Solution: Vigenère

Bae Ywynidr–Aaaylwg slkxeiye baezpmf id y baezpmf iy rpx ftctw oq qqznlj xkoncaliye eainf axrgca ts l dcgdlkmgtlj jkioem ueeumxn nmvmiyswns-egux stevtld yvw dtqkkeec-bbmp qqznlja. Bt pqbtbwgaaed y anfqgkbeyr khnogbboy dwk a dyuilp pime efim pppubtd y lbsnpmme dcyneyam hf dyuilpq bh clnbnrp yte tsc qgfzputttmv yrzk i voyrqguzsa-mixc abgyyt hf qgvbtp zigdhglmh.

amtrawnptbprqv_QIaZik

This is a Vigenère cipher, a type of polyalphabetic substitution cipher. It uses a series of different Caesar ciphers for each plaintext letter. The shift values for these ciphers are chosen based on a keyword, and they repeat with a period the same as the length of the keyword.

Cipher operation

Take each letter M of the plaintext and the corresponding letter K of the key. The key repeats as much as needed to fit the length of the plaintext (i. e. DELTADELTADELTA). The letters A-Z are represented as the numbers 0-25. To encrypt, ciphertext letter C is:

C = (M + K) mod 26

and to decrypt:

M = (C - K + 26) mod 26

Example

Plaintext:
THEQUICKBROWNFOX

Key: ORANGE, extended:
ORANGEORANGEORAN

If A=0, B=1, C=2, ... Z=25, then:

THEQUICKBROWNFOX = 19  7  4 16 20  8  2 10  1 17 14 22 13  5 14 23
ORANGEORANGEORAN = 14 17  0 13  6  4 14 17  0 13  6  4 14 17  0 13

         19  7  4 16 20  8  2 10  1 17 14 22 13  5 14 23
       + 14 17  0 13  6  4 14 17  0 13  6  4 14 17  0 13
       -------------------------------------------------
         33 24  4 29 26 12 16 27  1 30 20 26 27 22 14 36

(mod 26)  7 24  4  3  0 12 16  1  1  4 20  0  1 22 14 10

Ciphertext:
HYEDAMQBBEUABWOK

Subtract the key, add 26, then mod 26 to decrypt.

Cryptanalysis

By guessing the length of the key, a Vigenère cipher can be broken down into a set of Caesar ciphers, each of which can be cracked with basic statistical analysis. If the key length is 5, then the 1st, 6th, 11th, ... letters are one Caesar cipher, the 2nd, 7th, 12th, ... letters are another, and so on.

The Nyquist–Shannon sampling theorem is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth.

polyalphabetic_QXcRpk

The flag:

polyalphabetic_QXcRpk