Abstract
We present a proposal for a learning path for children to teach them cryptography during visits to the MuMa Science Centre. As the goal of the Math Museum (MuMa) for which the track is being developed is to make youngsters enthusiastic about mathematics and computer science, we have decided to focus on cryptography. In our past experience this proved to be very effective – children love secrets and spy games. We will prepare a set of CS-unplugged-like activities which will cover the broad range from the simplest, historical ciphers up to the Enigma cipher. In contrast to previously described CS-unplugged activities, we will focus on methods of breaking those ciphers, not on merely using them. Breaking of Enigma deserves attention thanks both to clever use of pure mathematics, but also due to its historical significance in ending WWII. In this paper we will present ideas for activities to teach cryptanalysis of the simplest ciphers, starting from Caesar and Vigenère ciphers, as well as the design for a simple, paper teaching aid that simulates the simplified Enigma to show its properties. We share pertinent feedback we have received after several presentations we had already made to small groups of children and adults.
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Acknowledgments
We would like to thank Małgorzata Bednarska-Bzdęga for her insightful comments on the Kid-Enigma.
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Appendix
Appendix
1.1 Kid-Enigma learning scenario
Age group: Junior high school and above
Presumed abilities of participants: Familiarity with Caesar shift ciphers
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1.
The activity is framed in the context of a story about scouts.
Dozens of teams of three have applied for a course on ciphers for scouts.
Preliminary interviews are about to begin. Now it’s time for Fran’s team.
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2.
The students are given about 5 min to solve Fran’s team’s cryptogram.
The teacher asks a volunteer to present a method for finding the shift (13). (A solution by guessing is: N and NA represent the articles A and AN.) Students are divided into teams and work to recreate the cipher alphabet:
Finally, the teams work on their own to decipher the whole message:
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3.
The activity continues with the story about the course for scouts.
The cipher alphabet used in preliminary task is written on the board.
“Can you see anything special in this alphabet?,” asks the instructor.
“A stands for N and N for A; B for O and O for B; etc.”
“Yes! The idea was to make the cipher reciprocal,” states the instructor, and adds, “A Caesar with a shift of 13 we call a half-reversed alphabet”.
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4.
Each team is given a sheet of cardboard with two circles printed on it.
The teacher explains how to make a device called a stepping reflector.
The encryption method (algorithm) is as follows:
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(1)
Turn the wheel until the arrow points to the letter A.
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(2)
Look at the first letter of the word to encrypt, select the appropriate line, follow the line and note down the letter at the other end of the line.
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(3)
Before encrypting the next letter, turn the wheel one step clockwise ...
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(1)
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5.
The teams encrypt a word of their choice and decrypt the ciphertext to see how useful the reciprocal ciphers are: encryption is the same as decryption.
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6.
The teacher poses a question about a number of reciprocal cipher alphabets.
If the students are advanced enough, it is worth encouraging them to work out the value themselves, otherwise the answer is given: \(26!/(2^{13}\cdot 13!) \approx 10^{13}\).
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7.
The second part of the activity begins with handing out a cryptogram.
A group discussion ensues about how to attack the cryptogram. If the brainstorming stalls, the teacher says to focus only on the first letters of words. The following tips are then presented by the teacher:
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The top letters at the beginning of English words are: T, A, I, S and O.
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The most common two-letter words are: TO, OF, IN, IT and IS.
Together, the teams should count all the first letters of the encrypted words.
The sequence of first observations about the cryptogram may be as follows:
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The most frequent letters are Y and G, followed by V, Z, and X.
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The only single letter is G.
The teacher asks: “What’s the conclusion?” (“Surely G is A, and Y is T”). The competitive phase begins. The teams should no longer work together, but try on their own to recreate all lines connecting letters on the wheel. The solution (the cipher key) shall be written on the board or flipchart. Students are then asked to decrypt the message. The teams can cooperate.
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8.
The teacher mentions some historic facts. Here is a suggested text to tell.
To prevent the use of statistical attacks (letter frequency analysis), i.e. exploitation of a large number (about 60–80) of cryptograms intercepted on the same day, the Enigma cryptosystem in 1930s used a three-letter message key: indicators of the initial positions of three rotors in the machine, chosen by the sender. There is some chance of an operator error or message corruption during transmission, so the three-letter key (e.g. DVR) was doubled (e.g. DVR DVR), encrypted using the daily key and sent as a message header (e.g. FSB QCH). The recipient decrypted the key (DVR) and set up the Enigma machine to read the message. Using an Enigma machine itself to encrypt the message key was a vicious circle... A gifted Polish mathematician Marian Rejewski made good use of this flaw. We will follow in his footsteps.
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9.
The teacher initiates a discussion on how to use the Kid-Enigma device more securely, directed in such a way as to reach the following conclusion:
If the initial position of the wheel (used for the first letter of a word) is continually changed from word to word, the method of frequency analysis will fail.
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10.
The last part of the activity begins. The teachers tells the following story:
A secret radio message sent in Morse code has been intercepted. Our intelligence supposes that Enigma-like ciphers are still being used, but a new encryption algorithm has been applied to prevent statistical attacks.” “You take on roles of the cryptologists”
The cryptogram is handed out.
The teacher states: “In the new algorithm the initial setting changes from word to word. We call it the word key. Before encrypting each word, the operator (starting from setting A) first encrypts the word key twice and then encrypts the word (starting from the setting indicated by the word key).”
The students should now analyse how a substitution of the Kid-Enigma changes after a letter is encrypted. It will lead them to notice the pattern in the relationships between the two letters used to encrypt the word key.
The teams may start with QL, so L should be written in the grid below Q. Then they should look for AR in the cryptogram. The next one is CB, and so on. Eventually they recreate two cipher alphabets, i.e. the substitutions (the lines on the wheel) for settings A and B. Finally, each team writes a duplicated alphabet on grid paper and cuts it out. Then they try to match the cipher alphabets with the duplicate alphabet:
Each team is tasked with deciphering one or two message keys and the associated word(s). The teams put together the decrypted words.
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Ren, M., Perekietka, P., Nitschke, Ł. (2025). From Caesar Shifts to Kid-Enigma. The CS Unplugged-Like Path in the MuMa Science Centre. In: Fernau, H., Schwank, I., Staub, J. (eds) Creative Mathematical Sciences Communication. CMSC 2024. Lecture Notes in Computer Science, vol 15229. Springer, Cham. https://doi.org/10.1007/978-3-031-73257-7_15
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