Lecture 8-Public Key Cryptography/RSA

Question 1

What is the importance of modular inversion?

Answer 1

If an inverse of an element in set Zn exists, then the function is invertible

Question 2

What is Fermat’s Theorem?

Answer 2

A way to compute inverses but only works on prime numbers

Question 3

What is Euler’s generalization of fermat’s?

Answer 3

It is the basis of RSA cryptography (what you coded)

Question 4

What is a hard problem to solve in the RSA case?

Answer 4

Dlog(discrete log). Given g^x compute x in Zp

Question 5

What is a trapdoor function?

Answer 5

A way to revert a public key encryption using a secret key

Question 6

How does PK encryption from TDF work?

Answer 6

Apply trapdoor function to a random value x using public key. Then hash x to create the key you use to encrypt the message. Results in output(y,c) where c is ciphertext and y is the output of trapdoor function. When you decrypt, use y on inverse of the trapdoor function applied and use secret key to get x back. Then hash x again to get the key. Use that key with the ciphertext to decrypt message

Question 7

What proves that the PK encryption from TDF is secure?

Answer 7

If Trapdoor is a secure TDF, The symmetric encryption algorithm provides authenticated encryption, and the hash is random

Question 8

Why is RSA Trapdoor function secure?

Answer 8

Easy to go from m to m^e mod N and hard to go the other way (easy only if d is known)