Caesar Cipher (The Beginning)

We are hopeful that this column is the beginning of a long and fruitful relationship with the children (whatever the relationship) of our faithful Krewe who wish to pass this fun hobby along to another generation. We also wish for this column to be useful to all of those Young at Heart aspirants interested in developing or fine tuning their solving techniques. Continue reading Caesar Cipher (The Beginning)

Substitution Ciphers

Caesar’s cryptic messaging with a simple alphabet shift soon became obvious to the least experienced cipher analysts. A fresh approach was needed. Let’s begin to look at the world of  the simple substitution cipher where letters are randomly chosen to depict other letters of the alphabet. Randomly selecting a cipher letter (ciphertext) to represent another letter (plaintext letter) revokes the ease of simply looking for the number of shifts that a letter had been moved. Continue reading Substitution Ciphers

Cipher Keys (Keyboard Cipher)

Webster defines ‘kid’ as the informal reference to a child. I like to think of a child as an analogy to the search for knowledge and wisdom.

The child’s unquenchable thirst for answers to its never ending list of questions supports the beginning of life’s journey on the endless path of learning. “The kid in all of us” never loses the inquisitiveness for the world around us or the curiosity for what the future may hold. Continue reading Cipher Keys (Keyboard Cipher)

Keyword Alphabet

ACA Conventions are a good time to begin lifetime friendships with many people who have similar interests. They are also a wonderful opportunity to pick up a lot of information and education about cryptography. It is not coincidental that many of the Krewe solution scores have increased greatly with convention attendance.

Our ACA convention sites allow a great opportunity for ACA Krewe to plan their summer vacation setting. Conventions provide a great opportunity to get to know other members of the Young Tyros and adult members of the ACA and the cultivation of lifelong friendships.

In our last chapter, we related how most ciphers (disguised messages) are based on a key that allows both the sender and the receiver to communicate in ciphertext.

Here is a simple way to construct a substitution cipher alphabet with the use of a keyword. Pick a keyword that is easy to remember. Write the alphabet in a row of upper case letters. Write a keyword directly above it in lower case letters followed by the rest of the alphabet that does not appear in the keyword. We refer to this procedure as a Key 1 Alphabet.

zcipherabdfgjklmnogstuvwxy
ABCDEFGHIJKLMNOPQRSTUVWXYZ

You will notice that we begin our keyword over the upper case (ciphertext) letter ‘B’. If we had started our keyword above the upper case letter ‘A’, the lower case or plaintext letter ‘e’ would be substituted for by the upper case letter ‘E’ .

A letter may never be substituted for itself under ACA rules for simple substitution ciphers. When placing a plaintext keyword over the ciphertext alphabet, no identical letters may appear above or beneath each other. No letter may stand for itself (self-encryption).

A keyword may be started at any point over the ciphertext alphabet as long as it does not cause a letter to be substituted for itself.

It is equally important that duplicate letters in a keyword not be repeated, to avoid duplicate ciphertext letters standing for the same plaintext letter. Keeping these principles in mind, each keyword selected will produce different ciphertext.

The knowledge of this keyword between the sender and the receiver allows the disguised ciphertext to be converted to an easily read plaintext message. When this key is not provided the work of the cryptanalyst is ready to begin.

Indicate whether each keyword alphabet below is correct.

KW1. crazybdefghijklmnopgstuvwx
KW2. cipherabdfgjklmnogstuvwxyz
KW3. vwxyzcipherabdfgjklmnoqstu
KW4. uvwxcryptogrambdefhijklnqs
     ABCDEFGHIJKLMNOPQRSTUVWXYZ

Aristocrat Substitution Cipher

We are ready to begin having fun with classic cryptography. Let us begin to discuss the tools and techniques that allow the cryptanalyst (that’s you) to find the ciphertext message without possessing the actual key.

The classical substitution type cipher, which retains word breaks and is seen most often in your local daily newspaper, is called the Aristocrat cipher.

Continue reading Aristocrat Substitution Cipher

Construction Principles

Let’s get back to classic cryptography after all of that fun we had in our last chapter with the null. We are going to focus our attention on the cipher construction process in this issue. It is the process of converting plaintext message text into disguised ciphertext. You will find the construction process to be one of the best ways of appreciating and learning the deciphering technique.

Continue reading Construction Principles

The Keyword Alphabet as a Solving Tool

It is not coincidental that many of the ACA top constructors (those are the devious Krewe members who send in diabolical ciphers to the Cm) are also among the ACA top solvers.

Cipher construction is one of the best ways of learning deciphering skills. Learning construction principles breeds familiarity with the makeup of cipher types and means to their solution.

In Chapter Eight, we spoke of using a Keyword Alphabet as a tool for the construction of a cipher. This chapter we’ll show how that very same Keyword Alphabet tool can be so helpful in the solving process. Take a look at a random ciphertext to plaintext letter simple substitution cipher that uses every letter of the English alphabet (pangram):

BXJ CQLWZ NAGSV PGD OQUEF GHJA T ITRK YGM
The quick brown fox jumps over a lazy dog.
Plaintext –  rtqxpsovleyigbjfuzwamnchdk
CIPHERTEXT - ABCDEFGHIJKLMNOPQRSTUVWXYZ

In her work, Cryptogram, A Pleasant Diversion, Jude Patterson, (JUDE) describes the random assignment of substitution letters as “alphabet soup.” It serves little useful purpose between the author of a ciphered message (cryptographer) and the receiver. Keep in mind that the original purpose of the cryptogram or disguised message is to send a secret message. If a message is constructed with a random alphabet, it becomes much more difficult for the recipient to read the message.

Keyword Alphabet Uses.

The keyword alphabet has two distinct purposes:

  1. Ease of cipher construction – Keyword alphabets  are easily followed and repetition of the use of the same ciphertext letter for more than one  plaintext letter is more easily avoided.
  2. Ease of message interpretation – A disguised message is easily read when the reader has the keyword used to construct the message.

Let’s discuss two of the keyword alphabets used in simple substitution ciphers. Description of these can be found in The ACA and You Handbook, P26

K1 Keyword Alphabet Keyword “cipher

In the K1 keyword alphabet, the plaintext alphabet contains the key. The ciphertext alphabet is normal.

Plaintext –    abdfgcipherjklmnoqstuvwxyz
CIPHERTEXT –   DEFGHIJKLMNOPQRSTUVWXYZABC

Plaintext alphabet contains the key. (cipher)

  • Ciphertext alphabet is normal.
  • Each alphabet must contain 26 letters.
  • Duplicate letters in the keyword are excluded.
  • No ciphertext letter may represent more than one plaintext letter
  • No ciphertext letter may represent the same plaintext letter (no self-encryption).

We begin the ciphertext alphabet above with the letter “D” because starting the alphabet with either A, B or C will result in a self-encrypted letter. (Test it.)

K2 Keyword Alphabet Keyword, “HAPPYDAYS.”

Plaintext –  abcdefghijklmnopqrstuvwxyz
CIPHERTEXT – HAPYDSBCEFGIJKLMNOQRTUVWXZ
  • Ciphertext alphabet contains the key.
  • Plaintext alphabet is normal.
  • Each alphabet must contain 26 letters.
  • Duplicate letters in the keyword are excluded.
  • No ciphertext letter may represent more than one plaintext letter.
  • No ciphertext letter may represent the same plaintext letter (no self-encryption).

The keyword(s), HAPPYDAYS, appears as HAPYDS in the ciphertext alphabet with its duplicate letters suppressed. We may begin the keyword(s) at any letter under the plaintext as long as we are careful not to have a letter represent itself.

Key word alphabets are the tools used by the senders and receivers of secret messages for ease of reading a disguised message. An agreed upon keyword eliminates the need for any cryptanalysis.  In a future column, we will examine how keyword alphabets can also aid the solving process for the non-possessor of the keyword (cryptanalyst).

K2 Alphabet Construction

Let’s use the same keyword alphabet as Chapter Eight with the keyword, “CIPHER.”

Plaintext -  abcdefghijklmnopqrstuvwxyz
CIPHERTEXT - XYZCIPHERABDFGJKLMNOQSTUVW
KW-1. Aristocrat. It's easy. K2 (32)    (SNEPA)     LIONEL
RO  RN  IXNV  OJ  TMROI   XGC  NIGC   CRNHQRNIC FINNXHIN.

Apply the principles that you have learned to convert the Caesar crib (SNEPA) into plaintext and begin designing a K2 Keyword Alphabet.

Look at what happens when we post the CIPHERTEXT letters under the plaintext letters (write) in the K2 Alphabet:

abcdefghijklmnopqrstuvwxyz
    I   R        M O  T

Our Caesar shift has provided us with CIPHERTEXT letters TMROI equaling the plaintext letters “write.” The spacing of TMROI in the CIPHERTEXT alphabet tells us that N must equal s and that two of the CIPHERTEXT letters PQS must fall between CIPHERTEXT letters O and T. (R is on the left hand side of the alphabet slide and we know it to be in the keyword.)

We can also make very good educated guesses on the plaintext letters represented by CIPHERTEXT letters, UVWXYZ, because of their location in the alphabet to CIPHERTEXT letter T.

This is an example of how the Keyword Alphabet can be helpful in generating additional plaintext letters. It is an invaluable tool to the deciphering process. It is a good habit to post the Keyword Alphabet simultaneously to the solving of the cipher to gain maximum insight to more plaintext. Pen or pencil known letters in red.

Continue the process through to completion for the KW Ciphers below.

Keyword Alphabet Quiz

KW-1. Generate K-1 Aristocrat plaintext.

KW-2. Identify Keyword Alphabet used.

KW-3. The Caesar shift used was equal to?

KW-4. The keyword Alphabet will be automatically complete after solving the cipher.

True or false?

Keyword Alphabet Review

1) abcdefghijklmnopqrstuvwxyz
   CIPHER
    CIPHER
          CIPHER
               CIPHER

2) abcdefghijklmnopqrstuvwxyz
           PETUNIA

3) abcdefghijklmnopqrstuvwxyz
   JMNOPQRSTVWXZL CK ABDEFGHI

Keyword Alphabet Review Quiz

KW-5. What is the correct placement of the keyword CIPHER above?

KW-6. Complete the 2nd keyword alphabet.

KW-7. What is the keyword in the 3rd keyword alphabet?

KW-8. True or False – All of the below statements are true.

  1. Keywords are used in many different cipher types.
  2. Keywords provide ease of communication between the sender and receiver.
  3. Self-encryption allows a letter to be substituted for itself.
  4. ACA practices do not allow for self-encryption.
  5. The cryptanalyst’s work begins in the absence of a keyword.

Patristocrat Cipher

The 2000 year old battle between encipherers and decipherers of secret messages continued to be a battle of wits. As one cipher type became solvable, another was introduced to take its place. Such is the case of the Aristocrat Cipher that we have examined over the past few chapters. As the solving techniques we have been discussing weakened one cipher’s cryptic value, another cipher came upon the scene eliminating word divisions. It is termed the Patristocrat Cipher.

A Patristocrat cipher is nothing more than an Aristocrat cipher with the word divisions or spaces between words removed. You will find them in the Cm in groups of five letter ciphertext constructions. Most of the principles that we have been discussing for the Aristocrat cipher in past chapters also apply to the Patristocrat cipher. Keep these fundamentals handy for both sets of cipher types. A summary appears in Appendix II.

The neat thing about working with the Patristocrat cipher is the fact that a crib will usually be provided. The crib will always appear as a Caesar Cipher and be in parenthesis. A review of Chapter One will remind you how to convert a Caesar cipher to plaintext.

Our benevolent Cm Patristocrat editor always uses a Caesar shift of six with the Patristocrat constructions. Count forward in the alphabet six letters, and you will arrive at the plaintext equivalent of the ciphertext.

Let’s take a look at the additional information that is provided in a Cm MJ 2002, P-1. Patristocrat, “Hidden writing” is the title of the cipher. The K2 indicates the keyword alphabet type. (91/19) indicates that the cipher is 91 letters long and contains 19 different letters of the alphabet. The second line indicates the number of times that each ciphertext letter appears in the text. (See frequency count analysis in Chapter Six.) In the absence of this information accompanying the construction it would be worthwhile to develop such information ourselves.

MJ 2002 P-1. Hidden writing. K2 (91/19) (XYNYWNCHA)     ANGO-KA
12L 10I 8ES 6CJ 5NOQZ 4R 3KWY 2BGH 1PX

RILNE  ZCNYE  OQSJI   LJQZS  PGLRQ  EHLEK  EOILK


ICIQL  JCXOG   ILYEN   LLROL  JSEWW  BSZKL  ILJIS
                                 de  tecti

ZNJCO  BYSNQ  IHSCW  EISCZ R.
ng

We are now ready to make an entry into this Patristocrat cipher. Our knowledge about solving the Caesar Cipher allows us to convert the Caesar crib XYNYWNCHA to plaintext “detecting.” Our next step is the determination of the proper crib placement.

“Detecting” is a pattern word (Chapter Six) with a pattern of 1-2-3-2-4-3-5-6-7. This means the second and third letters will repeat. Now look for ciphertext letters in our P-1 cipher with the same pattern.

We find this pattern only at letter positions 64 through 72 in the cipher text. Inserting the crib here will allow the recovery of much more plaintext with the known letters. Plaintext letters “h”, “o” and “s” now become visible and the plaintext begins to unravel. Use of K2 alphabet recovery procedures assist in the final demise of the cipher.

Patristocrat Quiz

P-1 Define the purpose of the Patristocrat cipher’s second line.

P-2. What number of letter shifts was used in the crib of this P-1 cipher?

P-3. The word “adapted” has a pattern. True or false?

P-4. What is the first plaintext (pt) word of the P-1 cipher?

Let’s continue to explore how a Patristocrat crib may be used as an entry into the cipher’s solution. In our example above we were fortunate to have only one place in the cipher where the crib would fit and the entry was relatively simple. What do we do when there is more than one place in the cipher construction in which the crib can be placed?

We talked about how the K2 keyword alphabet can be used to aid the solving process. This same tool can be useful in finding the right crib placement in Patristocrat ciphers where multiple locations exist. Let’s look a Cm JF 2002, P-2 cipher below.

JF 2002 P-2. Just a coward. K2 (93/20) (YUMCYL)     G4EGG

SQOQO  KMOUU  JAPQZ  OEMLU  HXKZQ  LQRPU  EMSMO

EYMPL  KQOWU  YLFSX  UQBZU  YHXUO  EXUME  XUYVU

PPMHZ  BLFSX  RZWWU  YEXQO  ZQL.
Replacement                                                    
K2 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Frequency 1 2     6 2   3   1 3 6 7   8 5 9 2 4   12 1 3 7 5 6

The Caesar cipher YUMCYL yields plaintext word “easier” with its six letter shift. We find that this pattern word (1-2-3-4-1-5) can fit into one of four places under ciphertext letters with the same pattern: MDEYMP, UQBZUY, UYHXUO and UMEXUY. Now what in the world is a cryptanalyst to do with such a revolting development?

K2 Keyword Alphabet Analysis

Our handy K2 Keyword Alphabet tool comes to the rescue. Let’s set the K2 alphabet up with the plaintext letters across the top and list the possible ciphertext placement letters beneath the crib plaintext letters “easier.”

       abcdefghijklmnopgrstuvwxyz
MOEYMP O   M   Y        PE
UQBZUY Q   U   Z        YB
UYHXUO Y   U   X        OH
UMEXUY M   U   X        YE

What does our cryptanalytic eye detect? We look for an alphabetical sequence in our ciphertext keyword alphabet and find it only in the UQBZUY placement. The three spaces between ciphertext letters Q and U allow for a nice alphabetical ciphertext letter fit of R, S and T . The three spaces between ciphertext letters U and Z allow the placement of ciphertext letters V, W and X. What happened to the letter Y? We see it sitting over to the right-hand side next to the letter B. This is an indication that the letter Y is the last letter of our keyword and the letter B the beginning of the ciphertext alphabet.

We see no such alphabetical sequencing possibilities in our other three crib placement location alternatives so we may now confidently place the crib under ciphertext letters UQBZUY. And just look at what all your good seed has sown. You have now identified 44 of the 93 ciphertext letters in the construction. Take the time to pencil in the recovered plaintext. This will allow you to make educated decisions on more plaintext and further your K2 alphabet recovery process. Chalk up another solution to your solution storekeeping.

When the given crib is not a pattern word, crib dragging can be a stimulating manual exercise. The given crib needs to be placed in each ciphertext letter position to observe those plaintext letters that are generated as a result of each position placement. Patience is surely a virtue and becomes its own reward in doctor’s offices as well as shopping malls.

Patristocrat Quiz

 P-5. True or False. Cribs with more than one possible placement location cannot be solved.

P-6. True or False. The position of letter Y in crib location UYHXUO makes this location unlikely.

P-7. Ciphertext RZWWUY equals what plaintext word with this K2 alphabet recovery?

P-8. Ciphertext E equals what plaintext letter in this cipher?

Let’s take a look at another tool we have at our disposal in the Patristocrat solving process. Pay close attention to the ciphertext frequency counts on the second line of the construction. High frequencies are often indicators of popular plaintext vowels and consonants (senorita).

This is particularly true when the constructor’s main interest is to disguise words with high frequency letters rather than to avoid their usage entirely. When letter frequencies are not given with the construction, make the process of determining the ciphertext letter frequencies one of your first efforts in attempting to discern potential vowels in the cipher.

As we continue to develop the skill of placing the pattern crib in the cipher we quite naturally begin to question the placement of the non-pattern crib. Let’s take a look at this process in a Patristocrat cipher from the JF 2002 Cm.

JF 2002 P-7. 100% fiction. K2 (97/20) (UVION)   L. TWIN

WGXGZ  ZZZYQ  PKDNL  DMQPR  KWGVK  ZJRUO  RKGUF

ORLNY  OFXGF  OWNZY  LZVNY  PRFWP  DNPQX  ZULFD

GUUUU  GDGFP  QGHPR  OQPKO  MIPRY   LF
 
Replacement                                                    
K2 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Frequency       5   7 9 1 1 1 5 5 2 5 6 9 5 7     7 2 4 3 5 8

The Caesar crib UVION translates into plaintext “about.” Notice the fairly uniform distribution of the high frequency ciphertext letters above. This will make the placement of high frequency plaintext letters into the construction a very difficult task. A successful method of crib placement analysis is to match low frequency plaintext letters to like low frequency ciphertext letters. This cipher’s crib contains the letter “b” which occurs in the English language approximately 1 percent of the time. We will attempt to match it to H, I and J, ciphertext letters appearing 1 percent of the time in this cipher.

Hypothesis Test

Let’s see how ciphertext letter groups with H, I and J as the second letter (GHPRO, MIPRY and ZJRUO) withstand the test of:

  1. Letter pattern match
  2. No letter self-encrypted
  3. Letter frequency match
  4. K2 keyword alphabet sequence

Place the ciphertext letters, GHPRO, MIPRY and ZJRUO under the plaintext letters, “about” in the K2 alphabet:

   abcdefghijklmnopqrstuvwxyz

1) GH            P    OR            (GHPRO)

2) MI            P    YR            (MIPRY)

3) ZJ            R    OU            (ZJRUO)

Test Results

Ciphertext ZJRUO can be ruled out because ciphertext “U” cannot stand for plaintext “u.”  (Self-encryption).

Ciphertext groups GHPRO and MIPRY meet the non-pattern letter match of the crib word, “about,” have no letters self-encrypted and have letter frequency percentages closely related to those in the English language.

This leaves us with the K2 keyword alphabet flow as the final choice determinant between the remaining cipher groups. GHPRO on line one reflects a desirable alphabet sequence on the left and right hand side of the alphabet line. MIPRY on line two gives no indication of a desirable alphabet sequence. Though it may be possible for an alphabet sequence to appear between plaintext alphabet letters “c” and “n” the lack of this probability rules this place out.

The ciphertext group of GHPRO accounts for 34 percent of the cipher. It is time to pencil in the known plaintext.

Patristocrat Quiz

True or false:

P- 9.  Patristocrat frequency counts are useless.

P-10. Non pattern cribs cannot be placed.

P-11. There are four tests in the placement of non-pattern cribs.

P-12. “Senorita” is an acronym for high frequency letter occurrences.

We will close our discussion of the Patristocrat cipher with a few brief notes. Remember that the constructor’s main interest on the first page of the Patristocrat column is to disguise letters with high frequency usage. The absence of word divisions in this cipher enables the constructor to accomplish this. Be sure to use the frequency counts that are provided with the construction to uncover the high frequency plaintext letters (senorita). If the frequency counts are not provided, make them your first order of business.

Page two of the ACA Cm Patristocrat column is another story. Here, the diabolical constructor is disguising plaintext that most often never aligns itself with general properties of the English language. Searching for repetitive ciphertext letters that may represent high frequency digraphs or trigraphs (er, re, the, ing) will be helpful here. Also, be aware of the value of titles for possible plaintext words and Google searches that may relate potential wording value.

Always use the keyword alphabet as a simultaneous solving tool (Chapter Nine) to the plaintext recovery process, posting known letters in red. This will allow the decipherment of many ciphertext letters alphabetically sequenced around the keyword. Two Patristocrats to solve from scratch follow.. Beware of the letter “Q” in P-13 and alliteration in P-14.

 P-13.  Q Power.  K2.   (97/18)    (KOCM)     LIONEL                                                 

BGMCC  TAERN  TBGMZ  DFBGZ  DFBGM  ZABGM CCKBG ZPUTD EBGTE

FBGZF  TBGZH  TCZDW  BGZJR  FZPBG  RCGNB  GZFBG  ZCUKB  GTEFZ

RDDMZ CT. 
 
Replacement                                                    
K2 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Frequency 2 14 8 6 4 7 15 1   1 2   5 2   2   4   8 2   1     13
P-14.  Alliteration. K2  (98/19)  (UFQUSM)    LIONEL                  

QCCQC  CRFXB  QFRKO  WXDRZ  ODQBX  QCLQN  DQUCX  QVFDK  YQVFR 


KOQUC  XQBFQ  CDKQI  ROFKQ  VGFXQ  WQZXD  QOWQF  FXOFR  JXQEE 


CRVQF  RKO.
Replacement                                                    
K2 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Frequency   8 1       2   6 4 7 3 9 1 1 2   1 20 1 3 9 6 2 11 1