Next generation block ciphers

1
Next Generation of Block
Ciphers Providing High-
Level Security
Roman Oliynykov
Associated Professor at
Information Technologies Security Department
Kharkov National University of Radioelectronics
Head of Scientific Research Department
JSC “Institute of Information Technologies”
Ukraine
Visiting professor at
Samsung Advanced Technology Training Institute
Korea
ROliynykov@gmail.com
May 7th, 2014

2
Outline
Block cipher basics, overview of their application
Requirements to block ciphers and their construction
principles
Basics of cryptanalysis: differential, linear, etc.
Advanced Encryption Standard: construction, advantages
and disadvantages
Directions of block ciphers further development: lightweight
and high-level security
Newly developed block ciphers providing high level
security: solutions from the USA, Russia, Belorussia and
Ukraine
Construction and properties of perspective cipher for
Ukraine, speed comparison
Beyond block cipher security: can encryption be broken if
we use high-level strength cipher?

3
About myself (I)
I’m from Ukraine (Eastern part of
Europe),
host country of Euro2012 football
championship
I live in Kharkov (the second largest
city in the country, population is 1.5
million people), Eastern Ukraine
(near Russia),
former capital of the Soviet Ukraine
(1918-1934)
three Nobel prize winners worked at
Kharkov National University

4
About myself (II)
Associated professor at Information Technologies
Security Department at Kharkov National
University of Radioelectronics
courses on computer networks and operation
system security, special mathematics for
cryptographic applications
Head of Scientific Research Department at JSC
“Institute of Information Technologies”
Scientific interests: symmetric cryptographic
primitives synthesis and cryptanalysis
Visiting professor at Samsung Advanced
Technology Training Institute
courses on computer networks and operation
system security, software security, effective
application and implementation of symmetric
cryptography

5
Block ciphers
one of the most popular
cryptographic transformations
most widely used cryptographic
algorithms for providing
confidentiality in commercial
systems
symmetric key cryptographic
transformation
very often used as main
construction element for hash
functions, pseudo random
number generators (PRNG),
etc.

6
Block cipher encryption:
electronic codebook mode (ECB)
NB: ECB mode is only used as basic block for more complex transformations

7
Block cipher
Encryption
Decryption
Main property for practical implementation
The same key is used for encryption and
decryption (opposite to RSA and other public key
crypto)

8
Applications of block ciphers:
encryption (confidentiality)
network connections: SSL/TLS
protocols (AES, Camellia, Triple DES,
etc. in CBC or GCM modes)
network traffic: IPsec protocol suite
(AES, Camellia, Triple DES,
GOST 28147-89 etc. in CBC, CTR or
GCM modes)
storage protection (AES in XTS mode)
etc.

9
integrity
verification, that the message was not
modified/forged during transmission via untrusted
channel (Internet, wireless networks, etc.):
CMAC (Cipher-based Message Authentication Code)
GMAC (Galois Message Authentication Code), GCM
(Galois/Counter Mode)

10
elements of other primitives
Hash function constructions:
Miyaguchi–Preneel
Davies–Meyer
Matyas–Meyer–Oseas

11
a permutation in sponge
construction
hash function (Keccak/SHA-3)
message authentication code
stream cipher
authenticated encryption

12
Ideal block cipher model
block cipher as a random permutation (fixed key gives one
permutation)
number of random permutations: (2n)!, where n is block size
in bits
practical implementation is impossible: requires 264·8 = 267
bytes just for simple 64-block encryption using the single key
real block cipher only takes 2k from (2n)!, where k is key
length

13
Block cipher: requirements
and construction principles
must behave like a random substitution (hiding all
redundancy of plaintext)
truly random substitution of corresponding size is
quite ineffective in implementation
iterative structure: sequential application of
different weak ciphers gives a strong one
each plaintext bit and each key bit must have
influence on each ciphertext bit
linear and non-linear operations must be used
(Shannon’s confusion and diffusion)
only small tables and simple operations
(repeating many times) may be used to archive
effective implementation

14
Practical implementation:
iterated block ciphers
Repeating weak round function many times.
Main constructions of block ciphers:
Feistel network
SPN structure
Lai-Massey scheme

15
Block cipher round function
Linear and non-linear layers for providing complex input/output
dependency;
One or few rounds can be easily broken, but enough will give a
strong cipher
Can be implemented:
S-boxes followed by linear transformations
sequence of addition, rotation and XOR (ARX-ciphers)
mix of above variants
Example: Camellia block cipher round function

16
Avalanche effect for block
ciphers and hash functions
changing one input bit (plaintext or key) leads to
changing approximately half output bits (ciphertext)
at random positions
non-linear blocks (S-boxes) give complex
dependency between S-box input bits (diffusion)
linear blocks (bit permutation, linear bit
transformations, including MDS matrix multiplication)
gives “difference spreading” to the rest of S-boxes
multiple rounds (product cipher) allow to get
complex non-linear dependencies of all output bits
on all plaintext and key bits
avalanche property is very important for strength to
different cryptanalysis methods

17
Practical (computational) security:
wide spread block ciphers and
their characteristics

18
Legacy block cipher:
Data Encryption Standard (DES)
64 bit block, 56 bit key
16-round Feistel
network
linear key schedule
(master key bit
permutation)
based on IBM
solution: Lucifer
NSA improvement:
decreased key length
and improved strength
to different
cryptanalytic attacks,
published later

19
Legacy block cipher:
DES round function
bit expansion E
(32 bit -> 48 bit)
round key addition
(XOR)
S-boxes (substitution
tables, 6 bit -> 4 bit)
bit permutation P

20
DES S-boxes
… … … … … … … … … … … … … … … …

21
DES
key schedule
56 bit of the
encryption key are
transformed into 16
round keys of 48 bit
each
cyclic shifts and bit
permutation of
encryption key are
only used
each round key is
just a selected and
permuted bits of
encryption key

22
Data Encryption Standard:
advantages and disadvantages
the first publically available worldwide spread cipher
with practically acceptable strength level
no effective attacks exploiting internal properties
completely breaking cipher strength were found (cf.:
FEAL)
improved version (TDEA or TripleDES with 168 bit
key is allowed to be used by NIST together with AES)
DES can be practically broken with brute-force
attacks or using precomputed tables due to 56-bit
key
slow in software (comparing to AES, etc.)
not effective as a lightweight solution

23
How ciphers are broken: examples
of basic cryptanalysis methods
brute force attacks
precomputed tables (Hellman, rainbow, etc.)
differential cryptanalysis and modifications
impossible differentials
truncated differentials
rectangle attack
boomerang attack
linear cryptanalysis and modifications
algebraic analysis
etc.

24
Differential cryptanalysis
very widely applied method of cryptanalysis for block ciphers,
hash functions, etc.
learns how the difference propagates via cryptographic
transformations
chosen plaintext attack (for most cases)
the first method for successful analytical attack against DES
(estimated complexity 247)
the first publication in open literature appeared in 1990 (IBM
researches say they discovered it in 1974 and optimized
DES against it, and NSA already knew about DC then)
many other attacks are based on differential cryptanalysis
some ciphers successfully had been practically broken (e.g.,
FEAL) with DC

25
Basics of differential
cryptanalysis
Difference
Linear function
Difference and round
key addition
Non-linear function

26
Difference distribution table of
DES S-box (S1)

27
Non-linear transformation
(S-box)
non-zero difference can be formed by limited (not all)
input and output values:

28
Differential cryptanalysis: the
last round of encryption

29
Differential cryptanalysis:
transformations in the last round
function
∆X, ∆Y are known
=> only several
variants of X
(not all) are
possible
R, R’ are known
(equal to right
halves of
ciphertext)
Possible key bits
values:
K = R ⊕ X

30
Differential characteristics: obtaining
necessary differences on the last round

31
Differential characteristics probabilities:
one round calculation
NB: random independent round keys (hypothesis stochastic equivalence)

32
Attack complexity and strength to
differential cryptanalysis
Probability of differential characteristic determines
the required number of chosen plaintext encryptions
(mathematical expectation)
Complexity of the attack (classic approach) depends
on
maximal probability of difference transformation on S-
box(es)
number of active S-boxes used in differential characteristic
Cryptographic primitive is resistant do differential
cryptanalysis, if the complexity of the attack is higher
than the brute force search

33
Complexity of DES differential
cryptanalysis

34
Linear cryptanalysis
very widely applied method of cryptanalysis for block
ciphers, hash functions, etc.
learns how the non-linear cryptographic
transformation can be approximated with
linear/affine equations
known (not chosen) plaintext attack (for most cases)
the first practically implemented method for
successful analytical attack against DES (with
complexity 243)
first publication in open literature appeared in 1992
(against FEAL cipher, then applied to DES)

35
S-box: non-linear element and
its approximation table

36
Linear
approximation of
several rounds
involving:
linear approximations
of S-boxes
plaintext and
ciphertext bits
round keys bits

37
Attack complexity and strength to
linear cryptanalysis
The required number of plaintext encryptions
is determined by the probability that linear
approximation (linear hull) holds
Complexity of the attack (classic approach)
depends on
maximal bias of linear approximation on S-box(es)
number of active S-boxes used in linear
approximation for the whole cipher
Cryptographic primitive is resistant to linear
cryptanalysis, if the complexity of the attack is
higher than the brute force search

38
Algebraic cryptanalysis
follows Claude Shannon idea (published 1949)
“breaking a good cipher should require as much
work as solving a system of simultaneous equations
in a large number of unknowns of a complex type”
known plaintext attack (usually)
requires small amount of plaintext-ciphertext pairs
(near to unicity distance)
usually crypto transformation is described with
overdefined system of a small (2-3) degree
several ciphers were successfully broken with
algebraic attacks
methods of solving multivariate overdefined systems
are being improved

39
Advanced Encryption
Standard (AES)
128 bits block and 128, 192 or 256 bits key
developed in Belgium, selected from 15 candidates
(proposal from the US, Denmark, Germany, Israel, Japan,
Switzerland, Armenia, etc.) during 4 year public
cryptographic competition held by US National Institute of
Standards (NIST)
adopted as the US standard in 2001
In 2002 allowed for protection of classified US government
information
the most researched cipher ever (in open publications)
NSA cannot break even AES-128 and employs thousands
of mathematician for this task (according to Ed.Snowden
files)
contemporary assumption: strong (practically unbreakable)
encryption

40
Advanced Encryption
Standard (AES)
transparent design
SPN construction (Substitution Permutation
Network)
10, 12 or 14 rounds for AES-128, AES-192
and AES-256 correspondingly
quite effective in software (32-bit platforms),
good for hardware implementation (not taking
into account lightweight solutions)

41
AES: presentation of processing
bytes as a “cipher state”

42
AES: high-level structure
(picture for 128 bit key)

43
AES: SubBytes transformation

44
AES: ShiftRows
transformation

45
AES: MixColumns
transformation

46
AES: AddRoundKey
transformation

47
AES round key generation (key
expansion)
NB: not all key length (128, 192, 256) must be supported; for many
applications it’s enough to have the single key length

48
AES round key generation:
RotWord

49
SubBytes

50
round constant application
NB: without Rcon there would be equal blocks in ciphertext if plaintext and
keys have equal blocks (1, 2 or 4 bytes repeats in plaintext and key)

52
AES effective software
implementation: 32-bit platform
three different operations can be united
into the single (!) look-up table access:
SubBytes (non-linear)
ShiftRows (linear)
MixColumns (linear)
cipher consists of look-up table accesses and
round key additions

53
AES recommendation
symmetric encryption on general purpose platform
(32 bit, 64 bit) for commercial systems: AES as the
main cipher is a good solution
recommended mode for confidentiality is CTR (if you
don’t use well researched authenticated encryption)
the longer the key, the slower cipher is (20% slower
for 192 bits and 40% slower for 256 bits comparing
to 128 bit key speed)
for very reliable systems implement AES-256 and
an additional cipher (e.g., Camellia, Serpent, etc.)
remember about implementation integrity check for
plaintext or ciphertext together with encryption

54
Advanced Encryption
Standard
Advantages
one of the most spread commercial and open
source solutions all over the world
high level of practical security
effective in software
many hardware accelerators, including Intel
processors AES instructions
Disadvantages
theoretical attacks more effective than brute force
are known
32-bit oriented (condition of the AES competition),
does not take all advantages of the 64-bit platform

55
Further development of block
ciphers: the first direction
Lightweight
constrained devices: RFID chips, embedded
medical devices, etc. (number of gates, available
memory, power consumption and so on)
acceptable strength level (cipher cannot be
broken in the near future by small group of
hackers)
not intended to be strong against powerful
adversary keeping theoretical strength for tens of
years

56
Further development of block
ciphers: the second direction
Governmental-level (high and
ultrahigh) security
must be cryptographically strong
must have enough security margin to be
protected (with high level of confidence)
of newly discovered attacks
not intended for highly constrained
devices (used on servers, routers, PC,
etc.)
must provide fast encryption

57
Newly developed block ciphers
providing high level security
Threefish (USA)
STB 34.101.31-2011 (Belorussia)
Kuznechik (Russia)
Kalyna (Ukraine)

58
Threefish block cipher
a main part of Skein hash function (supports
very big block sizes)
ARX-cipher (addition, rotation, XOR)
simple round function, many rounds

59
Threefish-512: 4 rounds of the 72

60
Threefish round key
generation

61
Threefish encryption
performance
Very fast software implementation:
4 Gb/s on Intel Core 2 Duo x64
or 6.1 clocks per byte for encryption

62
Belorussian standard
STB 34.101.31-2011 (Bel-T)
128 bit block
128, 192 or 256 bit key
8-round combination of Feistel network and
Lai-Massey scheme
Single fixed S-box (8 bit-to-8 bit) with good
properties
no key schedule (parts of encryption key are
used as round keys; key shorter than 256 bits
is just padded)
The latest version adopted in 2011

63
Belorussian standard
STB 34.101.31-2011 (Bel-T)
S
S
S
S
<<< k
Gk :

64
The new Russian cipher:
“Kuznechik” (“Grasshopper”)
well-researched AES-like construction (S-boxes,
ShiftRows, MixColumns)
10 rounds of encryption
MixColumns: a big (16x16) MDS matrix over GF(28)
generated by special method; cf.: AES has the 4x4 MDS
matrix
key schedule: Feistel network with constants as its round
keys; each round gives a round key for the main cipher
high level of security
slower in software comparing to other modern block ciphers
not adopted and officially published (only discussed on
several conferences in Russia): final version of S-boxes
and MDS matrix are not disclosed to public yet

65
Requirements to the new
perspective cipher for Ukraine
block size and key length: 128, 256 and 512 bits
(high and ultrahigh security level)
strength against known methods of cryptanalysis
security margin against future improved attacks
transparent design
effective high-speed software implementation on
the 64-bit platform
estimated time: at least 30 years (in condition of
quantum cryptanalysis impossibility)

66
Perspective block cipher
“Kalyna”
SPN-construction (AES-like)
increased size of linear transformation
matrix
several S-boxes generated with respect to
differential, linear and algebraic properties
quite new construction of key schedule,
simple in implementation

67
“Kalyna” encryption function
( ) 0
1
1
1
K
N
i
K
KK
r
i
rN
Kalyna
χγπθσ
γπθχ
ooooo
oooo
∏
−
=
+
=
K0
SubBytes
ShiftRows
MixColumns
KiNr -1 times
KNr
SubBytes
ShiftRows
MixColumns

68
“Kalyna”: number of rounds
18––512 (Nb = 8)
1814–256 (Nb = 4)
–1410128 (Nb = 2)
512
(Nk = 8)
256
(Nk = 4)
128
(Nk = 2)
Key length
Block size

69
S-boxes for “Kalyna”
4 different S-boxes (which are not CCZ-equivalent)
with the following characteristics:
3 (441 equations)Overdefined system degree
24Max. value of linear bias
8Max. value of difference distribution table
7Minimal algebraic degree of component
Boolean functions
104Nonlinearity
AES S-box: overdefined system degree: 2, nonlinearity: 112, dd: 4
The best known nonlinearity of S-boxes with 3rd degree:
Сrypton, Safer+, Skipjack, SNOW, Twofish, Whirlpool, СS, Anubis, Stribog

70
Number of active S-boxes depending on
required 64-bit processor instructions
for 4x4 and 8x8 MDS matrix over GF(28) for 128
bit (left) and 256 bit (right) block
0
20
40
60
80
100
120
32 64 96 128
Required instructions
NumberofactiveS-boxes
МДР64
МДР32
45
90
135
180
25
50
75
100
0
20
40
60
80
100
120
140
160
180
200
64 128 192 256
Required instructions
NumberofactiveS-boxes
МДР64
МДР32
Increased size of MDS matrix gives
essential advantages for required
cryptographic properties, and has
effective implementation on modern
platforms

71
“Kalyna” encryption function
design principles
well known wide trail design strategy (strength to
differential, linear cryptanalysis, etc.) combined with
modular pre- and post-whitening
clear construction, no trapdoors
new set of S-boxes (without essential algebraic
structure)
64-bit platform operations
(mod 264 addition, 8x8 MDS matrix)
direct transformation (encryption) is more often used
than reverse (decryption)
effective software implementation
developed for and most effective on 64-bit platforms

72
Optimization for direct
transformation (encryption)
block cipher based hashing does not need decryption
block cipher based pseudorandom number generation does
not need decryption
sponge construction does not need block cipher decryption
most block cipher modes of operation (CTR, OFB,
CFB, CCM, GCM, etc.) do not need block cipher
decryption:

73
Number of precomputed
tables:
AES (4 tables)
2 tables for encryption
2 tables for decryption
Kalyna (4 tables)
1 table for encryption
3 tables for decryption
More effective implementation for CTR,
OFB, CFB, CCM, GCM hashing, PRNG

74
Requirements to “Kalyna” key
schedule
non-linear dependence of every round key bit on
every encryption key bit
round key independence
high computational complexity of encryption key
recovery even having all round keys
strength to all known cryptanalytic attacks on key
schedule
absence of weak key worsen cryptographic
properties
implementation simplicity (application of round
transformation only)
partial protection from side-channel attacks

75
“Kalyna” key schedule
K
SubBytes
ShiftRows
MixColumns
K
K
SubBytes
ShiftRows
MixColumns
Nb+Nk+1(const)
SubBytes
ShiftRows
MixColumns
Kt
Kt+tmvi
SubBytes
ShiftRows
MixColumns
SubBytes
ShiftRows
MixColumns
K
k2i
Kt+tmvi
Kt+tmvi
)32(212 +⋅<<<=+ bii Nkk
tmv0=0x01000100…0100
tmvi+2= tmvi << 1
All operations
(excluding rotation and
shifting which can be
effectively implemented
by memory access
processor instructions)
are taken from the
encrypt function

76
“Kalyna” key schedule
properties
correspondence to requirements
all operations are taken from encryption function
round keys can be generated in order to encryption
and decryption with the same computational
complexity
effective countermeasure against round
transformation symmetry
minimal number of constants, their clearness
key agility is less than 2.5
(key schedule takes time less than 2.5 encryption of
one block)
non-bijective round keys dependency on encryption
key

77
Non-bijective round key
dependence
implemented in
Twofish
(AES competition finalist; key agility > 10)
Blowfish (widely used in public cryptographic libraries; key
agility > 10)
Fox (block cipher developed in Switzerland; key agility > 5)
key schedule works as PRNG with cryptographic
properties
no estimation was published in open literature
{ } { }( )rKKKKP ,...,,## 10≥

78
Percentage of unique round
keys for “Kalyna”
0.999978512512
0.981684512256
0.999665256256
0.981684256128
0.997521128128
Part of unique round keysKey lengthBlock size
Advantages:
good cryptographic properties
additional protection from different attacks, including side-channel
high computational complexity of encryption key recovery even having
all round keys
Disadvantage:
less than 2% of encryption keys might have equivalent keys (highly
pseudorandom dependence of equivalent keys, if there are any)

79
“Kalyna” (block size 128 bits, 10
rounds) strength to cryptanalytic
attacks
212043Boomerang
23Interpolation
26626256Impos. diff.
233+429756Integral
4Trunc. diff.
252,835Linear
negligible25545Differential
MemoryEncryptionsMax. rnds
Attack characteristicsMin.
rounds for
prevention
Type of the
attack
Similar results (enough security margin) are also obtained for 256 and 512-bit block

80
“Kalyna” output sequences NIST STS
statistical testing
Even round keys
generation
CTR encryption

81
Comparison of required operations for
one byte processing
GOST 28147-89:
72 operations/byte (32-bit memory accesses, modulo
232 additions, XORs, ANDs, shifts)
AES-128:
45.375 operations/byte (32-bit memory accesses,
XORs, ANDs, shifts)
STB (Bel-T):
modulo 232 additions and subtractions, XORs, ANDs,
shifts)
Kalyna_128/128:
modulo 264 additions, XORs, ANDs, shifts)

82
Encryption performance
(Windows/Visual C++)
0
200
400
600
800
1000
1200
1400
1600
Mbits / s
Block cipher / encryption performance (Mbits / s )
Intel Core i5 x64 / Windows Server 2008 R2 x64 / Visual C++ 2008
Ряд1 1538,31 1098,17 1256,23 977,61 995,72 1483,26 1095,19 376,3 609,18
K2-
128/128
K2-
128/256
K2-
256/256
K2-
256/512
K2-
512/512
AES-
128
AES-
256
GOST
28147
STB

83
Encryption performance
(Linux/gcc)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Mbits / s
Block cipher / encryption performance (Mbits / s)
Core 2 Duo E8500 / Linux (64 bit) /gcc
Ряд1 1828,57 1291,72 1219,05 948,148 948,148 1667,95 1254,01 492,31 753,5
K2-
128/128
K2-
128/256
K2-
256/256
K2-
256/512
K2-
512/512
AES-
128
AES-
256
GOST
28147
STB

84
Advantages of “Kalyna” block
cipher
has high and ultrahigh level of cryptographic
security
based on verified constructions and clear
solutions
fast on modern 64-bit processors
compact software implementation
perspective for application in common
cryptographic systems, Internet and banking
security, cloud computing security, etc.

85
Trends in block cipher
development
refusing of S-box algebraic structure (reverse
element in the finite field, etc.)
increasing size of MDS matrix
families of ciphers: different block sizes and
key lengths
combinations of XOR and modular addition
application of round function transformation
for round key generation

86
Beyond block cipher security
mode of operation security
BEAST attack (CBC mode)
implementation security
CRIME/BREACH attacks
heartbleed bug in OpenSSL
timing attacks: cache misses
side-channel attacks
software vulnerabilities (buffer and heap overflows, etc.)
high-level protocol security (e.g.: encryption key
generation)
we need to use highly secure block ciphers,
but should also pay a lot of attention to
security of the whole system

Next generation block ciphers

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