Cryptanalysis of the Caesar Cipher

If you need a reminder on how the Caesar Cipher works click here.

The Caesar Cipher is a very easy to crack as there are only 25 unique keys so we can test all of them and score how English they are using either Chi-Squared Statistic or N-Gram Probability.

Example

Ciphertext of “RCZIOCZXGJXFNOMDFZNORZGQZVOOVXF”

Shift | Decrypted Text                 | Chi-Sq Score
1       QBYHNBYWFIWEMNLCEYMNQYFPYUNNUWE  201.327499
2       PAXGMAXVEHVDLMKBDXLMPXEOXTMMTVD  599.489345
3       OZWFLZWUDGUCKLJACWKLOWDNWSLLSUC  267.058510
4       NYVEKYVTCFTBJKIZBVJKNVCMVRKKRTB  325.267580
5       MXUDJXUSBESAIJHYAUIJMUBLUQJJQSA  775.163340
6       LWTCIWTRADRZHIGXZTHILTAKTPIIPRZ  434.880892
7       KVSBHVSQZCQYGHFWYSGHKSZJSOHHOQY  554.916606
8       JURAGURPYBPXFGEVXRFGJRYIRNGGNPX  340.923863
9       ITQZFTQOXAOWEFDUWQEFIQXHQMFFMOW  1012.384679
10      HSPYESPNWZNVDECTVPDEHPWGPLEELNV  115.358434
11      GROXDROMVYMUCDBSUOCDGOVFOKDDKMU  91.670467
12      FQNWCQNLUXLTBCARTNBCFNUENJCCJLT  283.701596
13      EPMVBPMKTWKSABZQSMABEMTDMIBBIKS  194.299832
14      DOLUAOLJSVJRZAYPRLZADLSCLHAAHJR  385.733449
15      CNKTZNKIRUIQYZXOQKYZCKRBKGZZGIQ  1520.292006
16      BMJSYMJHQTHPXYWNPJXYBJQAJFYYFHP  801.523128
17      ALIRXLIGPSGOWXVMOIWXAIPZIEXXEGO  603.683962
18      ZKHQWKHFORFNVWULNHVWZHOYHDWWDFN  280.874579
19      YJGPVJGENQEMUVTKMGUVYGNXGCVVCEM  269.610988
20      XIFOUIFDMPDLTUSJLFTUXFMWFBUUBDL  176.849244
21      WHENTHECLOCKSTRIKESTWELVEATTACK  51.921327
22      VGDMSGDBKNBJRSQHJDRSVDKUDZSSZBJ  460.236803
23      UFCLRFCAJMAIQRPGICQRUCJTCYRRYAI  262.108135
24      TEBKQEBZILZHPQOFHBPQTBISBXQQXZH  1373.411997
25      SDAJPDAYHKYGOPNEGAOPSAHRAWPPWYG  90.715517

As you can see the lowest Chi-Squared value is 51.921327, which was using a shift of 21. If you read the decrypted text for a shift of 21 you can indeed see that it is English. Hence cipher has been broken!

WIP

 

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