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Substitution Cipher

Age 11 to 14
Challenge Level Yellow star
Secondary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources


Substitution Cipher printable sheet
 

In any language some letters tend to appear more often than others.

Which letters do you think are the most common in English?

Is the frequency of letters in the following sentence representative?

The quick brown fox jumps over the lazy dog.

In the coded text below, every letter in the original message was switched with  another letter. Find out which are the most (and least) common letters used in English to help you crack this coded message:
 

Vfj Uzyj fxc pjjw nzkrgwi tjkl fxkc xyy vfj uzkwgwi, qbkgwi-dyjxwgwi fgq ygvvyj fzuj. Hgkqv ngvf pkzzuq, vfjw ngvf cmqvjkq; vfjw zw yxccjkq xwc qvjbq xwc dfxgkq, ngvf x pkmqf xwc x bxgy zh nfgvjnxqf; vgyy fj fxc cmqv gw fgq vfkzxv xwc jljq, xwc qbyxqfjq zh nfgvjnxqf xyy ztjk fgq pyxdr hmk, xwc xw xdfgwi pxdr xwc njxkl xkuq. Qbkgwi nxq uztgwi gw vfj xgk xpztj xwc gw vfj jxkvf pjyzn xwc xkzmwc fgu, bjwjvkxvgwi jtjw fgq cxkr xwc yznyl ygvvyj fzmqj ngvf gvq qbgkgv zh cgtgwj cgqdzwvjwv xwc yzwigwi. Gv nxq quxyy nzwcjk, vfjw, vfxv fj qmccjwyl hymwi cznw fgq pkmqf zw vfj hyzzk, qxgc 'Pzvfjk!' xwc 'Z pyzn!' xwc xyqz 'Fxwi qbkgwi-dyjxwgwi!' xwc pzyvjc zmv zh vfj fzmqj ngvfzmv jtjw nxgvgwi vz bmv zw fgq dzxv. Qzujvfgwi mb xpztj nxq dxyygwi fgu gubjkgzmqyl, xwc fj uxcj hzk vfj qvjjb ygvvyj vmwwjy nfgdf xwqnjkjc gw fgq dxqj vz vfj ixtjyjc dxkkgxij-ckgtj znwjc pl xwguxyq nfzqj kjqgcjwdjq xkj wjxkjk vz vfj qmw xwc xgk. Qz fj qdkxbjc xwc qdkxvdfjc xwc qdkxppyjc xwc qdkzzijc xwc vfjw fj qdkzzijc xixgw xwc qdkxppyjc xwc qdkxvdfjc xwc qdkxbjc, nzkrgwi pmqgyl ngvf fgq ygvvyj bxnq xwc umvvjkgwi vz fguqjyh, 'Mb nj iz! Mb nj iz!' vgyy xv yxqv, bzb! fgq qwzmv dxuj zmv gwvz vfj qmwygifv, xwc fj hzmwc fguqjyh kzyygwi gw vfj nxku ikxqq zh x ikjxv ujxczn. 'Vfgq gq hgwj!' fj qxgc vz fguqjyh. 'Vfgq gq pjvvjk vfxw nfgvjnxqfgwi!' Vfj qmwqfgwj qvkmdr fzv zw fgq hmk, qzhv pkjjojq dxkjqqjc fgq fjxvjc pkzn, xwc xhvjk vfj qjdymqgzw zh vfj djyyxkxij fj fxc ygtjc gw qz yzwi vfj dxkzy zh fxbbl pgkcq hjyy zw fgq cmyyjc fjxkgwi xyuzqv ygrj x qfzmv. Emubgwi zhh xyy fgq hzmk yjiq xv zwdj, gw vfj ezl zh ygtgwi xwc vfj cjygifv zh qbkgwi ngvfzmv gvq dyjxwgwi, fj bmkqmjc fgq nxl xdkzqq vfj ujxczn vgyy fj kjxdfjc vfj fjcij zw vfj hmkvfjk qgcj.

Javkxdv hkzu 'Vfj Ngwc gw vfj Ngyyznq' pl Rjwwjvf Ikxfxuj

Xtxgyxpyj vz kjxc gw hmyy xv nnn.imvjwpjki.zki

If you want to work on a computer to solve the problem, you can download the message as a text file which doesn't contain any line breaks.

If you are interested in code breaking you might enjoy the Secondary Cipher Challenge.

You can read about Substitution Ciphers and Frequency Analysis on Simon Singh's website: http://www.simonsingh.net/The_Black_Chamber/crackingsubstitution.html

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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