16 1. HISTORICAL INTRODUCTION
Exercise 1.5.6. Come up with two messages that encrypt to the same
text under the Polybius checkerboard but have different meanings; each mes-
sage should make sense. Note there are not too many possibilities as almost
all letters have a unique decryption.
Exercise 1.5.7. One difficulty in using the Polybius checkerboard is that
it only has 25 squares, but there are 26 letters in the English alphabet. Show
how we can overcome this by either increasing the size of the board or by
considering a cube. What is the smallest cube that works?
Exercise 1.5.8. Create a nomenclator code book and alphabet, and use
it to encrypt the message: “Meet me at our favorite restaurant at 6 PM.”
Exercise 1.5.9. Using a Stager cipher, encode the message “Do you
believe in miracles?”
Exercise 1.5.10. Using a Stager cipher, encode the message “It was
early spring, warm and sultry glowed the afternoon.” ( Note: there is an in-
teresting history to this quote, which can be uncovered by an internet search.)
Exercise 1.5.11. The following message was encrypted with a Stager
cipher; what is it?
d f n o t i f r
o i t u h t t e
n r i s e e h y
o e l e w s e e
t u y e h o i s
Exercise 1.5.12. The following message was encrypted with a Stager
cipher; what is it?
a s l l u p o
s i i l t t r
k x o a a f m
f m n r c o o
o i d s c u r
r l o b e r e
Exercise 1.5.13. Deciphering the code in Exercises 1.5.11 and 1.5.12 is
fairly easy if you know to read it in columns. We can increase the security by
hiding the number of columns and writing it as d f n o t i f r o i t u
h t t e n r i s e e h y o e l e w s e e t u y e h o i s. While
this initially masks the number of columns, assuming we have at least two
columns and at least two rows, show there are only six possibilities.
Exercise 1.5.14. Suppose your friend is considering encrypting a mes-
sage to you through a Stager cipher. Having done Exercise 1.5.13, she knows
that it would be a mistake to write the message in columns, as then it can
be readily deciphered. She therefore decides to write it as a string of letters,
and only the two of you will know the number of rows and columns. If there
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