Secret Codes

In this mini-class, we learned a little about cryptology.

We learned methods for both encoding and decodingt  the following secret messages:

Cryptogram # 1

&  ?*--&”\   ;~   “)[*\#)”   )!   %&”)\#   +?$\{[%%~   )>\ ;!;\#)   )>\~   *\+&*\   )!   )?=\   #!    ;!$\    ;?)>\;?)&+” +![$”\”     )>\~    ;&@>)   }\   ?}%\   )!   >\?$    )>\   

“![#*   !{   +%!”&#@    *!!$”         ^\?$%  “   }[+=

We used our knowledge of the English language, and the most common letters, digraphs, and trigraphs in the English language to "crack" this cryptogram.  We found a "frequency distribution of the characters very helpful.

Solution:

 "I advise my students to listen carefully the moment they decide to take no more mathematics courses.  They might be able to hear the sound of closing doors."  -- Pearl S. Buck

Cryptogram # 2

VGVFV     ZCBFF     VOYRG     BORNZ     NGURZ     NGPVN     AJVGU     BHGOR     VATNC     BRGVA     FBHYF     BAVNX     BINYR     IFXLV

We used Maple to find the following frequency distribution for this cryptogram: 

[01 J, 01 L, 01 P, 01 T, 02 C, 02 H, 02 I, 02 U, 02 X, 03 O, 03 Y, 03 Z,  04 A, 06 , 06 R, O7 B, 07 G, 07 N, 10 V]

Based on this we eventually conjectured that the message had been encoded by shifting I to V  (add 13 to each letter value - mod 26).  We checked by using Maple to subtract (mod 26) this amount (13) from each letter -- and decoded the message as:

“It is impossible to be a mathematician without being a poet in soul.”  -- Sonia Kovalevsky

Cryptogram # 3

FPEGO      LSPIW       EVIAL        IVIKS         HHMZM    HIHFC DIVSW   XIZIR          AVMKL     X

[01 C, 01 D, 01 G, 01 O, 01 R, 02 A, 02 E, 02 F, 02 K, 02 P, 02 W, 02 X,  02 Z, 03 L , 03 M, O3 S, 04 H, 04 V, 08 I]

Maple indicated the frequency distribution was .

Thus we conjectured that an "E" was encrypted as an "I" -- (which is a shift of +4).  Using Maple to subtract 4 from each letter gave us the decoded message:

“Black holes are where God divided by zero.”  -- Steven Wright

Cryptogram # 4

HTAMA         ITAME           INAIC             VEDAS           OFECI        NRUTR          OCGNI           IEEFF             HTOTN          MEROE            LUAPS            SODRE

This is an example of a transposition cipher.  The frequency count indicates that there were no letter substitutions -- but the positions of the letters were rearranged.  In fact -- every 5 letters were reversed.  So  HTAMA  becomes   A Math...  

and  ITAME  is supposed to be  emati...

Solution:

“A mathematician is a device for turning coffee into theorems.”  – Paul Erdös

 Frequency count:

[01 G, 01 L, 01 P, 01 V, , 02 D, 02 H, 02 U, 03 C, 03 F, 03 M, 03 S,  04 N, 04 R , 05 O, O5 T, 06 A, 06 I, 08 E]

Cryptogram # 5

S A I T C L H N I G I L N D Y E S E E S R F R F I I N C T Z N H P S H A I I Y O E D N W I E G E L

 T T S I A T I K N W L O E A B A N C S A Y O E F C E T I I E S I A T E B L T T R A A D R T H W L S

 A quick look at the frequency distribution (below) indicates that it is another transposition cipher (not a substitution cipher).

[01 K, 01 P, 01 Z, , 02 B, 02 G, 03 D, 03 F, 03 O, 03 W, 03 Y,  04 C, 04 H, 04 R , 06 L, O7 N, 08 S, 09 A, 10 T, 06 A, 06 I, 11 E, 13 I]

This message was encrypted using the "Rail Fence Cipher".  Follow the lines shown below:

Solution:

“Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.”   -- HG Wells