A shift cipher was used to obtain the ciphertext kddmu
. Decrypt it by trying all possibilities.
In[1]:= allshifts[”kddkmu”]
kddkmu
leelnv
mffmow
nggnpx
ohhoqy
piiprz
qjjqsa
rkkrtb
sllsuc
tmmtvd
unnuwe
voovxf
wppwyg
xqqxzh
yrryai
zsszbj
attack
buubdl
cvvcem
dwwdfn
exxego
fyyfhp
gzzgiq
haahjr
ibbiks
jccjlt
As you can see, attack is the only word that occurs on this list, so that was the plaintext.
Encrypt the plaintext message cleopatra using the affine function :
In[2]:=affinecrypt["cleopatra", 7, 8]
Out[2]=whkcjilxi
The ciphertext mzdvezc was encrypted using the affine function . Decrypt it.
SOLUTION
First, solve for to obtain . We need to find the inverse of :
In[3]:= PowerMod[5, -1, 26]
Out[3]= 21
Therefore, . To change to standard form:
In[4]:= Mod[-12*21, 26]
Out[4]= 8
Therefore, the decryption function is . To decrypt the message:
In[5]:= affinecrypt["mzdvezc", 21, 8]
Out[5]= anthony
In case you were wondering, the plaintext was encrypted as follows:
In[6]:= affinecrypt["anthony", 5, 12]
Out[6]= mzdvezc
Here is the example of a Vigenère cipher from the text. Let’s see how to produce the data that was used in Section 2.3 to decrypt it. For convenience, we’ve already stored the ciphertext under the name vvhq.
In[7]:= vvhq
Out[7]=
vvhqwvvrhmusgjgthkihtssejchlsfcbgvwcrlryqtfsvgahwkcuhwauglqhnslrljs hbltspisprdxljsveeghlqwkasskuwepwqtwvspgoelkcqyfnsvwljsniqkgnrgybwl wgoviokhkazkqkxzgyhcecmeiujoqkwfwvefqhkijrclrlkbienqfrjljsdhgrhlsfq twlauqrhwdmwlgusgikkflryvcwvspgpmlkassjvoqxeggveyggzmljcxxljsvpaivw ikvrdrygfrjljslveggveyggeiapuuisfpbtgnwwmuczrvtwglrwugumnczvile
Find the frequencies of the letters in the ciphertext:
In[8]:= frequency[vvhq]
Out[8]=
{{a, 8}, {b, 5}, {c, 12}, {d, 4}, {e, 15}, {f, 10}, {g, 27}, {h, 16}, {i, 13}, {j, 14}, {k, 17}, {l, 25}, {m, 7}, {n, 7}, {o, 5}, {p, 9}, {q, 14}, {r, 17}, {s, 24}, {t, 8}, {u, 12}, {v, 22}, {w, 22}, {x, 5}, {y, 8}, {z, 5}}
Let’s compute the coincidences for displacements of 1, 2, 3, 4, 5, 6:
In[9]:= coinc[vvhq, 1]
Out[9]= 14
In[10]:= coinc[vvhq, 2]
Out[10]= 14
In[11]:= coinc[vvhq, 3]
Out[11]= 16
In[12]:= coinc[vvhq, 4]
Out[12]= 14
In[13]:= coinc[vvhq, 5]
Out[13]= 24
In[14]:= coinc[vvhq, 6]
Out[14]= 12
We conclude that the key length is probably 5. Let’s look at the 1st, 6th, 11th, ... letters (namely, the letters in positions congruent to 1 mod 5):
In[15]:= choose[vvhq, 5, 1]
Out[15]= vvuttcccqgcunjtpjgkuqpknjkygkkgcjfqrkqjrqudukvpkvggjjivgjggpfncwuce
In[16]:= frequency[%]
Out[16]= {{a, 0}, {b, 0}, {c, 7}, {d, 1}, {e, 1}, {f, 2}, {g, 9}, {h, 0}, {i, 1}, {j, 8}, {k, 8}, {l, 0}, {m, 0}, {n, 3}, {o, 0}, {p, 4}, {q, 5}, {r, 2}, {s, 0}, {t, 3}, {u, 6}, {v, 5}, {w, 1}, {x, 0}, {y, 1}, {z, 0}}
To express this as a vector of frequencies:
In[17]:= vigvec[vvhq, 5, 1]
Out[17]= {0, 0, 0.104478, 0.0149254, 0.0149254, 0.0298507, 0.134328, 0, 0.0149254, 0.119403, 0.119403, 0, 0, 0.0447761, 0, 0.0597015, 0.0746269, 0.0298507, 0, 0.0447761, 0.0895522, 0.0746269, 0.0149254, 0, 0.0149254, 0}
The dot products of this vector with the displacements of the alphabet frequency vector are computed as follows:
In[18]:= corr[%]
Out[18]=
{0.0250149, 0.0391045, 0.0713284, 0.0388209, 0.0274925, 0.0380149, 0.051209, 0.0301493, 0.0324776, 0.0430299, 0.0337761, 0.0298507, 0.0342687, 0.0445672, 0.0355522, 0.0402239, 0.0434328, 0.0501791, 0.0391791, 0.0295821, 0.0326269, 0.0391791, 0.0365522, 0.0316119, 0.0488358, 0.0349403}
The third entry is the maximum, but sometimes the largest entry is hard to locate. One way to find it is
In[19]:= Max[%]
Out[19]= 0.0713284
Now it is easy to look through the list and find this number (it usually occurs only once). Since it occurs in the third position, the first shift for this Vigenère cipher is by 2, corresponding to the letter c. A procedure similar to the one just used (using vigvec[vvhq, 5,2],..., vigvec[vvhq,5,5]) shows that the other shifts are probably 14, 3, 4, 18. Let’s check that we have the correct key by decrypting.
In[20]:= vigenere[vvhq, -{2, 14, 3, 4, 18}]
Out[20]=
themethodusedforthepreparationandreadingofcodemessagesissimpleinthe extremeandatthesametimeimpossibleoftranslationunlessthekeyisknownth eeasewithwhichthekeymaybechangedisanotherpointinfavoroftheadoptiono fthiscodebythosedesiringtotransmitimportantmessageswithouttheslight estdangeroftheirmessagesbeingreadbypoliticalorbusinessrivalsetc
For the record, the plaintext was originally encrypted by the command
In[21]:= vigenere[%, {2, 14, 3, 4, 18}]
Out[21]=
vvhqwvvrhmusgjgthkihtssejchlsfcbgvwcrlryqtfsvgahwkcuhwauglqhnslrljs hbltspisprdxljsveeghlqwkasskuwepwqtwvspgoelkcqyfnsvwljsniqkgnrgybwl wgoviokhkazkqkxzgyhcecmeiujoqkwfwvefqhkijrclrlkbienqfrjljsdhgrhlsfq twlauqrhwdmwlgusgikkflryvcwvspgpmlkassjvoqxeggveyggzmljcxxljsvpaivw ikvrdrygfrjljslveggveyggeiapuuisfpbtgnwwmuczrvtwglrwugumnczvile