# Cryptography and Network Security

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## Presentation Transcript

### Cryptography and Network Security :

Cryptography and Network Security Block Ciphers and Data Encryption Standard (DES)

### Modern Block Ciphers :

Modern Block Ciphers now look at modern block ciphers one of the most widely used types of cryptographic algorithms provide secrecy /authentication services focus on DES (Data Encryption Standard) to illustrate block cipher design principles

### Block vs Stream Ciphers :

Block vs Stream Ciphers block ciphers process messages in blocks, each of which is then en/decrypted like a substitution on very big characters 64-bits or more stream ciphers process messages a bit or byte at a time when en/decrypting many current ciphers are block ciphers broader range of applications

### Block Cipher Principles :

Block Cipher Principles most symmetric block ciphers are based on a Feistel Cipher Structure needed since must be able to decrypt ciphertext to recover messages efficiently block ciphers look like an extremely large substitution would need table of 264 entries for a 64-bit block instead create from smaller building blocks using idea of a product cipher

### Ideal Block Cipher :

Ideal Block Cipher

### Claude Shannon and Substitution-Permutation Ciphers :

Claude Shannon and Substitution-Permutation Ciphers Claude Shannon introduced idea of substitution-permutation (S-P) networks in 1949 paper form basis of modern block ciphers S-P nets are based on the two primitive cryptographic operations seen before: substitution (S-box) permutation (P-box) provide confusion & diffusion of message & key

### Confusion and Diffusion :

Confusion and Diffusion cipher needs to completely obscure statistical properties of original message a one-time pad does this more practically Shannon suggested combining S & P elements to obtain: diffusion – dissipates statistical structure of plaintext over bulk of ciphertext confusion – makes relationship between ciphertext and key as complex as possible

### Feistel Cipher Structure :

Feistel Cipher Structure Horst Feistel devised the feistel cipher based on concept of invertible product cipher partitions input block into two halves process through multiple rounds which perform a substitution on left data half, based on round function of right half & subkey and then have permutation swapping halves implements Shannon’s S-P net concept

### Feistel Cipher Structure :

Feistel Cipher Structure

### Feistel Cipher Design Elements :

Feistel Cipher Design Elements block size - increasing size improves security, but slows cipher key size - increasing size improves security, makes exhaustive key searching harder, but may slow cipher number of rounds - increasing number improves security, but slows cipher subkey generation algorithm - greater complexity can make analysis harder, but slows cipher round function - greater complexity can make analysis harder, but slows cipher fast software en/decryption – preclude hardware implementation ease of analysis – must be difficult to analyze the algorithm i.e. DES

### Feistel Cipher Decryption :

Feistel Cipher Decryption

### Feistel Cipher En/Decryption :

Feistel Cipher En/Decryption For encryption: LEi = REi-1 REi = LEi-1 X F(REi-1, Ki) For decryption: REi-1 = LEi LEi-1 = REi X F(REi-1, Ki) = REi X F(LEi, Ki)

### Data Encryption Standard (DES) :

Data Encryption Standard (DES) most widely used block cipher in world adopted in 1977 by NBS (now NIST) as FIPS PUB 46 encrypts 64-bit data using 56-bit key has widespread use has been considerable controversy over its security

### DES History :

DES History IBM developed Lucifer cipher by team led by Feistel in late 60’s used 64-bit data blocks with 128-bit key then redeveloped as a commercial cipher with input from NSA and others in 1973 NBS issued request for proposals for a national cipher standard IBM submitted their revised Lucifer which was eventually accepted as the DES

### DES Design Controversy :

DES Design Controversy although DES standard is public was considerable controversy over design in choice of 56-bit key (vs Lucifer 128-bit) and because design criteria were classified subsequent events and public analysis show in fact design was appropriate use of DES has flourished especially in financial applications still standardised for legacy application use

### DES Encryption Overview :

DES Encryption Overview

### Initial Permutation IP :

Initial Permutation IP first step of the data computation IP reorders the input data bits even bits to LH half, odd bits to RH half quite regular in structure (easy in h/w)

### DES Round Structure :

DES Round Structure uses two 32-bit L & R halves as for any Feistel cipher can describe as: Li = Ri–1 Ri = Li–1 ? F(Ri–1, Ki) F takes 32-bit R half and 48-bit subkey: expands R to 48-bits using perm E adds to subkey using XOR passes through 8 S-boxes to get 32-bit result finally permutes using 32-bit perm P

### DES Round Structure :

DES Round Structure

### DES Key Schedule :

DES Key Schedule forms subkeys used in each round initial permutation of the key (PC1) which selects 56-bits in two 28-bit halves 16 stages consisting of: rotating each half separately either 1 or 2 places depending on the key rotation schedule K selecting 24-bits from each half & permuting them by PC2 for use in round function F

### Avalanche Effect :

Avalanche Effect key desirable property of encryption algorithm where a change of one input or key bit results in changing approx half output bits making attempts to “home-in” by guessing keys impossible DES exhibits strong avalanche

### Strength of DES – Key Size :

Strength of DES – Key Size 56-bit keys have 256 = 7.2 x 1016 values brute force search looks hard recent advances have shown is possible in 1997 on Internet in a few months in 1998 on dedicated h/w (EFF) in a few days in 1999 above combined in 22hrs! still must be able to recognize plaintext must now consider alternatives to DES

### Strength of DES – Analytic Attacks :

Strength of DES – Analytic Attacks now have several analytic attacks on DES these utilise some deep structure of the cipher by gathering information about encryptions can eventually recover some/all of the sub-key bits if necessary then exhaustively search for the rest generally these are statistical attacks include differential cryptanalysis linear cryptanalysis related key attacks

### Strength of DES – Timing Attacks :

Strength of DES – Timing Attacks A timing attack is one in which information about the key or the plaintext is obtained by observing how long it takes a given implementation to perform decryptions on various ciphertexts. A timing attack exploits the fact that an encryption or decryption algorithm often takes slightly different amounts of time on different inputs. The AES analysis process has highlighted this attack approach, and showed that it is a concern particularly with smartcard implementations. DES appears to be fairly resistant to a successful timing attack.

### Differential Cryptanalysis :

Differential Cryptanalysis one of the most significant recent (public) advances in cryptanalysis known by NSA in 70's cf DES design Murphy, Biham & Shamir published in 90’s powerful method to analyse block ciphers used to analyse most current block ciphers with varying degrees of success DES reasonably resistant to it, cf Lucifer

### Differential Cryptanalysis :

Differential Cryptanalysis a statistical attack against Feistel ciphers uses cipher structure not previously used design of S-P networks has output of function f influenced by both input & key hence cannot trace values back through cipher without knowing value of the key differential cryptanalysis compares two related pairs of encryptions

### Differential Cryptanalysis Compares Pairs of Encryptions :

Differential Cryptanalysis Compares Pairs of Encryptions with a known difference in the input searching for a known difference in output when same subkeys are used

### Differential Cryptanalysis :

Differential Cryptanalysis have some input difference giving some output difference with probability p if find instances of some higher probability input / output difference pairs occurring can infer subkey that was used in round then must iterate process over many rounds (with decreasing probabilities)

### Differential Cryptanalysis :

Differential Cryptanalysis

### Differential Cryptanalysis :

Differential Cryptanalysis perform attack by repeatedly encrypting plaintext pairs with known input XOR until obtain desired output XOR when found if intermediate rounds match required XOR have a right pair if not then have a wrong pair, relative ratio is S/N for attack can then deduce keys values for the rounds right pairs suggest same key bits wrong pairs give random values for large numbers of rounds, probability is so low that more pairs are required than exist with 64-bit inputs Biham and Shamir have shown how a 13-round iterated characteristic can break the full 16-round DES

### Linear Cryptanalysis :

Linear Cryptanalysis another recent development also a statistical method must be iterated over rounds, with decreasing probabilities developed by Matsui et al in early 90's based on finding linear approximations can attack DES with 243 known plaintexts, easier but still in practise infeasible

### Linear Cryptanalysis :

Linear Cryptanalysis find linear approximations with prob p != ½ P[i1,i2,...,ia] ? C[j1,j2,...,jb] = K[k1,k2,...,kc] where ia,jb,kc are bit locations in P,C,K gives linear equation for key bits get one key bit using max likelihood alg using a large number of trial encryptions effectiveness given by: |p–1/2|

### DES Design Criteria :

DES Design Criteria as reported by Coppersmith in [COPP94] 7 criteria for S-boxes provide for non-linearity resistance to differential cryptanalysis good confusion 3 criteria for permutation P provide for increased diffusion

### Block Cipher Design :

Block Cipher Design basic principles still like Feistel’s in 1970’s number of rounds more is better, exhaustive search best attack function f: provides “confusion”, is nonlinear, avalanche have issues of how S-boxes are selected key schedule complex subkey creation, key avalanche

### Summary :

Summary have considered: block vs stream ciphers Feistel cipher design & structure DES details strength Differential & Linear Cryptanalysis block cipher design principles