avalanche effect in the family of block ciphers “sd-(n,k)” university “ss cyril and...

AVALANCHEAVALANCHE EFFECT IN THE FAMILY EFFECT IN THE FAMILY OF BLOCK CIPHERS “OF BLOCK CIPHERS “SD-(n,k)”SD-(n,k)”

AVALANCHEAVALANCHE EFFECT IN THE FAMILY EFFECT IN THE FAMILY OF BLOCK CIPHERS “OF BLOCK CIPHERS “SD-(n,k)”SD-(n,k)”

University “Ss Cyril and Methodius” – Skopje, RM

S. Markovski, PhD

A. Mileva, MSc

D. Gligoroski, PhD

V. Dimitrova, MSc

NATO Advanced Research Workshop

Velingrad, 21-25 October 2006

2

Kerckoff’s principle: “A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.”

Shannon maxime: “The enemy knows the system.”

Bruce Schneier: “Every secret creates potential failure point.”

Kerckoff’s principle: “A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.”

Shannon maxime: “The enemy knows the system.”

Bruce Schneier: “Every secret creates potential failure point.”

3

Introduction The family of block ciphers “SD-(n,k)” Avalanche effect in encryption Avalanche effect in decryption Future work Conclusion

Introduction The family of block ciphers “SD-(n,k)” Avalanche effect in encryption Avalanche effect in decryption Future work Conclusion

OutlineOutline

4

IntroductionIntroduction

Term first used by Horst FeistelThe avalanche effect refers to a desirable property of cryptographic algorithms, typically block-ciphers and hash functions. The avalanche effect is evident if, when an input is changed slightly (for example, flipping a single bit) the output changes significantly. Constructing a cipher to exhibit a substantial avalanche effect is one of the primary design goals. If a block cipher does not exhibit the avalanche effect to a significant degree, then it has poor randomization, and thus a cryptanalyst can make predictions about the input, being given only the output. This may be sufficient to partially or completely break the algorithm.

Term first used by Horst FeistelThe avalanche effect refers to a desirable property of cryptographic algorithms, typically block-ciphers and hash functions. The avalanche effect is evident if, when an input is changed slightly (for example, flipping a single bit) the output changes significantly. Constructing a cipher to exhibit a substantial avalanche effect is one of the primary design goals. If a block cipher does not exhibit the avalanche effect to a significant degree, then it has poor randomization, and thus a cryptanalyst can make predictions about the input, being given only the output. This may be sufficient to partially or completely break the algorithm.

5

The family of block ciphers “SD-(n,k)”


Based is on quasigroup operations and quasigroup string transformations

Arbitrary alphabet A={a0,a1,...,ar}

Quasigroup (A,*) of order r and two of its parastrophes (A,\) and (A, /)

e-, d-, e’-, d’- transformations

Based is on quasigroup operations and quasigroup string transformations

Arbitrary alphabet A={a0,a1,...,ar}

Quasigroup (A,*) of order r and two of its parastrophes (A,\) and (A, /)

e-, d-, e’-, d’- transformations

6

Blocks with length of n letters

Key K=K0K1...Kn+4k-1, KiA , where k is number of repeating of 4 different quasigroup string transformations in encryption/decryption functions

Input: plaintext m0m1...mn-1, miA

Output: ciphertext c0c1...cn-1, ciA

Blocks with length of n letters

Key K=K0K1...Kn+4k-1, KiA , where k is number of repeating of 4 different quasigroup string transformations in encryption/decryption functions

Input: plaintext m0m1...mn-1, miA

Output: ciphertext c0c1...cn-1, ciA



7

Subfamilies “SD4-(n,k)”, “SD16-(n,k)”, “SD256-(n,k)”For “SD4-(n,k)” examples in this talk we are using this quasigroup of order 4

0 1 2 31 2 3 03 0 1 22 3 0 1

Subfamilies “SD4-(n,k)”, “SD16-(n,k)”, “SD256-(n,k)”For “SD4-(n,k)” examples in this talk we are using this quasigroup of order 4

0 1 2 31 2 3 03 0 1 22 3 0 1



8

Key length in bits

k SD4-(40,k) SD16-(20,k) SD256-(10,k)

1 88 96 112

2 96 112 144

3 104 128 176

4 112 144 208

5 120 160 240

6 128 176 272

7 136 192 304

8 144 208 336

9 152 224 368

10 160 240 400



Example of avalanche effect in encryption in SD4-(4,1) subfamily

(flipping one bit in plaintext)


(flipping one bit in plaintext)


(flipping one bit in key)

12

Avalanche effect in encryptionAvalanche effect in encryption

Block size of 80 bits Subtract-with-borrow random number

generator with period 21492

Examination for each k={1,2,3,4,5,6,7,8,9,10} and for each subfamilies “SD4-(40,k)”, “SD16-(20,k)” and “SD256-(10,k)”

For every k, we use 1000 different random generated pairs of plaintext and keys

We compute mean and standard deviation of bit differences in ciphertext

Block size of 80 bits Subtract-with-borrow random number

generator with period 21492

Examination for each k={1,2,3,4,5,6,7,8,9,10} and for each subfamilies “SD4-(40,k)”, “SD16-(20,k)” and “SD256-(10,k)”

For every k, we use 1000 different random generated pairs of plaintext and keys

We compute mean and standard deviation of bit differences in ciphertext

13


Results for “SD4-(40, k)”: Flipping one bit in plaintext cause

already for k=2 50% different bits in ciphertext

Standard deviation is stabilized around 5,6 for k=3

Flipping one bit in key cause dropping of different bits in ciphertext from 50,57% for k=1 to 50,16% for k=10

Standard deviation drops from 6,31 for k=2 to 5,88 for k=10




Flipping one bit in key cause dropping of different bits in ciphertext from 50,57% for k=1 to 50,16% for k=10

Standard deviation drops from 6,31 for k=2 to 5,88 for k=10

14


Results for “SD4-(40, k)” different modes CBC, OFB and CFB: Random generated key and plaintext of

10000 bits IV – first n letter from key For OFB and CFB parameter r=8 Flipping one bit in last 4k letters in key

cause already for k=1 50% different bits in ciphertext in all modes

Standard deviation varies between 0,28 and 0,49 in all modes

15


Results for “SD16-(20, k)”: Flipping one bit in plaintext cause already

for k=1 50% different bits in ciphertext Standard deviation is stabilized around

5,6 for k=2 Flipping one bit in key cause dropping of

different bits in ciphertext from 50,15% for k=1 to 50,05% for k=10


Results for “SD16-(20, k)”: Flipping one bit in plaintext cause already

for k=1 50% different bits in ciphertext Standard deviation is stabilized around

5,6 for k=2 Flipping one bit in key cause dropping of

different bits in ciphertext from 50,15% for k=1 to 50,05% for k=10


16






17





Flipping one bit in key cause already for k=1 50% different bits in ciphertext





Flipping one bit in key cause already for k=1 50% different bits in ciphertext


18






Example of avalanche effect in decryption in SD4-(4,1) subfamily

(flipping one bit in ciphertext)

Example of avalanche effect in decryption in SD4-(4,2) subfamily

(flipping one bit in ciphertext)

21

Avalanche effect in decryptionAvalanche effect in decryption

Avalanche effect in decryption function is not really a issue

Avalanche effect in decryption function usually is not so significant as in encryption function

Avalanche effect in decryption function is not really a issue

Avalanche effect in decryption function usually is not so significant as in encryption function

22


Substract-with-borrow random number generator with period 21492

Examination for each k={1,2,...,20} and for each subfamilies “SD4-(40,k)”, “SD16-(20,k)” and “SD256-(10,k)”

For every k, we use 1000 different random generated pairs of ciphertext and keys

We compute mean and standard deviation of bit differences in plaintext

Substract-with-borrow random number generator with period 21492

Examination for each k={1,2,...,20} and for each subfamilies “SD4-(40,k)”, “SD16-(20,k)” and “SD256-(10,k)”

For every k, we use 1000 different random generated pairs of ciphertext and keys

We compute mean and standard deviation of bit differences in plaintext

23


Results for “SD4-(40, k)”: Flipping one bit in ciphertext cause

growing up different bits in plaintext from 6,46% for k=1 to 38,55% for k=10 and its stabilizing around 50% for k=19



growing up different bits in plaintext from 6,46% for k=1 to 38,55% for k=10 and its stabilizing around 50% for k=19


24



growing up different bits in plaintext from 12,06% for k=1 and its stabilizing around 50% for k=10





25








26

Future workFuture work

Cryptanalysis of “SD-(n,k)”• linear cryptanalysis and its extensions

and variants• differential cryptanalysis and its

extensions and variants• multiset cryptanalysis• other cryptanalysis

Practical implementationDesign improvement

Cryptanalysis of “SD-(n,k)”• linear cryptanalysis and its extensions

and variants• differential cryptanalysis and its

extensions and variants• multiset cryptanalysis• other cryptanalysis

Practical implementationDesign improvement

27

ConclusionConclusion

The “SD-(n,k)” is a new family of block ciphers, based on quasigroup string transformations and quasigroup operations

The “SD-(n,k)” exhibit a substantial avalanche effect in encryption function

Avalanche effect is evident in all basic modes of operation (ECB, CBC, OFB, CFB)

Avalanche effect in decryption function is not so significant as in encryption function, which was expectable

The “SD-(n,k)” is a new family of block ciphers, based on quasigroup string transformations and quasigroup operations

The “SD-(n,k)” exhibit a substantial avalanche effect in encryption function

Avalanche effect is evident in all basic modes of operation (ECB, CBC, OFB, CFB)

Avalanche effect in decryption function is not so significant as in encryption function, which was expectable

28

ConclusionConclusion

For avalanche effect, k must be at least:

3, for “SD4-(n,k)” subfamily 2, for “SD16-(n,k)” subfamily 1, for “SD256-(n,k)” subfamily

To satisfy today security needs for key length, k must be at least:


For avalanche effect, k must be at least:


To satisfy today security needs for key length, k must be at least:


THANKS FOR YOUR ATTENTION

avalanche effect in the family of block ciphers “sd-(n,k)” university “ss cyril and...

Documents

kexample of avalanche

substantial avalanche

ksubfamilies sd4n

kfor sd4n

kavalanche effect

encryptionavalanche

ciphertextavalanche

keyavalanche effect