Set 5: Polygraphic Substitution

1. Assume that the following Playfair square is used.

P A L M E

R S T O N

B C D F G

H I K Q U

V W X Y Z

a. Encipher "my pattern."

b. Decipher "RNKSO AUSLZ."

c. When a digraph (digram, bigram) is enciphered--for

example, "th" as "RK"--we may consider the first

plaintext letter--"t"--to be enciphered as the first

ciphertext letter--"R"--and the second plaintext

letter--"h"--to be enciphered as the second

ciphertext letter--"K." Then what are all the

possible letters that "e" may be enciphered as?

2. Answer the following questions about Playfair ciphers in

general.

a. If the bottom row of a 5 x 5 Playfair square is moved

to the top, then will the new square be equivalent to

the old one in the sense that they both encipher all

plaintext in the same way?

b. If the right-hand row of a 5 x 5 Playfair square is

moved to the left-hand side, then will the new square

be equivalent to the old one in the sense that they

both encipher plaintext in the same way?

c. If a Playfair square enciphers plaintext "re" as "QM,"

then what does it encipher "er" as?

d. Can the cryptogram gotten from a Playfair cipher have

an odd number of letters?

e. Can the cryptogram gotten from a Playfair cipher have

two consecutive letters the same?

3. Decipher the message

QPVBO GHXOF PWUFV KDSPQ KCXWU NBAMU DAQTA G

using the deciphering matrix

23 4

13 9 .

4. The following crypt was enciphered by a linear

transformation having the matrix

4 7

3 6

modulo 26. Decipher it.

DGSRD RFDNS GSXLV O

5. The following crypt was enciphered by a linear

transformation whose matrix is given by

17 3

8 9

modulo 26. (a) Decipher the crypt. (b) What is

special about the given matrix?

IGCRZ OGVPY LFHRV G

6. Solve the following cryptogram, which was enciphered

using Hill's digraphic system. Find not only the plaintext

but also either the enciphering matrix or the deciphering

matrix. The message contains the phrase "Gustavus Adolphus

music."

PBOXK BKYGM IZOUB FEAYT KBIVD NINGA YBEHI KDISS IWICP IQNNH TAQN

7. (Hill's digraphic system) Solve the following cryptogram.

It contains a statement of the American Cryptogram

Association.

UFMNF TTOHU DWRUQ LXWTQ AIPYD PWLMS FBYTE IXQWM GHBOY RPCNY

TCOGP EGHID ULKRR YCJSW IDTQS LWOSA GIYUM XCCJJ DIBAO MALDP

WLMSF BYTEI EPCCQ TQHRL ZCYRW KSPOX VKEWW MERDP SHMNR LYUUO

MKEYO GDPPM HSKEM IERPY IHOET OEMDP IDPEM RRLGD USAPQ SERIH

KMBJI DKJPY AYUSB YPCPD HSBON YTCOG PEHSU QPCEM IJQUP PMRDG

OODAT OHUQJ USMQU GMNNK BCBOX S

8. (Hill's digraphic system) Solve the following cryptogram.

MUZLM CIFMU PYBCW XBWHW OCAYZ LCQSR BMHEY ODBJI SRVFX RJISR

VFFYU RIVZL ARLPS KGXTV TSUOY OVHAG WCOHI DURIM QSZLO UMXMP

NJJIP SGAYO DBJIY EOMCI MIWXL IURAV DEBCU CUWZL OUMXM PNJJI

ELREB UYODO YMKVU ODYFN JIHWF KFQMY PMTVZ LUWQZ URFQM YPMTV

WXJQW JZLOC ZLEIC VXREL AJKDN ATVWX JQGAA GOCAY ZLEIC VXRZN

WHZLA YAGWC OHCO

Revised 1/16/01