Question 1

Encrypt the following message using a Vigeniere cipher with direct standard alphabets.  Key: JOSH. 

All persons born or naturalized in the United States, and 
subject to the jurisdiction thereof, are citizens of the
United States and of the state wherein they reside. No
state shall make or enforce any law which shall abridge 
the privileges or immunities of citizens of the United
States; nor shall any state deprive any person of life,
liberty, or property, without due process of law; nor deny
to any person within its jurisdiction the equal protection
of the laws.

Upper case only!  Turn plain and cipher text into 5 letter groups.
Calculate the index of coincidence of the plaintext and ciphertext.
Break the ciphertext into 4 columns.   
What is the index of coincidence of each column?

ALLPE RSONS BORNO RNATU RALIZ EDINT HEUNI TEDST ATESA NDSUB JECTT
OTHEJ URISD ICTIO NTHER EOFAR ECITI ZENSO FTHEU NITED STATE SANDO
FTHES TATEW HEREI NTHEY RESID ENOST ATESH ALLMA KEORE NFORC EANYL
AWWHI CHSHA LLABR IDGET HEPRI VILEG ESORI MMUNI TIESO FCITI ZENSO
FTHEU NITED STATE SNORS HALLA NYSTA TEDEP RIVEA NYPER SONOF LIFEL
IBERT YORPR OPERT YWITH OUTDU EPROC ESSOF LAWNO RDENY TOANY PERSO
NWITH INITS JURIS DICTI ONTHE EQUAL PROTE CTION OFTHE LAWS



Question 2

Break the Vigeniere based ciphertext below.  Plaintext and ciphertext alphabets are direct standard.
What is the key length?  What is the key? 
If the key length is k, how long a corresponding plain, ciphertext sequence be given to solve?  Can you give an upper bound on the pure ciphertext length needed?

IGDLK MJSGC FMGEP PLYRC IGDLA TYBMR KDYVY XJGMR TDSVK ZCCWG ZRRIP
UERXY EEYHE UTOWS ERYWC QRRIP UERXJ QREWQ FPSZC ALDSD ULSWF FFOAM
DIGIY DCSRR AZSRB GNDLC ZYDMM ZQGSS ZBCXM OYBID APRMK IFYWF MJVLY
HCLSP ZCDLC NYDXJ QYXHD APRMQ IGNSU MLNLG EMBTF MLDSB AYVPU TGMLK
MWKGF UCFIY ZBMLC DGCLY VSCXY ZBVEQ FGXKN QYMIY YMXKM GPCIJ HCCEL
PUSXF MJVRY FGYRQ 



Question 3

Consider a message source M(x) with the following distribution:
M: P(x=0)= p
M: P(x=1)= q, with p+q=1
and a one time pad selected from distribution P(x)
P: P(x=0)= ½
P: P(x=1)= ½
Consider the ciphertext formed by “xoring” the message m with the pad p, so that c= mÅp
What is the ciphertext distribution C?
Calculate H(M), H(P), H(C).
Calculate:  I(M|C)= H(M)-H(M|C)

Suppose, P: P(x=0)=3/4 and P(x=1)=1/4.  
What is the ciphertext distribution and H(M), H(P), H(C) and I(M|C) now.


Question 4

Calculate the output of the first two rounds of DES with input message  0x3132333435363738 and key 0x00abcdefabcdef89.   The input to round 1 (after initial permutation) and the first 2 round keys are given below.
For fixed key, DES is a permutation on 264 letters. 
Approximately how many such permutations are there?  (Hint: Use Stirling’s approximation.)  
Compare this to the size of the key space for DES.

Round 01 Key:   01001111 01010111 00000111 10111001 01011100 10101011
Round 02 Key:   00101111 00100111 01101001 00111011 01111111 00100100

Input to DES:   00110100 00110011 00110010 00110001 
                00111000 00110111 00110110 00110101
Round 1 Input:  00000000 11111111 11100001 10101010 
                00000000 11111111 00010000 01100110


Question 5

Given a one rotor machine, M, depicted below with equation 
C[i] R[-1] C[-i] U C[-i] R C[i] (p)=c with C, U, R below.
R:   ABCDEFGHIJKLMNOPQRSTUVWXYZ
     EKMFLGDQVZNTOWYHXUSPAIBRCJ
U:   ABCDEFGHIJKLMNOPQRSTUVWXYZ
     YRUHQSLDPXNGOKMIEBFZCWVJAT
C: The cyclic permutation A-->B, B-->C, etc

Calculate the ciphertext derived from the plaintext: HELLOWORLD 
What do you think the index of coincidence of the ciphertext
 from a 50 letter message is?
If the key was the “starting position,” i, of M, how many letters
of corresponding plain/cipher text would you need to find the key?  
How many ciphertext only letters?

The following may be helpful:
R[-1]  ABCDEFGHIJKLMNOPQRSTUVWXYZ
       UWYGADFPVZBECKMTHXSLRINQOJ