Inverse Functions
To determine if a function has an inverse from its graph, we use this test:
Horizontal Line Test
Let f(x)=2x-12 (mod 26). Find f(4).
22
A number a will have a inverse modulo n if…
a and n are relatively prime
What category of function do we use for the Affine function?
What is the name of the location where the allied codebreakers met during WWII?
In order to find an inverse function we…(3 words)
Switch and Solve
Is f(g(x)) necessarily equal to g(f(x))?
No
Name two numbers that are NOT relatively prime.
Answers vary.
How many different possible keys are there for the Affine Cipher?
312
Who came up with the best design for the rotor machine?
Arthur Scherbius
Give an example of a function that does not have an inverse
Answers vary
Let f(x)=x^2-4x+8 . Find f(10) mod 26
16
What is the inverse of 3 modulo 11?
4
Name one value that cannot be used for alpha in the key for an Affine Cipher.
Any even number or 13
What are all the components of the key for the Enigma?
rotors, starting positions of the rotors, plugboard settings
Find the inverse of the function f(x)=1/x + 3
f^-1(x)=1/(x-3)
Let f(x) = 3x-1 and g(x)=x^2+2. Find g(f(x)).
9x^2-6x+3
How many different numbers have an inverse mod 26?
12
What is the decryption function for the encryption function with key (15, 19)?
D(x)=7x+23(mod26)
Assuming a plugboard cable is connected to a letter, how many times does the letter change before it lights up on the lampboard?
8
Why do we need inverse functions for cryptography?
To find decryption functions
Let f(x)=x^3, g(x)=9x-2, and h(x)=x^2 +7. Find h(g(f(-2))).
5483
What is the inverse of 8 modulo 43?
27
Encrypt the word “autumn” using the key (9, 3)
DBSBHQ
How many possible combinations are there for the plugboard when 3 cables are used?
3453450