CSCI971 - Modern Cryptography Week 3

How to construct symmetric key encription

We will use computer complexity and check if scheme is secure

Roadmap Classic Cipher = Ceaser Cipher (algo based) One time pad = Shannon

How to design a block cipher

Confusion and Diffusion: Design Principles

Confusion = if a single bit key is changed, cypher text is significantly different Diffusion = if a single bit in plaintext is changed, cypher text is significantly different

Change in plain text and and key result significant change in cypher text

This is called avalanche effect

Block Cipher Message -> Enc(key) -> Cipher -> Dec(key) -> Message

Typical block size 64 bits 128 bits

Common Design Approaches iterated cipher => each iteration is called round. The output of each round is input to next round

DES = 16 rounds AES = 10 rounds

Each Round inside AES is: Subsitution Permutation network

DES (Data Encryption Standard)

why it is developed 1970 need standard encryption scheme

Standard need to have following properties

• high level security
• accordance with Kirchoff’s law
• economic
• adaptable

DES (64 bit input, 64 bit output, 56 bit key)

16 round Feistel Network

Feistel Network

introduced by Feistel

how it work

original input - divide into two part L0- 32 bit R0 - 32 bit

(check week 3 slides) R1 = R0 -> F(K) -> XOR L0 L1 = R0

Last Round

LN = R(N-1) RN = R(N-1) -> F(K) -> XOR L(N-1)

S-box

An S-box is a basic component in symmetric key algorithms, used to perform substitution. It takes an input of a fixed size (a string of bits) and transforms it into an output of a fixed size. This substitution process is nonlinear, which is essential for the cryptographic strength of the algorithm

Des shortcomming 2^56 keys = 10^17 keys (very short range keys)

we can test keys in parallel

3DES

AES (Good enough for today) (I think there was a video in youtube) Does not use Feistel

Is a blockcipher a secure symmetric-key encryption NO

it preserve statistacilly property of plain text (if you use it directly)

cypher text space should be much larger than plain text

Solution Randomize Choose ramdom IV M’ = IV XoR M C <- Enc(K,M’)

We say that the encryption is secure if no P.P.T adversary can win with a probability of ½+1/poly(λ)

The underlying blockcipher is assumed to be a pseudorandom function (PRF), i.e., outputs of the blockcipher is indistinguishable from random values.

Encrypt long message

Electronic Code Book Divide in block run cypher

CBC (Cypher block chain) Initialize vector

CFB (Cypher Feedback ) Cypher of one block use as input to other not IV

Output feedback mode (OFB)

Lecture 3