) and 'B' was represented by any arrow pointing up (e.g. ); so that the students had to figure out whether the direction of the arrow or the line was what indicated the difference.
There are three factors which affect the difficulty. First is the choice of symbols to represent the Baconian. The harder to distinguish, the more points the question should be worth. Second is how much of a clue is provided. Lastly is the size of the grouping. By picking a Line Width which is not a multiple of 5, it ensures that the students have to carefully manage wrapping a group of 5 across a line boundary.
Points:200-400. A Letter for letter with a single substitution and Line Width which is multiple of 5 should be worth 200 points. A Words Baconian with a complex pattern and a couple letters of clues would be worth 400.
Question Text:The question should indicate that the Baconian Cipher is being used and the origin of the phrase if known and any clue. For example:
The following symbols encodes a phrase by <person> using a Baconian alphabet. What does it say?
The following strange headlines encodes a phrase by <person> using a Baconian alphabet. You have been told that it starts out with “SOME” What does it say?
The following odd symbols were found when a tomb was opened, but you recognized it as a prankster who scratched it on the wall using the Baconian alphabet. What does it say?
This will be one of the hardest questions on the test, but it is good to have in order to provide a challenge.
Pick a Spanish phrase which primarily consists of words which a second-year Spanish class would cover. Phrases which have both la and las present are good choices as well as phrases which contain y or cognates (Spanish words which are substantially like their English equivalent words such as ciencia, composición and básico) are also good. For a good source see https://www.realfastspanish.com/vocabulary/spanish-cognates). Although it isn't strictly necessary, try to avoid phrases which depend on accented characters. As with the approach for the English Aristocrats, pay attention to the frequency of letters. The tool automatically calculates the Chi-Square Value to verify the match:
E | A | O | SNR | IL | DTUC | MP | BHQ | YVGÓÍ | FJZÁÉÑXÚKWÜ |
13% | 12% | 8% | 7% | 6% | 5% | 3% | 2% | 1% | - |
If the encoded string uses both N and Ñ, it is best to re-encode until you don't get them both to avoid confusion on the part of the teams. Although it is possible to get an encoding that doesn't use Ñ at all, it is perfectly fine to generate a question which has one. Having both both N and Ñ, increases the difficulty of the problem.
Setting Difficulty:The presence of cognates greatly reduces the difficulty. It is also expected that a K1 alphabet with an English key should be used. A K2 alphabet can be used, but it doesn't reduce the difficulty as much.
Points:600-700.
Question Text:The question should clearly indicate that it is a Spanish Xenocrypt and provide the source of the phrase (if known). It should also indicate the use of a K1 (or K2) alphabet with an English keyword. For example:
Solve this Xenocrypt which is a translation of a quote by <person> into Spanish and has been encoded with a K1 alphabet using an English keyword.
.
Points:150-600
Question Text:The question should indicate that they are to compute the decryption matrix using the Hill Cipher and provide the key. For example:
After solving the cryptarithm SEND+MORE=MONEY decode the phrase 9015 10992.
Generating CryptarithmsThere are several sites that allow for generation of cryptarithms including:
If the crib only contains letters that are multiple in the cipher text, it is harder. It is harder if the crib text appears in more than one row
Points:150-600
Question Text:The question should indicate that they are to use the crib text (given in the question text) to help determine the number of columns and the order of the columns to decode the cipher text. For example:
After solving the cryptarithm SEND+MORE=MONEY decode the phrase 9015 10992.
Choosing a CribA crib should contain unique letters from the cipher text.
For Regional and Invitational competitions, only the Compute Decryption option is used for the Hill Cipher. For this there needs to be a 4 character phrase which corresponds to an invertible matrix. (https://en.wikipedia.org/wiki/Invertible_matrix). Fortunately, the tool will tell you if it is not invertible. There is also a list of known valid word keys at https://toebes.com/codebusters/HillKeys.html (which is linked to at the top of the tool) for both the 2x2. Note that there are other keys that can be used which are not words, it is more likely to be invertible if you use the odd letters B, D, F, H, L, N, R, T, X and Z. as they are odd and non-prime, but you can mix in some other letters. Just make sure that the keyword is not an inappropriate phrase. A total non-sense phrase is perfectly acceptable, but it helps the style of the test if it looks like a word.
for both 2x2 and 3x3 matrices, we can improve the likelihood that the determinant is invertible if half to three-quarters of the letters are odd;
Setting Difficulty:There is little variability in the difficulty although letters at the end of the alphabet generate larger numbers.
Points:100.
Question Text:The question should indicate that they are to compute the decryption matrix using the Hill Cipher and provide the key. For example:
Using a key of TEST compute the decryption matrix for a 2x2 Hill with a 26 character alphabet.
Details on picking a keyFor a 2x2 matrix we can be explicit. Since it is very likely that we will want either the 2nd or 3rd letter to be a vowel, The more useful advice would be that one or both of the 2nd and 3rd letters should be vowels, while both the first and last letters come from the set of odd letters listed above. This would guarantee that the determinant is odd, and then we only need to check to make sure it isn't 0 (mod 13), which means we would succeed with probability 12/13.
For a 3x3 matrix it isn't as easy, but if we ask for about half the letters to be odd (same set as before), then there is a good chance that the determinant will be odd. In fact, assuming random placement of the odd letters, the exact odds for each possible number of odd letters is as follows:
0 | 0.000 |
1 | 0.000 |
2 | 0.000 |
3 | 0.071 |
4 | 0.286 |
5 | 0.571 |
6 | 0.426 |
7 | 0.500 |
8 | 0.000 |
9 | 0.000 |
Basically, we want 5, 6, or 7 odd letters in the mix in order to have a decent shot at being invertible mod 2. If we are lucky, we may get by with 4 odd letters; with only 3 odd letters we need to be extremely lucky; and for any other number of odd letters, it is simply impossible.
The Morbit Cipher encodes text by first converting the plain text into morse code with the space between characters represented by an × and the space between words represented by two × characters. The resulting morse code is then broken into pairs of characters (adding an × at the end if necessary). The numbers 1-9 are randomly assigned to the unique pairs of characters (●●, ●–, ●×, –●, ––, –×, ×●, ×–, ××,). The pairs of morse characters are then replaced with the corresponding number to generate the final cipher string. Decoding is done by reversing the process.
Setting Difficulty:The dificulty is driven by the number of letters and the variety of morse code combined with which letters are chosen. Looking at the generated solving guide can help guide the question writing. Not telling them which digit corresponds to ×× increases the difficulty.
Points:100-150.
Question Text:The question should be around 40 characters.
Solve this quote from <person> which has been encoded using the Morbit Cipher. You are told that 2=●●, 4=●–, 6=●×, 9=–●, 1=––, and 7=–×
The Pollux Cipher encodes text by first converting the plain text into morse code with the space between characters represented by an × and the space between words represented by two × characters. The resulting morse code is then randomly assigned to digits (0-9) chosen to represent the morse characters: (●, –, ×) The pairs of morse characters are then replaced with the corresponding number to generate the final cipher string. Decoding is done by reversing the process. Note that because one or more digits may represent a morse character piece, the mapping can be somewhat random.
Setting Difficulty:The dificulty is driven by the number of letters and the variety of morse code combined with which letters are chosen. Looking at the generated solving guide can help guide the question writing. Not telling them all the Hint Digits which correspond to × increases the difficulty. Assigning more characters for one morse digit, thereby reducing another, also increases the difficulty.
Points:100-150.
Question Text:The question should be around 40 characters.
Solve this quote from <person> which has been encoded using the Pollux Cipher. You are told that 2,3=●, 4,7=–, 9,1=×
The Fractionated Morse Cipher encodes text by first converting the plain text into morse code with the space between characters represented by an × and the space between words represented by two × characters. The resulting morse code is then randomly assigned to letters chosen to represent the morse characters: (●, –, ×) The sets of morse characters are then replaced with the corresponding letter to generate the final cipher string. Decoding is done by reversing the process..
Setting Difficulty:The dificulty is driven by the number of letters and the variety of morse code combined with which letters are chosen. Looking at the generated solving guide can help guide the question writing. Not telling them all the Hint Digits which correspond to × increases the difficulty. Assigning more characters for one morse digit, thereby reducing another, also increases the difficulty.
Points:100-150.
Question Text:The question should be around 40 characters.
Solve this quote from <person> which has been encoded using the Fractionated Morse Cipher and a keyword. You are told that E=●–●; R=×●●; S=×●–; T=●●×.
The Cryptarithm ...
Setting Difficulty:The dificulty is driven by .....
Points:100-150.
Question Text:The problem should be in base 10.
Solve this Cryptarithm..
Pick a phrase which is approximately 80 characters long. The actual content has little impact on the difficulty. By default there are four encoding texts (Gettysburg address, Declaration of Independence, Constitution of United States of America and MAGNA CARTA (In Latin)) but they can be changed by going to https://toebes.com/codebusters/EditRunningKeys.html
Setting Difficulty:There is little variability in the difficulty other than the length. Encode is slightly harder than Decode.
Points:200-250. Approximately 3 points per letter.
Question Text:The question should indicate that the Running Key Cipher is being used and whether they are to Encode or Decode. If they are to Encode, it should indicate which encoding text to use. For example:
The following quote from <person> has been encoded using a running key cipher against a famous document. What does it say?
Encode what <person> said about <topic> using a running key cipher against the MAGNA CARTA.
There can be one of these on a State/National test. There are no restrictions on the phrase, although try to avoid a phrase with a lot of a's in it. I.e.An amazing aardvark allows all answers would be a poor choice because the letter A is trivial to decode. As this question is nominally worth four points per letter, a 50 letter phrase is ideal.
Additionally there needs to be a Key to encode it with. It should be 5 or 6 characters with no repeating letters and avoid the letter a as it causes a letter to map to itself. By setting the Block Size to the same as the length of the Key, the problem is much easier than with the default Block Size of 0 that keeps the original spacing. Setting the Block Size to a size other than the length of the Key increases the difficulty somewhat.
For the decoding clue, pick a word in the phrase which is at least 5 characters long, carefully count to determine the position in the encoded phrase as well as the encoded character.
Setting Difficulty:The length of the phrase is the major
Points:200-250. If the Block Size is 0, add 25 points. If the Block Size is non-zero and different from the Key length, add 50 points.
Question Text:The question should indicate that the Vigenère Cipher is being used (don't forget the accented è), the length of the Key and the plain text corresponding to some part of the phrase. It is generally nice to give the origin of the phrase if it is known. For example:
<person> once said this about <topic>. It has been encoded using the Vigenère cipher using a very common five letter word. You have been told that the 17th through the 22nd letters in the code (YMNCHU) actually is the word REASON. What does the message decode to?
There can be one of these on a State/National test. There are no restrictions on the phrase, although try to avoid a phrase with a lot of a's in it. I.e.An amazing aardvark allows all answers would be a poor choice because the letter A is trivial to decode. As this question is nominally worth four points per letter, a 50 letter phrase is ideal.
Additionally there needs to be a Key to encode it with. It should be 5 or 6 characters with no repeating letters and avoid the letter a as it causes a letter to map to itself. By setting the Block Size to the same as the length of the Key, the problem is much easier than with the default Block Size of 0 that keeps the original spacing. Setting the Block Size to a size other than the length of the Key increases the difficulty somewhat.
For the decoding clue, pick a word in the phrase which is at least 5 characters long, carefully count to determine the position in the encoded phrase as well as the encoded character.
Setting Difficulty:The length of the phrase is the major
Points:200-250. If the Block Size is 0, add 25 points. If the Block Size is non-zero and different from the Key length, add 50 points.
Question Text:The question should indicate that the Porta Cipher is being used, the length of the Key and the plain text corresponding to some part of the phrase. It is generally nice to give the origin of the phrase if it is known. For example:
<person> once said this about <topic>. It has been encoded using the Porta cipher using a very common five letter word. You have been told that the 17th through the 22nd letters in the code (YMNCHU) actually is the word REASON. What does the message decode to?
There are several variants of the RSA question. The Safe Combo and Exchange Keys options test the knowledge of the RSA algorithm by presenting randomized order of RSA components with randomized values. The Quantum Computer and Compute d options test using the extended Euclidean Algorithm compute the inverse. Decode Year tests using Rapid Modular Exponentiation to compute the mod of a prime raised to a large factor. All of these dynamically generate and update the question text with all of the computed values.
For the Safe Combo
and Exchange Keys choices, it is good to pick values for the Prime Digits and Safe Combination Digits/Data Digits so that the generated RSA keys and numbers provide lots of similar digits. The Randomize button will regenerate the values. Note that the student names are also randomized, picking from the names which were common around the turn of this century.For the other options, click on the Randomize button until it generates a problem which has the desired level of difficulty.
Setting Difficulty:The choice of question type and the size of the digits in the key are the major impact on difficulty.
Points:Safe Combo: 100 points
Quantum Computer, Compute d: 15 points per step of the extended Euclidean Algorithm (shown by the tool) with a minimum of 120 points.
Decode Year:15 points per 1 bit and 5 points per 0 bit in the binary representation of d (shown by the tool) with a minimum of 120 points.
Exchange Keys:120 points
Question Text:The question text should be automatically generated, but can be edited. Note that the tool keeps track of all the edits so that if it generates new values, the edits are kept in place.
Pick a phrase to encode. As a rule of thumb for a 2x2 matrix, every pair of letters is worth 20 points. Ideally you want an odd length string to force them to use a padding Z. For a 3x3 matrix, every group of three letters is worth 25 points. It is important to pick a phrase which is not a multiple of 3 characters long so that they must add the appropriate number of padding characters.
Pick an encoding key. For a 2x2 it is 4 characters long and for a 3x3 it is 9 characters long. This is probably the hardest part to making the test as the matrix has to be invertible (https://en.wikipedia.org/wiki/Invertible_matrix). Fortunately, the tool will tell you if it is not invertible. There is also a list of known valid keys at https://toebes.com/codebusters/HillKeys.html for both the 2x2 and 3x3 encodings. In general, it is more likely to be invertible if you use the letters B, D, F, H, L, N, R, T, X and Z. as they are odd and non-prime, but you can mix in some other letters. Just make sure that the keyword is not an inappropriate phrase. A total non-sense phrase is perfectly acceptable, but it helps the style of the test if it looks like a word.
Setting Difficulty:Encrypt is harder than Decrypt and 3x3 is harder than 2x2. The other factor is the number of characters for them to encode.
Points:160-250.
Question Text:The question should indicate whether they are to Encode or Decode using the Hill Cipher with a 26 character alphabet along with the Key. For example:
Using a key of CARNIVALS encode the string ASTROBIOLOGIST using the Hill Cipher with a 26-character alphabet.
Using a key of LOST decode the string QNFWNQNAFCCT using the Hill Cipher with a 26 character alphabet.
There should be a single one of these on the State/National test. It should use a phrase about 25 characters long that doesn't have too many occurrences of the letter a in it, preferably with as large a variety of letters as possible. (e.g. The quick brown fox jumps over the lazy dog isn't actually bad).
Pick a value for a which is coprime with 26 (1,3,5,7,9,11,15,17,19,21,23 or 25). The actual value doesn't matter, but larger ones tend to be slightly harder. If you are generating tests for multiple regions, pick numbers that are near each other. I.e. 7, 9 and 11 would be good to have as equivalent a values.
Pick a value for b between 1 and 25 inclusive. Unlike a where the larger values become slightly harder, the value of b can truly be any number and be the same level of difficulty.
Setting Difficulty:There is very little variability in the difficulty other than the length of the string. Larger values of a are only slightly harder while the value of b has no real impact on the difficulty. Picking the two mapping letters so that they are toward the end of the alphabet also increase the difficulty. Having phrases which use the letters G, W, Y, B, V, K, X, J, Q, and Z increase the difficulty slightly.
Points:140-240. A good rule of thumb is 6 points per character plus 6 points for each of the letters G, W, Y, B, V, K, X, J, Q, and Z that are used.
Question Text:The question should state to use the Affine Cipher and the indication of what two letters map to. It should not give the values of a or b. For example:
A message from <person> encrypted with the Affine Cipher using an alphabet of 26 characters has been received. You have been told that the first two letters are TH. With that knowledge, what does this message say?
The Dancing Men Cipher (also known as the Running Men Cipher) is one of the easiest Ciphers for students to decode because the alphabet is fixed. The letter E will always be represented by a person with both arms up in the air and both legs split. There can be a couple of Dancing Men Cipher questions on a test.
Setting Difficulty:The only factor for difficulty with this question is in the number of characters in the phrase. The choice of letters/words/word length has no impact on the difficulty. In general the question should be approximately 100 characters.
Points:A Dancing Men Cipher Decode should be worth 100 points (approximately 1 point per character in the Plain Text).
Question Text:The question should clearly indicate that cipher has been encoded using the Dancing Men Cipher as well as the origin of the phrase or quote. It should not include a hint. Some examples:
Solve this quote from <person> which has been encoded with the Dancing Men Cipher.
The PigPen/Masonic Cipher is one of the easiest Ciphers for students to decode because the alphabet is fixed. The letter E will always be represented by a square. There can be a couple of PigPen Cipher questions on a test.
Setting Difficulty:The only factor for difficulty with this question is in the number of characters in the phrase. The choice of letters/words/word length has no impact on the difficulty. In general the question should be approximately 100 characters.
Points:A PigPen Cipher Decode should be worth 100 points (approximately 1 point per character in the Plain Text).
Question Text:The question should clearly indicate that cipher has been encoded using the PigPen Cipher as well as the origin of the phrase or quote. It should not include a hint. Some examples:
Solve this quote from <person> which has been encoded with the PigPen Cipher.
The Tap Code is is a simple cipher to decode because the mapping is is fixed. A single dot followed by a single dot will always stand for the letter a. What makes it slightly more challenging is that the students need to memorize the table or just know how to recreate it on the test. There should be one or two Tap Code Cipher questions on a test.
Setting Difficulty:The two factors for difficulty with this question is in the number of characters in the phrase and how far down in the alphabet the letters are. The further in the alphabet, the more characters that they have to count.
Points:A Tap Code Cipher should be worth 100 points.
Question Text:The question should clearly indicate that cipher has been encoded using the Tap Code Cipher. It should not include a hint. Some examples:
Solve this quote from <person> which has been encoded with the Tap Code Cipher.
The rail fence cipher encodes messages by 'zig-zagging' the letters along 2 to 6 'rails'. The cipher can be decoded by brute force; trial and error; or procedurally by applying some simple math and understanding spacing of characters in the rail patterns.
Setting Difficulty:The difficulty gets slightly higher with more rails because it requires more diligence when solving.
Points:100-150. A rule of thumb: 2 rails = 100; 3 rails = 110; 4 rails = 120; 5 rails = 130; 6 rails = 140 points. 150 points for when only the range of rails is given.
Question Text:The question should be around 75 characters.
Solve this quote from <person> which has been encoded with the rail fence cipher. The message was encoded with <rail count> rails.
The Morbit Cipher encodes text by first converting the plain text into morse code with the space between characters represented by an × and the space between words represented by two × characters. The resulting morse code is then broken into pairs of characters (adding an × at the end if necessary). The numbers 1-9 are randomly assigned to the unique pairs of characters (●●, ●–, ●×, –●, ––, –×, ×●, ×–, ××,). The pairs of morse characters are then replaced with the corresponding number to generate the final cipher string. Decoding is done by reversing the process.
Setting Difficulty:The dificulty is driven by the number of letters and the variety of morse code combined with which letters are chosen. Looking at the generated solving guide can help guide the question writing. Not giving them Hint Digits which exposes the digit corresponding to ×× increases the difficulty.
Points:150-200.
Question Text:The question should be around 40 characters.
Solve this quote from <person> which has been encoded using the Morbit Cipher. You are told that the first four letters are SOME.
The Pollux Cipher encodes text by first converting the plain text into morse code with the space between characters represented by an × and the space between words represented by two × characters. The resulting morse code is then randomly assigned to digits (0-9) chosen to represent the morse characters: (●, –, ×) The pairs of morse characters are then replaced with the corresponding number to generate the final cipher string. Decoding is done by reversing the process. Note that because one or more digits may represent a morse character piece, the mapping can be somewhat random.
Setting Difficulty:The dificulty is driven by the number of letters and the variety of morse code combined with which letters are chosen. Looking at the generated solving guide can help guide the question writing. Not giving them Hint Digits which exposes all the digits corresponding to × increases the difficulty. Assigning more characters for one morse digit, thereby reducing another, also increases the difficulty.
Points:150-200.
Question Text:The question should be around 40 characters.
Solve this quote from <person> which has been encoded using the Pollux Cipher. You are told that the first four letters are SOME.