A **substitution cipher** is a form of cryptography. 

In a substitution cipher, a rule is used to change each letter of the message, one at a time. The rule says to replace (or "substitute") each letter with another letter from the alphabet. 

For instance, this table gives a rule for a substitution cipher:

|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
| T | H | A | N | K | Y | O | U | V | E | R | M | U | Z | X | W | S | Q | B | C | D | F | G | I | J | L |

Using this rule, the sentence "Jack and Jill went up the hill" is changed to "Etar tzn Evmm gkzc dw cuk uvmm". The Caesar cipher is one example of a substitution cipher.

Substitution ciphers are not safe enough to use for important messages. Substitution ciphers can be broken by an idea called *frequency analysis*. Some letters are more common than others in English sentences: *E* is the most common, then *T*, then *A*, and so on. A message that has been changed by a substitution cipher will have different common letters, but this gives a hint about the rule. The most common letters in the changed message are likely to be the most common letters in English. Breaking *cryptograms* (messages hidden with a substitution cipher) is a common puzzle often found in newspapers.

In past centuries substitution ciphers were sometimes strengthened by combining them in superencryption with transposition ciphers. Improvements in cryptanalysis caused this method to be abandoned in the early 20th century.

Example
-------

  

Suppose the changed message is:

```
LIVITCSWPIYVEWHEVSRIQMXLEYVEOIEWHRXEXIPFEMVEWHKVSTYLXZIXLIKIIXPIJVSZEYPERRGERIM
WQLMGLMXQERIWGPSRIHMXQEREKIETXMJTPRGEVEKEITREWHEXXLEXXMZITWAWSQWXSWEXTVEPMRXRSJ
GSTVRIEYVIEXCVMUIMWERGMIWXMJMGCSMWXSJOMIQXLIVIQIVIXQSVSTWHKPEGARCSXRWIEVSWIIBXV
IZMXFSJXLIKEGAEWHEPSWYSWIWIEVXLISXLIVXLIRGEPIRQIVIIBGIIHMWYPFLEVHEWHYPSRRFQMXLE
PPXLIECCIEVEWGISJKTVWMRLIHYSPHXLIQIMYLXSJXLIMWRIGXQEROIVFVIZEVAEKPIEWHXEAMWYEPP
XLMWYRMWXSGSWRMHIVEXMSWMGSTPHLEVHPFKPEZINTCMXIVJSVLMRSCMWMSWVIRCIGXMWYMXXLIYSPH
KTY
```

For this example, capital letters are used for unknown letters, and lowercase letters are used to denote letters we know or can guess. 

By counting up the letters, we see that the most common is I, which we will guess is an e. X is also quite common, and XLI is found many times; we guess that this is the, the most common three-letter group in English.

E is the second most common letter. We already have a guess for e and t, so we guess that E is a. We now have:

```
heVeTCSWPeYVaWHaVSReQMthaYVaOeaWHRtatePFaMVaWHKVSTYhtZetheKeetPeJVSZaYPaRRGaReM
WQhMGhMtQaReWGPSReHMtQaRaKeaTtMJTPRGaVaKaeTRaWHatthattMZeTWAWSQWtSWatTVaPMRtRSJ
GSTVReaYVeatCVMUeMWaRGMeWtMJMGCSMWtSJOMeQtheVeQeVetQSVSTWHKPaGARCStRWeaVSWeeBtV
eZMtFSJtheKaGAaWHaPSWYSWeWeaVtheStheVtheRGaPeRQeVeeBGeeHMWYPFhaVHaWHYPSRRFQMtha
PPtheaCCeaVaWGeSJKTVWMRheHYSPHtheQeMYhtSJtheMWReGtQaROeVFVeZaVAaKPeaWHtaAMWYaPP
thMWYRMWtSGSWRMHeVatMSWMGSTPHhaVHPFKPaZeNTCMteVJSVhMRSCMWMSWVeRCeGtMWYMttheYSPH
KTY
```

We can now make some more guesses: heVe may be here; Rtate may be state, and atthattMZe could be atthattime. Filling in these guesses, we get:

```
hereTCSWPeYraWHarSseQithaYraOeaWHstatePFairaWHKrSTYhtmetheKeetPeJrSmaYPassGasei
WQhiGhitQaseWGPSseHitQasaKeaTtiJTPsGaraKaeTsaWHatthattimeTWAWSQWtSWatTraPistsSJ
GSTrseaYreatCriUeiWasGieWtiJiGCSiWtSJOieQthereQeretQSrSTWHKPaGAsCStsWearSWeeBtr
emitFSJtheKaGAaWHaPSWYSWeWeartheStherthesGaPesQereeBGeeHiWYPFharHaWHYPSssFQitha
PPtheaCCearaWGeSJKTrWisheHYSPHtheQeiYhtSJtheiWseGtQasOerFremarAaKPeaWHtaAiWYaPP
thiWYsiWtSGSWsiHeratiSWiGSTPHharHPFKPameNTCiterJSrhisSCiWiSWresCeGtiWYittheYSPH
KTY
```

This lets us make more guesses, which lead to more, until we have guessed everything:

```
hereuponlegrandarosewithagraveandstatelyairandbroughtmethebeetlefromaglasscasei
nwhichitwasencloseditwasabeautifulscarabaeusandatthattimeunknowntonaturalistsof
courseagreatprizeinascientificpointofviewthereweretworoundblackspotsnearoneextr
emityofthebackandalongoneneartheotherthescaleswereexceedinglyhardandglossywitha
lltheappearanceofburnishedgoldtheweightoftheinsectwasveryremarkableandtakingall
thingsintoconsiderationicouldhardlyblamejupiterforhisopinionrespectingitthegold
bug
```

At this point, we can insert spaces and punctuation:

*Here upon le grand arose with a grave and stately air and brought me the beetle  
from a glass case in which it was enclosed. It was a beautiful scarabaeus and  
at that time unknown to naturalists of course; a great prize in a scientific  
point of view. There were two round black spots near one extremity of the back  
and a long one near the other. The scales were exceedingly hard and glossy with  
all the appearance of burnished gold. The weight of the insect was very  
remarkable and taking all things into consideration I could hardly blame jupiter  
for his opinion respecting it.* (The Gold-Bug)

If we had made a wrong guess, we would have found out at some point, and could go back and make a new guess.