hw1

Homework 1
Due: Friday, August 26

The following message was encrypted using a shift-cipher. What does it say?
BJQHTRJ GFHP YT HXZ.

-OIF
Your instructor typically signs messages with his initials.
Recall from class the fraudulent ogham, Caesar, and ROT13 ciphers; these correspond to shifting by 1, 3 and 13, respectively.
$\begin{alphabetize} \par \item One of these ciphers decrypts itself; $C(C(M)) = ... ... M$. Do some shift ciphers eventually repeat? Do all? Explain. \end{alphabetize}$
Here are two ciphers sometimes used in ancient Hebrew:
- Atbash The first and last letters of the alphabet are exchanged; the second and next-to-last letters are exchanged; and so on.
- Albam The alphabet is split in two, and the two halves are equated. Thus, the first letter of the first half is exchanged with the first letter of the second half, and so on.
$\begin{alphabetize} \item Is encrypting a message with {\em atbash} and then wit... ... BGURE'F ZNVY.\\ \null\hspace{3in}--U. FGVZFBA \end{quotation}\end{alphabetize}$
These partial tables say that, for example, the sum of an odd number and an even number is odd, while the product of an odd number and an even number is even.

EVEN ODD

EVEN

ODD ODD

$\cdot$ EVEN ODD

EVEN

ODD EVEN

$\begin{alphabetize} \item Fill in the rest of each table. \item Prove that the p... ...e written $n = 2m$, and odd if it can be written $n = 2m+1$.} \end{alphabetize}$

Jeff Achter