Vigenère Cipher Type

Does Chapter Eighteen constitute appropriate Young Tyro fodder? Our Tyro nomenclature and the column’s dedication, “to the young at heart” should not exclude a visionary concept, one of entertaining a goal of translating cipher solving rudimentary study into a skill which can yield lifelong satisfaction and contentment, a temporary escape from real life tasks and commitments which surround us. We will continue to attempt to reduce many advanced cipher types to their simplest terms to allow us to take on a myriad of ACA cipher types.

We will now analyze a polyalphabetic cipher type that will allow us to use the Kasiski Factoring System of Period Determination discussed in the previous chapter. The Vigenère cipher was named after Blaise De Vigenère, a French diplomat and cryptographer, who surprisingly thought cryptanalysis as “a worthless cracking of the brain.”

Nonetheless, the highly competitive battle of wits between cryptographers and cryptanalysts led to his design of the Vigenère Square, a 26 x 26 matrix for use in the construction of polyalphabetic (Periodic) ciphers. David Kahn refers to this square as “probably the most famous cipher system of all time.” Let’s examine its design and purpose as we study its features. Plaintext letters (lower case) are on the top row of the matrix with ciphertext letters (UPPER CASE) posted down the remaining twenty-six rows.

Vigenère Square
  abcdefghijklmnopqrstuvwxyz pt
A ABCDEFGHIJKLMNOPQRSTUVWXYZ
B BCDEFGHIJKLMNOPQRSTUVWXYZA
C CDEFGHIJKLMNOPQRSTUVWXYZAB
D DEFGHIJKLMNOPQRSTUVWXYZABC
E EFGHIJKLMNOPQRSTUVWXYSABCD
F FGHIJKLMNOPQRSTUVWXYZABCDE
G GHIJKLMNOPQRSTUVWXYZABCDEF
H HIJKLMNOPQRSTUVWXYZABCDEFG
I IJKLMNOPQRSTUVWXYZABCDEFGH
J JKLMNOPQRSTUVWXYZABCDEFGHI
K KLMNOPQRSTUVWXYZABCDEFGHIJ
L LMNOPQRSTUVWXYZABCDEFGHIJK
M MNOPQRSTUVWXYZABCDEFGHIJKL CT
N NOPQRSTUVWXYZABCDEFGHIJKLM
O OPQRSTUVWXYZABCDEFGHIJKLMN
P PQRSTUVWXYZABCDEFGHIJKLMNO
Q QRSTUVWXYZABCDEFGHIJKLMNOP
R RSTUVWXYZABCDEFGHIJKLMNOPQ
S STUVWXYZABCDEFGHIJKLMNOPQR
T TUVWXYZABCDEFGHIJKLMNOPQRS
U UVWXYZABCDEFGHIJKLMNOPQRST
V VWXYZABCDEFGHIJKLMNOPQRSTU
W WXYZABCDEFGHIJKLMNOPQRSTUV
X XYZABCDEFGHIJKLMNOPQRSTUVW
Y YZABCDEFGHIJKLMNOPQRSTUVWX
Z ZABCDEFGHIJKLMNOPQRSTUVWXY

A keyword whose number of letters is equal to the cipher period is used. It may consist of more than one word and unlike single substitution cipher keywords, duplicate letters are permitted to be repeated. We will use TYROGRAMS as our keyword(s) to encipher our plaintext message with the Key Square.

    TYR OG RAMSTYRO G RAMSTYRO

Pt: how to encipher a Vigenere

CT: AMN HU VNOAIFVF G MISWGCIS

To obtain the ciphertext, read down the first column on the left until you reach the key letter “T.” Read across the row until you reach the column of the first plaintext letter “h.” The ciphertext letter “A” is located at the intersection of this row and column. Repeat this procedure for each letter of the plaintext to determine the ciphertext. Become familiar with this process. Did you notice that the Vigenère allows a plaintext letter to stand for itself?

(Self-encryption)

Let’s review the Vigenère Cipher usage with a Cm cipher. Notice the construction five letter groupings which is standard format for the Vigenere cipher construction.

SO2004 Cm. Vigenère.       Good advice.                          ERNO

GLSTO EBYUZ YZZTU TUDJS OZWSF KSUUN FEHUT OTNCZ
Buyno twhat youca nuseb utwha tyouc annot dowit
HZZKQ NAEDF OJOYT KHKEO NJXKA CFKUT YAWZW KCLYF.
houtw hatyo udono tneed isdea ratan ypric ecato.

Cryptanalysis development begins with an understanding of a cipher’s origin or construction process. Let’s see how the Vigenère Square is used to develop the ciphertext for the plaintext that appears beneath it by referring to the construction process appearing below.

The constructor chose the keyword, FRUGAL, as a basis for a period six cipher. The Period six matrix that appears further down the text will allow you to refer to the Vigenère Square to follow the relationship of the ciphertext to the plaintext. The encipherment process is begun by writing the plaintext horizontally beneath the chosen keyword. All letters in the first column are then enciphered using F as a key, the second column using R as a key, the third using U and so on. The ciphertext generated by the key letters of each column is beneath the plaintext.

A look at the Vigenère Square key will reveal how each column key letter in a keyword is used to generate ciphertext for the plaintext. Run your finger across the ciphertext of row

F for the first column key letter F until you arrive at plaintext letter b (top row). You will find ciphertext G. It becomes the first letter of the ciphertext. Second column key letter R in row R will yield ciphertext L for plaintext “u.” Third column key U reveals ciphertext S for plaintext y. Continue searching for the remainder of the ciphertext letters to see if you can duplicate the ciphertext in the original Vigenère construction shown above.

Construction Process

F R U G A L F R U G A L F R U G A L F R U G A L F R U G A L
B u y n o t w h a t y o u c a n u s e b u t w h a t y o u c

F R U G A L F R U G A L F R U G A L F R U G A L F R U G A L
a n n o t d o w i t h o u t w h a t y o u d o n o t n e e d

F R U G A L F R U G A L F R U G A L F R U G A L F R U G A L
i s d e a r a t a n y p r i c e c a t o.

Cryptanalysis

Of course, armed with the constructor’s key, we are not yet practicing the art of cryptanalysis. Read on for some insight in how to attack this cipher type without the key.

The Vigenère Cipher, reduced to its simplest terms, is a series of simple substitution ciphers. Each period or column is a single substitution cipher in itself. Its complexity is two-fold in that its period must be determined (see Chapter Eighteen) and its single substitution columns are all short reads with no intelligible message within the column.

A shortcut to period determination but not always purely definable can be found with a check into The ACA & You Handbook to determine the required length of the Vigenère Cipher type. It is stated as having rows ten to fifteen lines deep. This standard would limit the cipher that follows (75 letters) to a Period of five through seven. We will save you the Period determination work on this cipher and define it as Period 5.

V-1. Vigenère.  Common word.     LIONEL

MOINS   KKXYI   BZSEI  HMXYI   FVWKY

LLHNS   KKWZR   MOIVR  ZSMJL   EHRXY

TNIRR   WIIXM   GZQRR   RZIEX  XUGVW.

The five letter ciphertext grouping is always used in a Vigenère cipher construction regardless of period length.

You will remember that a Vigenère Cipher is written in horizontally across its Period length, so we will insert the ciphertext horizontally over five column lengths.

Treat each matrix column as a single substitution cipher. You need to find the key letter for each column that will produce the most high frequency letters (senorita) in that column. The five column keys will spell a keyword.

All of our learned simple substitution strategies can be applied to each column’s solutions. Look for repeated ciphertext letters within each column to represent high frequency letters. We have highlighted highly repeated ciphertext letters as likely “senoritas.”

Might there be a letter “e” among them?

Vigenère Matrix
1 2 3 4 5
_ _ _ _ _ (Keyword)
M O I N S
K K X Y I
B Z S E I
H M X Y I
F V W K Y
L L H N S
K K W Z R
M O I V R
Z S M J L
E H R X Y
T N I R R
W I I X M
G Z Q R R
R Z I E X
X U G V W

Check the Vigenère Square to determine how the assignment of senorita letters to high frequency ciphertext letters impact each column letter decipherment. Those letters generating the most high frequency letters and the least low frequency letters in a column will best create word formations when grouped together with the adjacent columns.

Each column must be treated as a separate single substitution cipher and is independent of the other columns. Ciphertext letter I in column three may or may not be the same plaintext letter as ciphertext letter I in column five, depending upon the key letter of each column. Keep in mind the most frequently use trigraph (three letters) in the English language and the most frequent opening trigraph found in much text.

Become highly aware and adept with this Vigenère Square and cipher system that David Kahn exclaims as “the most famous cipher system of all time.”  Future study will reveal how cryptographers worked at modifying this cipher to stay one step ahead of the cryptanalysts.

It would be unfair to leave our talk on the Vigenère Cipher without a word or two on a means to limit the labor intensity of peering through the rows and columns of the 26 x 26 Vigenère Square. A slide device neatly fits the Square’s intent and is a useful aid.

Vigenère Slide

The slide is a simply crafted device that allows the alignment of the total 26 ciphertext and plaintext letters of the Vigenère Square with a very simple apparatus that looks like this:

(pt)
   abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz
   DEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABC
(CT)

It is very reminiscent in likeness to the Caesar Shift, and in fact, allows us to make mono-alphabetic Caesar Shift recovery. The chief distinction of the Vigenère Cipher is that it is polyalphabetic in nature and requires the need to use more than one alphabet per cipher. The Vigenère Slide allows us to easily meet this requirement while allowing a shift in either direction. Construct your slide so the plaintext top line is stationary and the cipher- text bottom line is movable.

Let’s use the slide in a review of the solving process of the Vigenère Cipher that appeared

in the SO200404 Cm by ERNO which appears earlier in this chapter. This cipher has been identified as a period six type and requires us to recover a six-letter keyword.

SO2004 Cm. Vigenère Cipher.  Good advice.        ERNO

GLSTO EBYUZ YZZTU TUDJS OZWSF KSUUN

FEHUT OTNCZ HZZKQ NAEDF OJOYT KHKED

NJXKA CFKUT YAWZW KCLYF.

We post it horizontally to six columns.

Key ? ? ? ? ? ? (Keyword)

   G L S T O E
   B Y U Z Y Z
   Z T U T U D
   J S O Z W S
   F K S U U N
   F E H U T O
   T N C Z H Z
   Z K Q N A E
   D F O J O Y
   T K H K E D
   N J X K A C
   F K U T Y A
   W Z W K C L
   Y F

Use your slide to perform a column by column search for the high frequency letters “senorita” and to recover the keyword. Each column has its unique key letter that identifies its plaintext. The Vigenère slide will allow you to analyze each column of text with a different key letters. Each key letter will generate a different set of plaintext letters. Find the key letter for each column by determining which key letter generates the highest frequency plaintext letters and the least fewest frequency plaintext letters.

Align a ciphertext letter on the bottom of the slide under plaintext “a.” The letter appearing directly above the ciphertext letter is its corresponding plaintext letter. The ciphertext letter aligned below the plaintext letter “a” becomes the key letter for the column.

V-2. Vigenere. High Frequency.                         LIONEL

OIPOE ZXMWQ OSIBA EESFH LAXDD

IGHVZ LIFXU SVVZL AWUZR VZUSK

RKZBA TZIJC ILLEF SEWKI MHSXH

GVATL DSSHY MVOEQ BBFVX S.

The Universal PhoeBee Cipher Slide

The PhoeBee circular cipher slide was developed in 1998 by HONEYBEE and PHOENIX. It can be used as a cipher solving slide for all of the Vigenère type ciphers along with the Porta and Portax cipher types. This slide can be ordered from Honeybee. See the For Sale section on page fourteen of the Cm.

Beaufort, Gronsfeld, Variant Ciphers

As cryptanalysts became able to solve the Vigenère Cipher, spinoff ciphers appeared to challenge their skill. The Beaufort, Gronsfeld and Variant Cipher are variations of the polyalphabetic Vigenère Cipher that we should identify and become familiar with their solving process.

The history of the battle of wits between the cryptographer and the cryptanalyst is an interesting study in the creativity of mankind. Each time a cipher type’s security is breeched, another type arises to take its place. This is true of the Vigenère cipher.

When the Vigenère Square was first developed as the basis of the polyalphabetic cipher, it appeared to be the cipher to end the need of future cipher types. But, alas, it became recognizable and decipherable after repeated use. The need to add to its complexity became a necessity.

Enter, the Beaufort, Gronsfeld and Variant Ciphers that generated slight variations upon the Vigenère in order to make decipherment more complex. The four cipher slides are shown below. We have noted their differences. Remember that these slides are used only to convert ciphertext letters to plaintext letters. Each column’s key letter dictates the positioning of the slide. Let’s compare the Vigenère slide to its three spin-off replicas.

Vigenère Slide – pt = plaintext, CT = CIPHERTEXT

(pt)   abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz
(CT)   DEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVWXYZABC

The ciphertext letter on the bottom of the slide aligned under plaintext “a” represents the column key letter. The letter that appears directly above each ciphertext letter is the plaintext.

Variant Slide

The only difference from the Vigenère is that the column key letter appears in the plaintext alphabet below the A of the ciphertext alphabet that we place at the top of the slide. Remember that each column key letter appears directly over the plaintext slide letter “a.” Use the plaintext start beneath the slide to find the keyword and complete the cipher.

(CT) XYZABCDEFGHIJKLMNOPQRSTUVWXYZABCDEFGHIJKLMNOPQRSTUVW
(Pt) abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz

MJ2008 E-2. Variant. Man vs. machine. (QILECHA)        DANEEL

YMQFV XRHTX PQGLM UARYD UVQQB ATHST TGKBF GMAGL CTXVR EBATH
Parto fthei nhuma nityo fthe
CTTCV UKODV YPABB GMMMP DGPKX CIBYN AAZJY XIKBO NYWDC TTAAQ
AMQZL GSPPE JEHYV N.

Beaufort Slide

The Beaufort cipher simply reverses the ciphertext alphabet beneath the plaintext alphabet to create a reciprocal encipherment. W = a or a = W, so it does not really matter which alphabet is labeled plaintext or ciphertext. We will label the top of the slide as plaintext. Find the keyword of the cipher below with its plaintext beginning and complete the cipher.

(Pt) abcdefghijklmnopqrstuvwxyzabcdefghijklmnopqrstuvwxyz
(CT) ZYXWVUTSRQPONMLKJIHGFEDCBAZYXWVUTSRQPONMLKJIHGFEDCBA

JF 2008 E-2. Beaufort. Shooting off your mouth.  (MJYYWB)  DANEEL

NFNIE YLBHT UUUBB UECXW SSRTU UYKUJ FIEQZ YQQEW BAQQN GHWEL
Speak wheny arean gryan
YJXDQ XBDAE IDOMT TICTB RCNHG QBDQ.

Gronsfeld Slide

The Gronsfeld Cipher uses key numbers from 0 to 9 instead of letters. The key number sequence does not generally come from a keyword. Numbers may be repeated since any number of columns requiring a key number may be used. Each ciphertext letter is displaced to the left of the plaintext by the number of letters equal to the key number.

Four displacements are shown.

(Pt)  abcdefghijklmnopqrstuvwxyz
(CT1) BCDEFGHIJKLMNOPQRSTUVWXYZABCD..
(CT2) CDEFGHIJKLMNOPQRSTUVWXYZABCDE..
(CT3) DEFGHIJKLMNOPQRSTUVWXYZABCDEF..
(CT4) EFGHIJKLMNOPQRSTUVWXYZABCDEFG..

These four slide placements each reflect a period displacement. CT1 = a displacement of one. CT2 = a displacement of two. CT3 = a displacement of three. CT 4 = a displacement of four. Displacements up to nine can be used. Each column will contain its own number of displacements.  Key # displacements are tried for each column to determine the key # that will create the most high frequency letters. Determine the key numbers used in the cipher below to complete the plaintext.

MA 2008 E-3. Gronsfeld. Thinker rethought common wisdom.     RIG R MORTIS

XUHUW LRLWV URWPL RLUWZ CITLN IQWBN UBVKN UNKJK ICQXU TQVOI
Plato didno jogdi etort ake
LAIMA JQMHU BMWBR VOBWQ MJSUP QBBQL HZMJB NZUPQ WLAHO KMCWU
PGM.