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# DATA ENCRYPTION

STANDARD
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 CIPHERS
A block cipher operates on a plaintext block of n bits to
produce a ciphertext block of n bits.
A block cipher is an encryption/decryption scheme in which a
block of plaintext is treated as a whole and used to produce a
ciphertext block of equal length
Typically, a block size of 64 or 128 bits is used
FEISTEL CIPHER STRUCTURE
It is a design model
A cryptographic system based on Feistel cipher
structure uses the same algorithm for both encryption
and decryption.
BLOCK CIPHER PRINCIPLES
most symmetric block ciphers are based
on a Feistel Cipher Structure
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
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:
(S-box)
substitution
permutation (P-box)
provide confusion & diffusion of message
& key
CONFUSION AND DIFFUSION
cipher needs to be completely obscure statistical
properties of original message
a one-time pad does this
more practically Shannon suggested combining S & P
elements to obtain:
In diffusion, the statistical structure of the plaintext is
dissipated into long-range statistics of the ciphertext.
This is achieved by having each plaintext digit affect
the value of many ciphertext digits; generally, this is
equivalent to having each ciphertext digit be affected by
many plaintext digits
On the other hand, confusion seeks to make the
relationship between the statistics of the ciphertext
and the value of the encryption key as complex as
possible, again to thwart attempts to discover the key.
Thus, even if the attacker can get some handle on the
statistics of the ciphertext, the way in which the key
was used to produce that ciphertext is so complex as to
make it difficult to deduce the key. This is achieved by
the use of a complex substitution algorithm.
FEISTEL CIPHER ENCRYPTION
The input block to each round is divided into two halves
that can be denoted as L and R for the left half and the
right half.
In each round, the right half of the block, R, goes through

## unchanged. But the left half, L, goes through an operation

that depends on R and the encryption key. First, we apply
an encrypting function f that takes two input the key K
and R. The function produces the output f(R,K). Then, we
XOR the output of the mathematical function with L.
In real implementation of the Feistel Cipher, such as DES,

## instead of using the whole encryption key during each

round, a round-dependent key (a subkey) is derived from
the encryption key. This means that each round uses a
different key, although all these subkeys are related to the
original key.
The permutation step at the end of each round
swaps the modified L and unmodified R.
Therefore, the L for the next round would be R of
the current round. And R for the next round be
the output L of the current round.
Above substitution and permutation steps form a
round. The number of rounds are specified by
the algorithm design.
Once the last round is completed then the two
sub blocks, R and L are concatenated in this
order to form the ciphertext block.
FEISTEL CIPHER STRUCTURE
FEISTEL CIPHER DESIGN ELEMENTS
block size
key size
number of rounds
subkey generation algorithm
round function
fast software en/decryption
ease of analysis
FEISTEL CIPHER DECRYPTION
FEISTEL CIPHER DECRYPTION
The process of decryption with a Feistel cipher is
essentially the same as the encryption process.
The rule is as follows: Use the ciphertext as input
to the algorithm, but use the subkeys Ki in
reverse order.
That is, use Kn in the first round, Kn1 in the
second round, and so on until K1 is used in the
last round.
This is a nice feature because it means we need
not implement two different algorithms, one for
encryption and one for decryption.
DATA ENCRYPTION
STANDARD (DES)
most widely used block cipher in world
DES is an implementation of a Feistel Cipher.
It uses 16 round Feistel structure.
The block size is 64-bit.
Though, key length is 64-bit, DES has an effective key
length of 56 bits, since 8 of the 64 bits of the key are not
used by the encryption algorithm
adopted in 1977 by NBS (now NIST)
as FIPS PUB 46
DES HISTORY
IBM developed Lucifer cipher
by team led by Feistel in late 60s
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 ENCRYPTION OVERVIEW
STEPS:LEFT-HAND SIDE OF THE
FIGURE
The processing of the plaintext proceeds in three phases.

## First, the 64-bit plaintext passes through an initial

permutation (IP) that rearranges the bits to produce the
permuted input.
This is followed by a phase consisting of sixteen rounds

## of the same function, which involves both permutation

and substitution functions.
The output of the last (sixteenth) round consists of 64

## bits that are a function of the input plaintext and the

key. The left and right halves of the output are swapped
to produce the preoutput.
Finally, the preoutput is passed through a permutation

## that is the inverse of the initial permutation function, to

produce the 64-bit ciphertext.
STEPS: RIGHT-HAND SIDE OF THE
FIGURE
Initially, the key is passed through a permutation
function.
Then, for each of the sixteen rounds, a subkey (Ki ) is
produced by the combination of a left circular shift and a
permutation.
The permutation function is the same for each round, but
a different sub key is produced because of the repeated
shifts of the key bits.
INITIAL PERMUTATION IP
first step of the data computation
IP reorders the input data bits

example:

## IP(675a6967 5e5a6b5a) = (ffb2194d

004df6fb)
INITIAL PERMUTATION
DETAILS OF SINGLE ROUND
DES ROUND STRUCTURE
uses two 32-bit L & R halves
as for any Feistel cipher can describe as:
Li = Ri1
Ri = Li1 F(Ri1, 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
SUBSTITUTION BOXES S
have eight S-boxes which map 6 to 4 bits
The first and last bits of the input to box form a 2-bit
binary number to select one of four substitutions
defined by the four rows.
The middle four bits select one of the sixteen columns.
The decimal value in the cell selected by the row and
column is then converted to its 4-bit representation to
produce the output.
For example, in S1, for input 011001, the row is 01 (row
1) and the column is 1100 (column 12).The value in row
1, column 12 is 9, so the output is 1001.
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

note practical use issues in h/w vs s/w
DES DECRYPTION
decryption must unwind steps of data
computation
with Feistel design, do encryption steps again
using subkeys in reverse order (SK16 SK1)
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
must now consider alternatives to DES
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
differentialcryptanalysis
linear cryptanalysis
related key attacks
STRENGTH OF DES TIMING
ATTACKS
attacks actual implementation of cipher
use knowledge of consequences of
implementation to derive information about
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
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 90s
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 value of the key
differential cryptanalysis compares two related
pairs of encryptions
DIFFERENTIAL
CRYPTANALYSIS COMPARES
PAIRS OF difference
with a known ENCRYPTIONS
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 243 known plaintexts, easier
but still in practise infeasible
LINEAR CRYPTANALYSIS
find linear approximations with prob p !=
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

## effectiveness given by: |p1/2|

DES DESIGN CRITERIA
as reported by Coppersmith in [COPP94]
7 criteria for S-boxes provide for
non-linearity
resistanceto differential cryptanalysis
good confusion
3 criteria for permutation P provide for
increased diffusion
BLOCK CIPHER DESIGN
basic principles still like Feistels in 1970s
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
ADVANCED
ENCRYPTION
STANDARD
ORIGINS
clear a replacement for DES was needed
have theoretical attacks that can break it
have demonstrated exhaustive key search attacks
can use Triple-DES but slow, has small
blocks
US NIST issued call for ciphers in 1997
15 candidates accepted in Jun 98
5 were shortlisted in Aug-99
Rijndael was selected as the AES in Oct-2000
issued as FIPS PUB 197 standard in Nov-
2001
AES REQUIREMENTS
private key symmetric block cipher
128-bit data, 128/192/256-bit keys
stronger & faster than Triple-DES
active life of 20-30 years (+ archival use)
provide full specification & design details
both C & Java implementations
NIST have released all submissions &
unclassified analyses
AES EVALUATION CRITERIA
initial criteria:
security effort for practical cryptanalysis
cost in terms of computational efficiency
algorithm & implementation characteristics
final criteria
general security
ease of software & hardware implementation
implementation attacks
flexibility (in en/decrypt, keying, other factors)
AES SHORTLIST
after testing and evaluation, shortlist in Aug-
99:
MARS (IBM) - complex, fast, high security margin
RC6 (USA) - v. simple, v. fast, low security margin
Rijndael (Belgium) - clean, fast, good security margin
Serpent (Euro) - slow, clean, v. high security margin
Twofish (USA) - complex, v. fast, high security margin
then subject to further analysis & comment
saw contrast between algorithms with
fewcomplex rounds verses many simple rounds
which refined existing ciphers verses new proposals
THE AES CIPHER - RIJNDAEL
designed by Rijmen-Daemen in Belgium
has 128/192/256 bit keys, 128 bit data
an iterative rather than feistel cipher
processes data as block of 4 columns of 4 bytes
operates on entire data block in every round
designed to be:
resistantagainst known attacks
speed and code compactness on many CPUs
design simplicity
RIJNDAEL
data block of 4 columns of 4 bytes is state
key is expanded to array of words

## has 9/11/13 rounds in which state undergoes:

byte substitution (1 S-box used on every byte)
shift rows (permute bytes between groups/columns)
mix columns (subs using matrix multipy of groups)
add round key (XOR state with key material)
view as alternating XOR key & scramble data bytes
initial XOR key material & incomplete last
round
with fast XOR & table lookup implementation
RIJNDAEL
BYTE SUBSTITUTION
a simple substitution of each byte
uses one table of 16x16 bytes containing a
permutation of all 256 8-bit values
each byte of state is replaced by byte indexed
by row (left 4-bits) & column (right 4-bits)
eg.byte {95} is replaced by byte in row 9 column 5
which has value {2A}
S-box constructed using defined
transformation of values in GF(28)
designed to be resistant to all known attacks
BYTE SUBSTITUTION
SHIFT ROWS
a circular byte shift in each each
1strow is unchanged
2nd row does 1 byte circular shift to left
3rd row does 2 byte circular shift to left
4th row does 3 byte circular shift to left
decrypt inverts using shifts to right
since state is processed by columns, this
step permutes bytes between the columns
SHIFT ROWS
MIX COLUMNS
each column is processed separately
each byte is replaced by a value dependent on all
4 bytes in the column
effectively a matrix multiplication in GF(28) using

## prime poly m(x) =x8+x4+x3+x+1

MIX COLUMNS
MIX COLUMNS
can express each col as 4 equations
to derive each new byte in col
decryption requires use of inverse matrix
with larger coefficients, hence a little harder
have an alternate characterisation
each column a 4-term polynomial
with coefficients in GF(28)
and polynomials multiplied modulo (x4+1)
ADD ROUND KEY
XOR state with 128-bits of the round key
again processed by column (though effectively a
series of byte operations)
inverse for decryption identical
since XOR own inverse, with reversed keys
designed to be as simple as possible
a form of Vernam cipher on expanded key
requires other stages for complexity / security
ADD ROUND KEY
AES ROUND
AES KEY EXPANSION
takes 128-bit (16-byte) key and expands into
array of 44/52/60 32-bit words
start by copying key into first 4 words

## in previous & 4 places back

in 3 of 4 cases just XOR these together
1st word in 4 has rotate + S-box + XOR round constant
on previous, before XOR 4th back
AES KEY EXPANSION
KEY EXPANSION RATIONALE
designed to resist known attacks
design criteria included
knowing part key insufficient to find many more
invertible transformation
fast on wide range of CPUs
use round constants to break symmetry
diffuse key bits into round keys
enough non-linearity to hinder analysis
simplicity of description
AES DECRYPTION
AES decryption is not identical to encryption
since steps done in reverse
but can define an equivalent inverse cipher with
steps as for encryption
but using inverses of each step
with a different key schedule
works since result is unchanged when
swap byte substitution & shift rows
swap mix columns & add (tweaked) round key
AES DECRYPTION
IMPLEMENTATION ASPECTS
can efficiently implement on 8-bit CPU
byte substitution works on bytes using a table of 256
entries
shift rows is simple byte shift
add round key works on byte XORs
mix columns requires matrix multiply in GF(28)
which works on byte values, can be simplified to use
table lookups & byte XORs
IMPLEMENTATION ASPECTS
can efficiently implement on 32-bit CPU
redefine steps to use 32-bit words
can precompute 4 tables of 256-words
then each column in each round can be computed
using 4 table lookups + 4 XORs
at a cost of 4Kb to store tables
designers believe this very efficient
implementation was a key factor in its selection
as the AES cipher
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