Lecture 6: Symmetric Key Encryption, PRG

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Intro to Block Ciphers

As we'll see later in the class, everytime you use the internet you're using block ciphers! The most common block cipher used today is called AES which we'll discuss in a bit.

Fun fact: Prof. Wagner was part of the team that came up with a block cipher called TwoFish which was one of the top 5 block cipher designs chosen internationally when NIST was attempting to find a standard.

Random Functions and Permutations

(True/False) A Gaussian distribution is considered random

False. A Gaussian distribution has a bias towards it’s mean. We consider the Uniform distribution to be random.

How many bits would it take to represent a truth table of a random permutation with input length of n bits?

2^n * 2n. There are 2^n entries each of length 2n. Notice, that for something like n=128 this is more space than all the computers in the world combined have! Thus, it’s not feasible to use actual random functions so we’ll need to use something that’s ‘pseudorandom’ or ‘looks like’ a random function.

Block Cipher Security

What does a block cipher need to computationally indistinguishable from in order to be considered secure? (Computationally indistinguishable means an efficient (ie. polynomial time) attacker can't distinguish)

A random permutation. If this is true, we call a block cipher ‘pseudo-random’.

Why Only Efficient Attackers?

Which input could an unbounded attacker brute force to win the block cipher distinguishing game?

The secret key

Information Leakage of a Block Cipher

If an adversary could learn first bit of M when given E(K, M) where E is encryption for a secure block cipher, how would this lead to a contradiction?

Because this would allow the attacker to distinguish the block cipher from a random function which contradicts our security assumption about block ciphers. This type of contradiction argument is called a reduction and is very common when proving security of cryptographic schemes.

Overview of AES

If you could prove a block cipher was unconditionally secure, what else would you likely prove in the process?

That P!=NP (Don’t worry if you don’t know what this means - but it’s very significant in theoretical computer science!)

ECB Mode

Which property of ECB Mode makes it not IND-CPA secure?

It’s deterministic

CBC Mode

Which property must a block cipher have in order for CBC to be decryptable?

It must be bijective ie. invertible

CBC Security and Pseudo-Random Number Generators (PRNGs/PRGs)

What undesirable property would CBC mode have if we always picked the same IV?

It would become deterministic

Where might computer hardware get sources of weak randomness?

Environment (e.g. temperature), network traffic, key presses, etc.

CTR Mode

(True/False) CTR mode also relies on a block cipher being invertible in order to be decryptable

False. CTR mode never needs to use block cipher decryption since the message is never run through the block cipher.

CTR Security

(True/False) Like CBC mode, in CTR mode the nonce must be chosen randomly

False. We only need to guarantee that the same nonce isn’t used for different messages since the block cipher provides the randomness we need.

Padding

Would appending a sequence of alternating bits (ie. 101010) be a valid padding scheme?

No. A message might end in 10 and you would accidently remove it when stripping the padding

PRGs

(True/False) A block cipher is a type of PRG

False. A PRGs output is much longer than it’s input. Since a block cipher is a permutation its input and output sizes are the same. However, we can use a block cipher to build PRGs using block cipher modes like we’ve seen.