Modern Cipher

Information Security
BS_CS 6th
 Modern Block Ciphers
• will now look at modern block ciphers
• one of the most widely used types of cryptographic algorithms
• provide secrecy and/or authentication services
• in particular will introduce DES (Data Encryption Standard)
 Block vs Stream Ciphers
• block ciphers process messages in into 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
• hence are focus of course
 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
 Claude Shannon and Substitution-Permutation
Ciphers
• in 1949 Claude Shannon introduced idea of substitution-permutation (S-P)
networks
• modern substitution-transposition product cipher
• these form the basis of modern block ciphers
• S-P networks are based on the two primitive cryptographic operations we have seen
before:
• substitution (S-box)
• permutation (P-box)
• provide confusion and diffusion of message
 Confusion and Diffusion
• cipher needs to completely obscure statistical properties of original message
a one-time pad does this
• more practically Shannon suggested combining 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
• 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
• then have permutation swapping halves
• implements Shannon’s substitution-permutation network concept
Feistel Cipher Structure
 Feistel Cipher Design Principles
• 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
• greater complexity can make analysis harder, but slows cipher
• Round function
• greater complexity can make analysis harder, but slows cipher
• Fast software en/decryption & ease of analysis
• are more recent concerns for practical use and testing
 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
• IBM developed Lucifer cipher
• by team led by Feistel
• 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
• 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
• DES has become widely used, esp in financial applications
DES Encryption
 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)
• see text Table 3.2
• example:
IP(675a6967 5e5a6b5a) = (ffb2194d 004df6fb)
 DES Round Structure
• uses two 32-bit L & R halves
• as for any Feistel cipher can describe as:
Li = Ri–1
Ri = Li–1 xor F(Ri–1, Ki)
• takes 32-bit R half and 48-bit subkey and:
• expands R to 48-bits using perm E
• adds to subkey
• passes through 8 S-boxes to get 32-bit result
• finally permutes this using 32-bit perm P
DES Round Structure
 Substitution Boxes S
• have eight S-boxes which map 6 to 4 bits
• each S-box is actually 4 little 4 bit boxes
• outer bits 1 & 6 (row bits) select one rows
• inner bits 2-5 (col bits) are substituted
• result is 8 lots of 4 bits, or 32 bits
• row selection depends on both data & key
• feature known as autoclaving (autokeying)
• example:
S(18 09 12 3d 11 17 38 39) = 5fd25e03
 DES Key Schedule
• forms subkeys used in each round
• consists of:
• initial permutation of the key (PC1) which selects 56-bits in two 28-bit halves
• 16 stages consisting of:
• selecting 24-bits from each half
• permuting them by PC2 for use in function f,
• rotating each half separately either 1 or 2 places depending on the key rotation schedule
K
 DES Decryption
• decrypt must unwind steps of data computation
• with Feistel design, do encryption steps again
• using subkeys in reverse order (SK16 … SK1)
• note that IP undoes final FP step of encryption
• 1st round with SK16 undoes 16th encrypt round
• ….
• 16th round with SK1 undoes 1st encrypt round
• then final FP undoes initial encryption IP
• thus recovering original data value
 Avalanche Effect
• key desirable property of encryption alg
• 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
• 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
• now considering alternatives to DES
 Strength of DES – Timing Attacks

• attacks actual implementation of cipher

• use knowledge of consequences of implementation to derive knowledge of
some/all subkey bits
• specifically use fact that calculations can take varying times depending on the
value of the inputs to it
• particularly problematic on smartcards
 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
 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 1990
• 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
• 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 values of
the key
• Differential Cryptanalysis compares two related 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
• 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
• 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
• 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 247 known plaintexts, still in practise infeasible
 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–½|
 Block Cipher Design Principles
• basic principles still like Feistel in 1970’s
• number of rounds
• more is better, exhaustive search best attack
• function f:
• provides “confusion”, is nonlinear, avalanche
• key schedule
• complex subkey creation, key avalanche
 Modes of Operation
• block ciphers encrypt fixed size blocks
• eg. DES encrypts 64-bit blocks, with 56-bit key
• need way to use in practise, given usually have arbitrary amount of
information to encrypt
• four were defined for DES in ANSI standard ANSI X3.106-1983 Modes of
Use
• subsequently now have 5 for DES and AES
• have block and stream modes
 Electronic
• message Codebook
is broken into Book
independent blocks which (ECB)
are encrypted
• each block is a value which is substituted, like a codebook, hence
name
• each block is encoded independently of the other blocks
Ci = DESK1 (Pi)
• uses: secure transmission of single values
Electronic Codebook Book (ECB)
 Advantages and Limitations of ECB

• repetitions in message may show in ciphertext

• if aligned with message block
• particularly with data such graphics
• or with messages that change very little, which become a code-book analysis problem
• weakness due to encrypted message blocks being independent
• main use is sending a few blocks of data
 Cipher Block Chaining (CBC)
• message is broken into blocks
• but these are linked together in the encryption operation
• each previous cipher blocks is chained with current plaintext block, hence
name
• use Initial Vector (IV) to start process
Ci = DESK1(Pi XOR Ci-1)
C-1 = IV
• uses: bulk data encryption, authentication
Cipher Block Chaining (CBC)
 Advantages and Limitations of CBC
• each ciphertext block depends on all message blocks
• thus a change in the message affects all ciphertext blocks after the change as well as the original
block
• need Initial Value (IV) known to sender & receiver
• however if IV is sent in the clear, an attacker can change bits of the first block, and change IV to compensate
• hence either IV must be a fixed value (as in EFTPOS) or it must be sent encrypted in ECB mode before rest
of message
• at end of message, handle possible last short block
• by padding either with known non-data value (eg nulls)
• or pad last block with count of pad size
• eg. [ b1 b2 b3 0 0 0 0 5] <- 3 data bytes, then 5 bytes pad+count
 Cipher FeedBack (CFB)
• message is treated as a stream of bits
• added to the output of the block cipher
• result is feed back for next stage (hence name)
• standard allows any number of bit (1,8 or 64 or whatever) to be feed back
• denoted CFB-1, CFB-8, CFB-64 etc
• is most efficient to use all 64 bits (CFB-64)
Ci = Pi XOR DESK1(Ci-1)
C-1 = IV
• uses: stream data encryption, authentication
Cipher FeedBack (CFB)
 Advantages and Limitations of CFB

• appropriate when data arrives in bits/bytes

• most common stream mode
• limitation is need to stall while do block encryption after every n-bits
• note that the block cipher is used in encryption mode at both ends
• errors propogate for several blocks after the error
 Output FeedBack (OFB)
• message is treated as a stream of bits
• output of cipher is added to message
• output is then feed back (hence name)
• feedback is independent of message
• can be computed in advance
Ci = Pi XOR Oi
Oi = DESK1(Oi-1)
O-1 = IV
• uses: stream encryption over noisy channels
Output FeedBack (OFB)
 Advantages and Limitations of OFB
• used when error feedback a problem or where need to encryptions before message is
available
• superficially similar to CFB
• but feedback is from the output of cipher and is independent of message
• a variation of a Vernam cipher
• hence must never reuse the same sequence (key+IV)
• sender and receiver must remain in sync, and some recovery method is needed to ensure this
occurs
• originally specified with m-bit feedback in the standards
• subsequent research has shown that only OFB-64 should ever be used
 Counter (CTR)
• a “new” mode, though proposed early on
• similar to OFB but encrypts counter value rather than any feedback value
• must have a different key & counter value for every plaintext block (never
reused)
Ci = Pi XOR Oi
Oi = DESK1(i)
• uses: high-speed network encryptions
Counter (CTR)
 Advantages and Limitations of CTR

• efficiency
• can do parallel encryptions
• in advance of need
• good for bursty high speed links
• random access to encrypted data blocks
• provable security (good as other modes)
• but must ensure never reuse key/counter values, otherwise could break (cf OFB)
 Summary
• have considered:
• block cipher design principles
• DES
• details
• strength
• Differential & Linear Cryptanalysis
• Modes of Operation
• ECB, CBC, CFB, OFB, CTR