# Using an affine transformation to cryptanalyze an enciphered message

Number Theory Level pending

Let $$A \rightarrow 0, B \rightarrow 1, \ldots , Z \rightarrow 25$$. 

The most common letters in the English alphabet are $$E$$ and $$T$$, respectively.

Suppose we know that an affine transformation of the form $$a * P + b \equiv C \mod{26} \: (0 <= C <= 25)$$, has been used for enciphering the enciphered message: $$USLEL \: JUTCC \: \: YRTPS \: \: URKLT \: \: YGGFV \: \: ELYUS \: \: LRYX$$. 

Cryptanalyze the enciphered message using the frequency of letters in the enciphered message. If $$L_{j}$$ has the largest frequency and $$L_{k}$$ has the second largest frequency, then let $$E$$ and $$T$$ correspond to $$L_{j}$$ and $$L_{k}$$ respectively. If $$L_{k}$$ and $$L_{m}$$ have the same frequency then choose one of the two, say $$L_{k}$$, and determine if the message is intelligible. If not then try using $$L_{j}$$ and $$L_{m}$$. I constructed the problem so that the message will be intelligible, but you may have to do some guess work.

When you obtain an intelligible message, express the answer as a string of integers. List a string of the first 33 integers. 

Note: The site only allows 33. 

What does the message state?

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