# Solution: Cryptogram

Hv wjt tkjgef, Sjeojyg–Cedjvbjy wjt tkjgef, vdojm dctje odtkjodthphdvw Jevwt Sjeojyg dvm Dzedkdo Cedjvbjy, hw dv dlhgodthp wfwtjo tkdt qdw regrgwjm hv tkj jdeyf tqjvthjtk pjvtnef hv gemje tg cgeonydtj d tkjgef gc wjtw cejj gc rdedmgljw wnpk dw Enwwjyy'w rdedmgl. Tgmdf, Sjeojyg–Cedjvbjy wjt tkjgef, qhtk tkj khwtgehpdyyf pgvtegxjewhdy dlhgo gc pkghpj (DP) hvpynmjm, hw tkj wtdvmdem cgeo gc dlhgodthp wjt tkjgef dvm dw wnpk hw tkj ogwt pgoogv cgnvmdthgv gc odtkjodthpw. Sjeojyg–Cedjvbjy wjt tkjgef qhtk tkj dlhgo gc pkghpj hvpynmjm hw dzzejxhdtjm SCP, qkjej P wtdvmw cge "pkghpj", dvm SC ejcjew tg tkj dlhgow gc Sjeojyg–Cedjvbjy wjt tkjgef qhtk tkj dlhgo gc pkghpj jlpynmjm. Tkj inhpb zegqv cgl anorjm gxje tkj ydsf mgu. wtdthwthpdy_dvdyfwhw_QbIUr4

This is a simple alphabetical substitution cipher. Each letter in the English alphabet is replaced with a different letter. Since the ciphertext is fairly long, it's susceptible to several forms of statistical analysis. Letters don't appear with consistent frequency: the letter "e" makes up about 13% of all English text, followed by "t" (9.1%) and "a" (8.2%). Automated tools are available to use this analysis (possibly in combination with a dictionary to detect whole words) to break a simple substitution cipher.

The plaintext, as found by an automated solver:

ciphertext alphabet: dzpmjcukhabyovgriewtnxqlfs plaintext alphabet: abcdefghijklmnopqrstuvwxyz In set theory, Zermelo–Fraenkel set theory, named after mathematicians Ernst Zermelo and Abraham Fraenkel, is an axiomatic system that was proposed in the early twentieth century in order to formulate a theory of sets free of paradoxes such as Russell's paradox. Today, Zermelo–Fraenkel set theory, with the historically controversial axiom of choice (AC) included, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics. Zermelo–Fraenkel set theory with the axiom of choice included is abbreviated ZFC, where C stands for "choice", and ZF refers to the axioms of Zermelo–Fraenkel set theory with the axiom of choice excluded. The quick brown fox jumped over the lazy dog. statistical_analysis_WkQGp4

The flag:

statistical_analysis_WkQGp4

Online tools:

- quipqiup (fast and automated cryptogram solver)

*This page uses material from the Wikipedia article "Zermelo–Fraenkel set theory", which is released under the Creative Commons Attribution-Share-Alike License 3.0.*