Gregory V. Bard

Associate Professor of Mathematics
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Cryptograms can be great fun for someone interested in mathematics, statistics, linguistics, or all three. They can be an enjoyable way to pass a snowy afternoon, or they can be a superb in-class activity. Cryptograms can be a great way to discover cryptography, or to pass the time during a boring meeting.

For several years, Cryptograms have served as the nucleus for an exciting Science Olympiad event, called Codebusters. Then Codebusters also adds several mathematical ciphers, culminating in the RSA algorithm---the most common cipher on the internet today. In fact, I have run the Codebusters event for Wisconsin Science Olympiad since November of 2013.

Below, you'll find some resources that I've developed for those who wish to play around with a few cryptograms. First, I have an example. Second, I will share some vocabulary. Third, I will discuss some books that are great for learning about cryptography. Fourth, I have a horde of online interactive webpages for practice examples. If you'd like to just dive in and have fun with cryptograms, then just scroll to the bottom of this page and skip everything else.

Here's an example, so that you know what we're talking about:


Which actually translates into

The word cryptography comes from Greek. The word KRYPTOS means "secret" and the word GRAPHOS indicates "writing." Therefore, cryptography is the science of secret writing. Cryptography has been important to national security since the era of Julius Ceaser, who has a cipher named after him.

Cryptograms are divided by hobbyists (and Science Olympiad) into three major categories. One like the above, with the spaces included, is called an Aristocrat. When the spaces are removed, we call it a Patristocrat. A special category of Arisotracts are the Xenocrypts, which are Aristocrats in a language other than the assumed native language of the student. In the USA, Xenocrypts are often in Spanish.

Science Olympiad also includes other historical ciphers, such as the pigpen cipher, the Atbash cipher, the Caesar cipher, the Baconian cipher, the Vigenere cipher, the affine cipher, the Hill cipher, and RSA.

These are the best books for learning about cryptograms, or preparing for Codebusters in Science Olympiad.

  1. (first choice) Janet Beissinger and Vera Pless. The Cryptoclub: Using Mathematics to Make and break Secret Codes, published by CRC Press in 2006. The National Science Foundation (!) funded the writing of that book. It is the best of its kind, ideal for 9th grade and up, or highly motivated 7th and 8th graders. The artwork can (at times) suggest a younger audience but don't judge the author's work by the illustrator's work! Available on There is also a black-and-white workbook to accompany the above, with lots of additional examples and practice problems. Also available on

  2. Margaret Cozzens and Steven Miller. The Mathematics of Encryption: An Elementary Introduction, published by The American Mathematical Society in 2013. This book covers cryptograms but quickly moves on to mathematical schemes, such as the affine cipher, the Hill cipher, and RSA. This is more suited for 11th and 12th grade, or highly motivated 10th graders.

  3. Abraham Sinkov and Todd Feil. Elementary Cryptanalysis: A Mathematical Approach, 2nd edition, published by the Mathematical Association of America in 2009. The original was published by the Mathematical Association of America in 1966, but reprinted many times since. The 2nd edition is a fairly accessible book, covering a lot of classical code-breaking (such as solving cryptograms) all the way through one-time pads and RSA, but it is rather readable. However, be sure to get the latest edition, because Todd Feil did a major rewrite, modernizing the notation, and adding several cryptosystems. Before you buy it, I recommend you make sure that both authors' names are on the cover, because the various reprintings of the first edition have antiquated notation that will confuse students.

  4. Simon Singh. The Code Book: How to Make It, Break It, Hack It, Crack It, Second Edition, published by "Delacorte Books for Young Readers" in 2002. This book is ideally suited for young people who find cryptograms to be fun. The book claims to be good for students in 7th grade and up, but perhaps 9th grade and up, including highly motivated 8th graders, is a more realistic claim.

  5. Wade Trappe and Larry Washington. Cryptography with Coding Theory, Second Edition, published by Pearson/Prentice Hall in 2005. The aim of this book is for the computer scientist, mathematician, or computer engineer who actually wants to construct or understand secure cryptographic communications. It starts out with fun and simple problems (like cryptograms) in Chapter 2, but before Chapter 9 is over you're well versed in modern, real-world encryption systems such as the RSA algorithm. We use this book for Math-380: Cryptography here at UW-Stout. The book should be somewhat comprehensible to a student who has studied no mathematics beyond Calculus iii (or even those who stopped at Calculus i), yet you'll get a lot more out of it if you've taken a university-level course in Discrete Mathematics.

  6. Do Not Purchase: Gregory Bard. Algebraic Cryptanalysis, published by Springer in 2009. I wrote this one myself, but this book is intended for PhD-students in mathematics attempting to break real-world modern ciphers. The Trappe-Washington text would be a pre-requisite, along with a few 300-level or 400-level university mathematics courses.

Here are some useful online resources:
  • You can find many more cryptograms at, the webpage of The American Cryptogram Association (the ACA).

  • The website Puzzle Baron includes cryptograms, along with tons of other fun puzzles of many kinds.

In collaboration with Brendan Bard, and my colleague Prof. Seth Dutter, the following examples have been made available for you with an interactive web-based interface. The cryptograms can be great practice, and lots of fun.

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Also, for Baconian Cipher examples and exercises with full solutions (19 in total), see my module for the Baconian cipher in my electronic textbook-in-progress for Discrete Mathematics.

Last updated March 7th, 2019.