# Replacement Cipher

Replacement cipher: Let τ be a permutation of the alphabet, and apply τ to each letter of the message. Frequency analysis is useful for breaking this type of code. Decode the following, which was encoded using a replacement cipher.

MIZVN KXXHA XRRTK NXYEX QIZVI IZXWM NXYGT JWVHC YTOXX QNHTI JYTWV NMHUR XOYLN ZTJTE XYAZX RWMHU XEMRK LIJYT WNWVR REXPV IMTHN OTHIM HLVRR GYXCX VIXQ --- NVWLX RBTZH NTH

I have made a frequency table of the occurrence of each letter in the above code.

X-18 T-12 H-10 N-10 R-10 I-9 V-9 Y-8 M-7 W-7 Z-6 E-4 J-4 L-4 K-3 O-3 Q-3 A-2 C-2 G-2 U-2 B-1 P-1 D-0 F-0 S-0

Comparing this with the frequency of letters occurring in English leads me to believe that X corresponds with E and that T corresponds with T. However this is where I get stuck.

• Are you just looking for a hint for the next step? – xnor Nov 21 '14 at 1:36
• Yes, a hint would be great. Any help would be great. The only instructions I was given was to use a frequency analysis and guessing. – UserX Nov 21 '14 at 1:40
• For reference, this was previously asked at math.stackexchange.com/q/1031736/18398, where it currently has no answers. I asked the OP to try asking at this site. – Joel Reyes Noche Nov 21 '14 at 1:50
• You should also look for common double letters combinations...such as "tt", "oo", etc after looking for common words like "the", "I", "am", etc. This link has all of the common words/digrams/double letters in english scottbryce.com/cryptograms/stats.htm – stackErr Nov 21 '14 at 2:31

You are correct that X corresponds to E. E is the most commonly used letter and X is the letter that appears most commonly in your cipher.

T is the next common letter so it makes sense to try another vowel for this one. Try O. See how you go with these tips.

Here is the solution to the cipher if you find you get too stuck:

IT HAS BEEN WELL OBSERVED THAT THE MISERY OF MAN PROCEEDS NOT FROM A SINGLE CRUSH OF OVER WHELMING EVIL BUT FROM SMALL VEXATIONS CONTINUALLY REPEATED SAMUEL JOHNSON

• Using O instead of T in place of T made all of the difference! Thank you so much! – UserX Nov 21 '14 at 2:32
• @Michelle, I'm glad I was able to be of assistance. Sometimes you have to experiment with the vowels, and T etc and see what one fits the best :) – Kenshin Nov 21 '14 at 2:34
• @Michelle Yes, and thanks for bringing this puzzle to us :D – d'alar'cop Nov 21 '14 at 12:18

After doing frequency analysis, you often have a guess at what ciphertext letters correspond to the most common letters ETAOIN. What I often try to do next is pin these down.

1) Check for doubled letters. E, T, O, and N can be doubled, but A and I cannot be except in rare cases of the letter being at the end of a word and the start of the next word.

2) Check for the possible common substring THE, which uses the T and the E. This is a good way to test your hypothesis about those letters. THAT and THERE also can be useful cribs. Actually, finding reused substrings is useful in general.

This is generic advice; I haven't applied it to your specific ciphertext.

• Just an addition to this great post, also L can be doubled and will be of use in this cipher. – Kenshin Nov 21 '14 at 2:31