L,'bytes');
end:

> vigenere_cipher(p, "arthurdoyle");

> # HOMEWORK
#

> #

> # 1)
# The Nero cipher exchanges a and z, b and y, c and x etc.
# Write a procedure to encrypt using the Nero cipher.
# Take your favourite text and encrypt it with
# 7 Caeser, one Nero and 12 more Caesar ciphers.
# What do you get?
# How do you decipher it?
# Can you decipher it using only one n-fold Caesar and one Nero step?

> # 2) re-write thefunction vigenere_decipher() to use an Array
#    (to make it work for long strings.)
#    Then decipher the following piece (the key is jane)
#    "Wnv, sv wkxt, vqn jwlz mgut, Mou. Lqgm utep mnxv Nbvakohbkif op mghgg ya g ahaki sxp uc egoix cqkzrpx cths vak phxqj uc Etdntta"
#
# 3) re-write the functions vigenere_cipher and vigenere_cipher
#    to also encrypt capital letters.

> # Use this function the encrypt the text of 2) with the key jane.