Problem 1. The following Enigma ciphertext contains the crib "HEILHITLER":

SRUPH TEPPQ LZREF MNIJT EPAZL SDHPQ WCVTP IQASY UFLIW CGFPO MULCD

State all of the positions in the ciphertext that it could occur.

Problem 2. In the following sentences, all vowels and spaces have been removed. See if you can reconstruct the original sentence. (Note: it is possible that the answer is not unique.)

1. MYFVRTCLSSSCRYPTGRPHY
2. THRNNSPNFLLSMNLYNTHPLN
3. CNTGTNSTSFCTN

Problem 3. Compute the following:

1. 27 mod 13
2. 270 mod 13
3. gcd(1,18325769)
4. gcd(0,18325769)
5. gcd(17,18325769)
6. 35^18325769 mod 17
7. 35³³ mod 11

Problem 4. Consider the following method of using DES to encipher a message consisting of English text assuming Alice and Bob share a secret key K: Convert each letter in the message to a number by setting a = 0, b = 1, ... , z = 26, convert each number to binary, pad each equivalent binary number with 0s to make it 64 bits long (e.g., c becomes 62 0's followed by 10), encrypt the result using DES with the key K and send the resulting 64 bit cipher letter. Why isn't this very secure for a message containing 50 or more characters? What could Alice and Bob do to make it more secure?

Problem 5. Bob asks Alice to marry her by sending the message "Will you marry me?" in the clear on the channel so that Eve can read it. Alice sends her answer by either sending "yes" = 1 or "no" = 0 encrypted using Bob's public RSA key. How can Eve figure out what Alice's answer was? How can Alice prevent Eve from figuring it out?

Bonus #1. Compose a paragraph (as long as you possibly can make up) which makes sense and avoids using any of a given symbol which is conspicuously missing from a problem you are reading now. (Such a paragraph is called a lipogram.)

Bonus #2. Derive a more naturally sounding statement for Bonus #1 (which also avoids using the character not mentioned).

Report problems to dkrizanc at wesleyan dot edu