The Vigenère Cipher: User Guide

Since the software is being updated frequently, the images on this guide page may not be up-to-date. However, most changes and differences will be minor.

This program, VIGvisual, is designed to support the activities discussed on previous pages. It has three tabs: Demo, Practice and Attack. The Demo tab provides an animated demonstration of the Vigenère cipher. The Practice tab offers a chance for the user to practice encryption and decryption operations. The Attack tab has Kasiski's method and the Index of Coincidence (IOC) method for estimating a possible length of the unknown keyword, and the χ² method to recover the keyword given the length estimation. To break the Vigenère cipher completely, a number of iterations and other skills would be needed.

The Demo Tab

VIGvisual always starts with the Demo tab. The top portion of this window has the fields for plaintext, keyword and ciphertext. The bottom portion has four sets of buttons. The Input set has three buttons: New clears the input areas so that the user can enter a new plaintext (or ciphertext) and a new keyword, RandPT generates a randomly selected plaintext and a keyword, and RandCT generated a randomly selected ciphertext and a keyword. The Operations set also has three buttons: Encrypt and Decrypt are for encryption and decryption, respectively, and Align is to align the plaintext/ciphertext with the keyword. The Tools set has three buttons: Table displays the Vigenère table, Disk and Slide show the cipher disk and Saint Cye slide, respectively. The right-most Animation set is designed to perform animation and step-wise execution of encryption and decryption.

Input

A demo session usually starts with a plaintext/ciphertext and a keyword. The user may click New to start a new session and enter a plaintext and a keyword for encryption or a ciphertext and a keyword for decryption. Or, the user may click RandPT to generate a randomly selected plaintext and keyword pair, or click RandCT to generate a randomly selected ciphertext and keyword pair.

In an encryption session with user input, the user enters the plaintext and keyword and the system fills in the ciphertext when clicking Encrypt. In a decryption session with user input, the user enters the ciphertext and keyword and the system fills in the plaintext when clicking Decrypt.

Operations: Encryption and Decryption

Once a pair of plaintext (or ciphertext) and keyword appears, the user clicks Encrypt to encrypt the plaintext or click Decrypt to decrypt the ciphertext. Note that after clicking Encrypt or Decrypt, the plaintext, keyword and ciphertext change to all upper case.

By default, the keyword is repeated and aligned with the original word structure as shown above. Clicking Align switches to the view of breaking the plaintext/ciphertext to align with the keyword as shown below.

Animation

Click Start to perform the encryption or decryption animation, click Stop to stop the current animation, and use the slide to adjust the animation speed. Once the animation starts, the Start button changes to Pause. Click on Pause to pause the current animation and the button changes to Resume. Click Resume to resume the animation and it changes back to Pause. Clicking Stop changes Pause or Resume back to Start. As the animation is in progress, the plaintext letter, keyword letter and ciphertext letter are shown in different colors, and this color scheme is also used by the tools. The following image shows that the plaintext letter V is encrypted by the keyword letter S to the ciphertext letter N. Conversely, the ciphertext letter N is decrypted by the keyword letter S to the plaintext letter V.

During an animation, the user may place the cursor between any two letters in the plaintext, keyword or ciphertext, and the animation will continues with the next letter. Moreover, the user may click Pause to suspend the animation and the Pre and Next buttons become available. The user may click between two letters in the plaintext, keyword or ciphertext, followed by Pre (resp., Next) to move to the previous (resp., next) position. In this way, the user is able to move to anywhere in the text and step through the encryption or decryption process. Click Resume to resume the animation and Stop to end it.

Tools: Table, Disk and Slide

The user may bring up one or more tools (e.g., table, disk or slide) to see how the tools are being used. For example, the following three images show how the plaintext letter V is encrypted by the keyword letter S to the ciphertext letter N using the table, disk and slide. The table, disk and slide use the same colors as shown in the plaintext, keyword and ciphertext areas. The table rows and columns, the top disk and the bottom slide all change according to the current triplet of plaintext letter, keyword letter and ciphertext letter. In this way, the user would have a clear picture of how the tools are being used.

The Practice Tab

The Practice tab puts the system to the practice mode, allowing the user to practice encryption and decryption without animation and the color scheme. The window is divided into plaintext, keyword, ciphertext, answer and buttons areas. The user selects Encrypt or Decrypt (lower right of the image below) to enter the encryption mode or decryption mode. The Random button generates a randomly selected plaintext or ciphertext; the New button clears all text areas so that the user can enter her/his own plaintext, keyword and ciphertext; the Redo button allows the user to redo the current encryption or decryption; and the Align button aligns the plaintext or ciphertext using the keyword length.

To perform a practice, the user may bring up the Vigenère table, disk or slide. For example, consider the second letter L in the plaintext ALWAYS.... It is encrypted by the second letter H. The corresponding letter in the ciphertext is found at the intersection of row H (keyword letter) and column L (plaintext letter). The result is S.

To use the cipher disk, rotate the top disk by dragging until the keyword letter H aligns with the letter A of the bottom disk. Then, the corresponding plaintext and ciphertext letters are on the bottom and top disks, respectively. Hence, the plaintext letter L is encrypted to the ciphertext letter S. Conversely, the ciphertext letter S is decrypted by the keyword letter H to the plaintext letter L.

To use the slide, slide the lower part left and right by dragging until the keyword letter H aligns with the letter A of the top fixed part. Then, the corresponding plaintext and ciphertext letters are on the top and bottom part, respectively. Hence, the plaintext letter L is encrypted to the ciphertext letter S. Conversely, the ciphertext letter S is decrypted by the keyword letter H to the plaintext letter L.

You may stop the encryption/decryption process at any time and click the Check button. Then, the correct answer is shown in the Answer area, and each incorrect letter in the plaintext or ciphertext area is shown in red or a question mark if there is no input for that letter. Note that once clicking Check you are not able to make changes to the keyword and plaintext/ciphertext. Click Redo to modify the keyword or plaintext/ciphertext, or click Random or New to start a new session.

The Attack Tab

The Attack tab provides you with tools to break the Vigenère cipher.

Use the New button to clear the ciphertext area and enter your ciphertext. Or, use the Random button to generate a randomly selected ciphertext:

This tab has Kasiski's Method and the Index of Coincidence method for estimating the length of the unknown keyword. Use the Kasiski (resp., IOC) button to bring up the Kasiski's method (resp., Index of Coincidence) window. The estimated keyword length is shown next to that method's button.

The Hint Buttons

There are a number of Hint buttons at the lower left or the lower right corner to help you get hints and do simple exercises. The Hint button on the Attack tab has four buttons:

The Algorithm button brings up a window showing the procedure for breaking the Vigenère cipher.

The IOC button brings up the IOC hint window as shown in the first image below. Click the New button to generate an input on a 5-letter alphabet (i.e., A, B, C, D and E) and the count of each letter. The system expects the user to fill in the Index of Coincidence of this string in the IoC field. The user may click the Check button to the answer next to the input field.

The Coset button brings up the coset hint window as shown below. Click the New to generate a short string and the number of cosets. The system expects the user to enter the coset and the index of coincidence of that coset in the Coset and IC fields, and the average of all index of coincidence values in the Average field. The user may click the Check button to see the answer of each field.

The Chi-Squared button brings up the χ² hint window. Click the New button to generate a short string and the letter counts, observed (Obs) frequencies and expected frequencies (Exp). The system expects the use to compute and enter the χ² in the Chi Squared field. The user may click Check to see the answer,

Kasiski's Method

Clicking the Kasiski button brings up the Kasiski window. The system will search for repeated strings. Since this search may take some time to finish for a longer ciphertext that has many repeated sunstrings, the system shows the following reminder:

The following is the Kasiski window:

The lower right corner has a Hint button. Clicking it brings up the procedure of Kasiski's method as shown below.

The right panel of this window shows all repeated strings found in the ciphertext and the left panel shows the distances and their factors, and the count of each factor (See the Kasiski's Method page).

Clicking a repeated string highlights it in the ciphertext area of the Attack tab. The right figure below shows the repeated string TTI is selected and the left figure shows the highlighted ciphertext. Since this string appears in three places (i.e., positions 119, 203 and 322), you may have to scroll up and down to see the result. If you click the positions (e.g., 119-203(84)), only the repeated string in positions 119 and 203 are shown.

Scroll up and down (and left and right) of the left panel and find the factor corresponding to the largest count (i.e., the most common one). This factor is usually a good estimate of the length of the unknown keyword. The following figure shows that the largest count is 16 which corresponds to the factor 7. Click on the factor to export it to the Attack tab. This means you have found a possible length. If you wish to use a different keyword length, clicking on the Kasiski button will bring you back to this table for you to select a different length.

Once a length is selected, its value appears next to the Kasiski button of the Attack tab:

Two Important Notes

Only factors no larger than 20 are reported, which means this system will not be able to find the length of a keyword larger than 20. This should not be a problem for practicing the process.

This system only reports significant repeated strings to reduce confusion. For example, if ABCDE is a repeated string, the system only reports ABCDE and ignores ABCD, BCDE, ABC, BCD, CDE, AB, BC, CD, DE, etc. This is because the distance between the two ABCDE's is identical to the distance between the two ABCD's, the distance between the two BCDE's, etc.

The Index of Coincidence Method

Clicking the IOC button brings up the Index of Coincidence window. The first column of this window shows possible lengths from 1 to 20 of the unknown keyword, the second column has the cosets, the third column displays the index of coincidence of each coset, and the fourth column is the average. Note again that the keyword length is limited to no higher than 20.

The lower right corner has a Hint button. Clicking it brings up the procedure of applying index of coincidence to each coset to find a possible keyword length.

The second column of this table only shows a portion of each coset. Clicking on a coset will show the complete coset in the bottom area.

This system shows the largest three index of coincidence values in blue on the fourth column. In general, the length corresponding to the largest average value works fine. Scroll this table to the bottom to find the largest average index of coincidence, and click the length value to select and export it. The following figure shows that the length of 7 is selected.

Once a length is selected, its value appears next to the IOC button of the Attack tab:

Recover the Unknown Keyword with the χ² Method

The Select Len button is used to select an estimate of the unknown keyword length. Since the selections from Kasiski's method and the Index of Coincidence method may be different, the Select Len button allows you to choose a length no higher than 20. If you feel the length from either the Kasiski's method or the index of coincidence method is a correct one, clicking on the circular button sets that length to the Select Len field. The following figure shows that the IOC estimation 7 is selected, and this value appears in the Select Len field.

After an estimation is chosen, clicking the Select Len button brings up the Keyword Recovery window as shown below. This window has two portions. Each column of the top portion has the χ² values of each coset, and each row corresponds to the shift of a letter. For example, the χ² value of shifting the first coset to G is 5.11, the χ² value of shifting the second coset to G is 20.8, etc. The smallest χ² of each coset (i.e., column) is shown in blue, and the letter corresponding to the smallest χ² of each coset is shown in the Key row. The following table shows the possible keyword being AMERICA

Scrolling the top portion to the bottom, you will see the current keyword and a portion of the decrypted text:

The recovered keyword also appears in the Key field of the Attack tab as shown below.

The lower right corner of the Keyword Recovery window has a Hint button. Clicking it brings up the procedure of applying the χ² method to recover the unknown keyword.

The recovered keyword may not be correct, and, in this case, you have to modify it in order to correctly decrypt the ciphertext. VIGvisual shows at most three frequency graphs at any time for this purpose. Initially, the bottom part of the Keyword Recovery window shows the English frequency graph:

The horizontal axis of this graph has the 26 letters and the vertical axis shows the percentage values from 0% to 20%. Since each letter in the recovered keyword corresponds to a coset, click the coset number to select that coset to modify. For example, coset 4, which corresponds to R, is selected and is highlighted as shown below. At the same time, the frequency graph of the R shift is shown. Note that the frequency graph of the R shift matches the trend of the English frequency very well.

Suppose that you do not think the R shift is the right choice. Click the letter below the horizontal axis you wish to use and the frequency graph of that letter appears. Moreover, the corresponding letters in the keyword in this window and the keyword in the Attack tab also change. In the following image, the letter T is selected. It appears in the Key field and the frequency graph of the T shift is shown. This T shift frequency graph does not match the English frequency very well. As a result, the T shift is unlikely to be a correct choice. In general, if the frequency graph of a shift matches the English frequency well, the corresponding χ² is small. Of course, the frequency graph that can generate the smallest χ² matches the English frequency better than other shifts. However, in many cases the shift that corresponds to the smallest χ² is not the best choice, and you have to edit the recovered keyword to find another letter. Usually, trying a few of the smallest χ² values and checking their frequency graphs can provide additional information for selecting a correct keyword.

The frequency graph of English and the frequency graph of the smallest χ² are always shown. Clicking any letter causes a new (i.e., the third) graph to appear and this graph will be replaced by future graphs.

Except for the English frequency graph the computed frequency graph of a coset shifts to the left or right as you click on letters. For example, the following shows the frequency graphs of U, V, W, X and Y. The peak at letter E of the correct shift R shifts to the position of C (i.e., two positions to the left of E) when the letter T (i.e., two positions to the right of R) is selected. As we move to the right from U to Y, the peak moves to the left from B to X in a cyclic way.

The Default button restores the keyword back to the one corresponding to the smallest χ² values.

Example 1

Let us take a look at an example to illustrate the editing using frequency graphs. Example 3 on the Complete Examples page has the following ciphertext:

LPROZ OOGRJ ZGFLV TUKMC WFDQM PZXIJ LVRWQ XEOSZ ZHTEK UYSCR
PTFCZ UHXIJ LPPTD CPRBY OSMGY TLEVD UAQMF IFMZV LVYTO QDLHX
LBPLL KYCQY ODRKS ACTEU XZEVO UAQMF OSDSU BKMBJ QEORF WFQCK
HKSOD INGJZ SHGVV LMSZD WWHFJ AVQGF NUWMW AOIXT CSRYC YPPTP
LFUCR AVQHR RVRES QCKHM LGARF YHXZP CSNWS NCRQV GHRLR ZEDHF
JVUPC XZJQC ATISQ SCGXN BALWY MAQCY OSD

The recovered keyword with the χ² method is THEILIADQFHOMER, which looks like "THE ILIAD QF HOMER"" and the letter Q is not right. The following image shows the frequency graph of the Q shift.

If you look at the χ² values, you should see that the shift of Q has the smallest χ² of coset 9 (2.82) and the next smallest χ² value is the O shift (3.32). Click O in the frequency graph and its frequency graph appears. Now, it is clear that the frequency graph of O matches the trend of the English frequency better than the shift of Q does. As a result, the keyword should be "THE ILIAD OF HOMER". ♦

Decryption

After recovering a possible keyword, click the Decrypt button to decrypt the ciphertext. You don't need to enter the possible keyword in the Key field, because it is updated on-the-fly as you make changes in the Keyword Recovery window. If you are not satisfied with the recovered keyword, you could edit it to whatever you want. Then, click Decrypt to see the result in the plaintext area:

The following is the actual plaintext with spaces and punctuation added:

O say can you see by the dawn's early light,
What so proudly we hailed at the twilight's last gleaming,
Whose broad stripes and bright stars through the perilous fight,
O'er the ramparts we watched, were so gallantly streaming?
And the rockets' red glare, the bombs bursting in air,
Gave proof through the night that our flag was still there;
O say does that star-spangled banner yet wave,
O'er the land of the free and the home of the brave?