TWO PLUS TWO IS GREATER THAN FIVE, FOR SUFFICIENTLY LARGE TWO.
2. Encipher the following message using .
MY GIRLFRIEND’S GOT A GUN - I’LL SPEND THE REST OF MY LIFE PLAYING HIDE AND SEEK1 3. Verify the keyspace for 2x2 matrix encryption. You may do this by either writing a computer program to check the determinants of all possible 2x2 matrices to see which are invertible or by applying the formula provided in Overbey, Jeffrey, William Traves, and Jerzy Wojdylo, On the Keyspace of the Hill Cipher, Cryptologia, Vol. 29, No. 1, January 2005, pp. 59-72 Available online at http://jeff.actilon.com/keyspace-final.pdf,.
4. Can every possible digraphic substitution be realized by matrix encryption? Hint: compare keyspaces.
5. Verify the keyspace for 3x3 matrix encryption. You are strongly encouraged to solve this by applying the formula provided in the reference given in exercise 3, although you may write a program and patiently wait…
6. The unicity point for a random N-gram substitution cipher is .90 log(26N)!2 How do you think this compares to that for encryption with an NxN matrix? Explain your reasoning. In chapter 10, I’ll reveal a formula for computing unicity points and an exercise will ask you to go back and calculate it for 2x2, 3x3, and 4x4 matrix encryption, but for now I want you to simply think about it. Perhaps you’ll figure out the key component in the formula before it is unveiled!
7. Can an enciphering matrix have the form ? Justify your answer!
8. H. Gary Knight provided the following 2x2 matrix encryption ciphertext as his very first problem for readers of his column in Cryptologia.3 QHDIW QQQEI WFRLI YLUIO WQUVC NQDHV SNTQV YRLEP RVMND ERMOA
Prior to enciphering, Knight converted the letters to numbers using the assignments A=1, B=2, C=3,… Z=26. He gave two probable words, SUBMARINE and OBSERVING, as hints. Feel free to apply Levine’s attack or brute force a solution with a computer.
9. Levine’s attack depends on parity (even or odd). Is it significant (i.e., cryptanalytically useful) that all vowels are even, if we start our numbering with A=0? We have A=0, E=4, I=8, O=14, U=20, Y=24.
10. Using the assignments A=1, B=2, C=3,…, Y=25, Z=0, and a 3x3 matrix for encryption, Levine obtained the following ciphertext message:
MIU GNJ WWU YHZ DNS WVK RFV LLK AMP IGS MIU
In the May 1961 paper4 where Levine detailed his crib attack, he provided the probable plaintext THREE CONGRUENCES and showed how it may be used to recover the message. Go ahead and do this without referring to the original paper. Note: in the 2x2 example there were 4 possible forms, but for the 3x3 case, there will be 8.
11. Decipher the following message enciphered using a 2x2 matrix.
WVUQU HSCZR LXLVH IIGZR FVVRE TFAQK KVOYM DFAIT UHESO JOKFN FPOJS LXGWI FFUKU QCEHA JOSFG PDDXL NMYUO MDYMT RDBHN MWIRD NJSMT VXMEC EPKZO FWORX KLYDE PEIUR DYWML NKROF XGCEK TNZXG
JDCUG EVEHH YIRAW REGTU WYAMQ IFXCH WKVXX TEJGK RWJQD KJAIT NAWTE ZXGQM BOPHQ HWCGM DGNTD PEQHT WPYQB DRPTV EIOFG DBSWY XLZJJ VSJPT XBMCX VHXSU SCYEH NKOWH QKQFJ E
14. How many plaintext/ciphertext pairs are needed to uniquely determine a 3x3 matrix? If your answer is denoted by n, will any n pairs suffice? If not, what condition must hold to make them sufficient?