Decrypt the ciphertext DGFEH LDJNE DNPOF DEFHV LU encrypted using a polyalphabetic cipher that a

Decrypt the ciphertext DGFEH LDJNE DNPOF DEFHV LU encrypted...

Key Concepts

Affine Cipher

An affine cipher is a type of substitution cipher where each letter in the plaintext is mapped to its numeric equivalent, transformed using a linear function of the form f(x) = ax + b modulo m, and then converted back to a letter. Its security relies on the multiplicative part 'a' having an inverse modulo m, which is used in decryption to reverse the process.

Polyalphabetic Cipher

A polyalphabetic cipher uses multiple cipher alphabets to encrypt a message, switching between different encryption functions during the encryption process. This cycling through different schemes makes frequency analysis more difficult, increasing resistance to simple cryptanalytic attacks compared to monoalphabetic ciphers.

Modular Arithmetic

Modular arithmetic is a system of arithmetic for integers, where numbers wrap around upon reaching a certain value, the modulus. In cryptography, it ensures that all arithmetic operations, such as those in affine ciphers, yield results that map correctly within a fixed range, typically corresponding to the number of letters in the alphabet.

Decryption Process with Inverses

Decryption of ciphers like the affine cipher involves determining the inverse of the encryption function, particularly by finding the modular multiplicative inverse of the key coefficient. This inverse allows the decryption function to reverse the encryption mapping and recover the original plaintext.

Cipher Alternation Pattern

In polyalphabetic ciphers, the alternation or cycling through different encryption functions (such as different affine ciphers) follows a set pattern. Understanding and identifying this pattern is essential for accurate decryption, as it dictates which inverse function to apply at each stage of the decryption process.

Transcript

00:01 Okay, so for this one, we're told we have some encrypted messages that were encrypted using the cipher p plus 10 mod 26.

00:17 And now this was the encryption cipher.

00:20 So to decrypt it, we need to undo that, right? so we're going to use the decryption cipher p minus 10 mod 26.

00:42 All right, so for a, are given.

00:45 Message is c, e, b, ox, n -o -b, x, y, and g.

01:04 Okay, so first we need to convert that into numerics, where a equals zero, b equals one, c equals two, okay, so the c is going to be equal to two, e is four, one, one, 14, 23, 13, 14, and 1.

01:37 And we'll get 23, 24, and 6.

01:45 So now we can run it through our algorithm where we take the number, subtract 10, and then take mod 26, right? so 2 minus 10 would be negative 8, mod 26, which is really 18.

01:59 All right, so now we'll convert it into those numbers.

02:04 So we get 18.

02:06 Same thing here.

02:07 We get negative 6 mod 26.

02:08 So that would be 20.

02:12 Okay.

02:13 Then we get 17, 17, 4, 13, 3, 4, 17, 17, 13, 13, 14, and 22.

02:35 And then we just need to translate that back into the alphabet.

02:39 So this is going to be an s, u, r, r, r, e, n, d, e, r, n -o -w.

02:53 Spooky.

02:54 It says, surrender now.

02:57 It's probably how some of this homework makes you feel...