1. Block cipher and modes of encryptions

2. Block cipher
Other name for fixed-length encryption scheme

3. Problem with just encrypting each block of the message using a randomized encryption scheme
Each block uses k bits of randomness
If we have 𝑑 blocks, it requires 𝑑𝑘 bits of randomness.
Randomness is expensive

4. Solution to minimize randomness
Create an initial state
May use some randomness (called Nonce or IV).
Encrypt the current block using the current state
Update the state after each use of the block cipher

5. Goals (block cipher) Security
Is it secure?
What level of security does it have?
Parallelizable: Can we encrypt/decrypt each block in parallel
We don’t need to wait for the previous part to encrypt the next part.
Forward: Do we need to use decryption operation
Better if we don’t
Error-resilient: If one block of the ciphertext becomes corrupted

6. ECB mode 𝐼𝑛𝑖𝑡() 𝑂𝑢𝑡𝑝𝑢𝑡 𝑚 𝑖 , 𝑆 𝑖 𝑈𝑝𝑑𝑎𝑡𝑒( 𝑚 𝑖 , 𝑠 𝑖 ) 𝑆 1 ←0
𝑂𝑢𝑡𝑝𝑢𝑡 𝑚 𝑖 , 𝑆 𝑖
𝑐 𝑖 ←𝐸𝑛 𝑐 𝑘 ( 𝑚 𝑖 )
𝑈𝑝𝑑𝑎𝑡𝑒( 𝑚 𝑖 , 𝑠 𝑖 )
𝑆 𝑖+1 ← 𝑆 𝑖

7. Electronic codebook mode (ECB)

8. Electronic codebook mode (ECB)
Secure?
Parallelizable
Forward
Error-resilient No
yes no
Unless the plaintext has high entropy.

9. Problem with ECB mode

10. Counter mode (CM) 𝐼𝑛𝑖𝑡() 𝑂𝑢𝑡𝑝𝑢𝑡 𝑚 𝑖 , 𝑆 𝑖 𝑈𝑝𝑑𝑎𝑡𝑒 𝑚 𝑖 , 𝑠 𝑖
𝑛𝑜𝑛𝑐𝑒 ∈ 𝑅 0,1 𝑠/2
𝑆 1 ←(𝑛𝑜𝑛𝑐𝑒, 0 𝑠/2 )
𝑂𝑢𝑡𝑝𝑢𝑡 𝑚 𝑖 , 𝑆 𝑖
𝑐 𝑖 ←𝐸𝑛 𝑐 𝑘 𝑆 𝑖 ⊕ 𝑚 𝑖
𝑈𝑝𝑑𝑎𝑡𝑒 𝑚 𝑖 , 𝑠 𝑖
𝑠 𝑖+1 ← 𝑠 𝑖 +1

11. Counter mode (CM)

12. IV security reduced by half
Counter mode
Secure?
Parallelizable
Forward
Error-resilient
Yes but
yes
IV security reduced by half

13. Cipher block chaining 𝐼𝑛𝑖𝑡() 𝑂𝑢𝑡𝑝𝑢𝑡 𝑚 𝑖 , 𝑆 𝑖 𝑈𝑝𝑑𝑎𝑡𝑒 𝑚 𝑖 , 𝑠 𝑖
𝐼𝑉 ∈ 𝑅 0,1 𝑠
𝑆 1 ←𝐼𝑉
𝑂𝑢𝑡𝑝𝑢𝑡 𝑚 𝑖 , 𝑆 𝑖
𝑐 𝑖 ←𝐸𝑛 𝑐 𝑘 𝑚 𝑖 ⊕ 𝑆 𝑖
𝑈𝑝𝑑𝑎𝑡𝑒 𝑚 𝑖 , 𝑠 𝑖
𝑠 𝑖+1 ← 𝑐 𝑖

14. Cipher block chaining (CBC)

15. Cipher block chaining Secure? Parallelizable Forward Error-resilient
Yes no