Gregory V. Bard
Associate Professor of Mathematics
Preserving the look-and-feel of the World Wide Web as it was, in 1998.
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
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:
BCU YSZO TZNXBSGZFXCN TSEUV KZSE GZUUL. BCU YSZO LZNXBSV EUFIV "VUTZUB" FIO
BCU YSZO GZFXCSV RIORTFBUV "YZRBRIG." BCUZUKSZU, TZNXBSGZFXCN RV BCU VTRUITU
SK VUTZUB YZRBRIG. TZNXBSGZFXCN CFV HUUI REXSZBFIB BS IFBRSIFA VUTWZRBN
VRITU BCU UZF SK DWARWV TUFVUZ, YCS CFV F TRXCUZ IFEUO FKBUZ CRE.
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.
- (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 amazon.com.
There is also a black-and-white workbook to accompany the above, with lots of
additional examples and practice problems. Also available on amazon.com.
- 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.
- 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.
- 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.
- Wade Trappe and Larry Washington. Cryptography with Coding
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.
- 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 cryptogram.org,
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.
- Aristocrats (click to expand):
- Telegrams (click to expand):
- With hint (click to expand):
- Without hint (click to expand):
- With hint, but spelling errors (click to expand):
- No hint and spelling errors (click to expand):
- Patristocrats (click to expand):
- Easy, with a large hint (click to expand):
- Medium, with a medium hint (click to expand):
- Hard, with a small hint (click to expand):
- Very hard, with no hint (click to expand):
- Xenocrypts (click to expand):
Also, for Baconian Cipher examples and exercises with full solutions (19 in total),
see my module
for the Baconian cipher in
textbook-in-progress for Discrete Mathematics.
Last updated March 7th, 2019.