1. Seyed Amir Hossain Naseredini
Cryptographic Hash Functions
Definition, History and Cryptanalysis
Seyed Amir Hossain Naseredini
Computer and Information Technology Engineering Department
Spring, 2017

2. Outline About our laboratory Introduction History2
Outline
About our laboratory
Introduction
History
Cryptographic hash function
Application
ARX-Design hash function
An example
Cryptanalysis
Hash functions’ cryptanalysis
Why cryptanalysis
Conclusion

3. About our laboratory Data Security Research Laboratory
Under supervision of Professor B. Sadeghiyan
Research Area
Cryptography
Cryptanalysis
Security protocols
Computer forensic
Malware detection
Vulnerability Detection

4. Introduction Cryptographic hash function
Introduced by Diffie and Hellman
Security requirement
Collision resistance
Pre-image resistance
Second pre-image resistance
MD4 was the first cryptographic hash function
SHS hash function
By NIST
Hash function cryptanalysis by Wang et al.
SHA-3 competition
Select a standard hash function
Cryptanalysis
To find a flaw

5. Early History Introduced by Diffie and Hellman
1976
The first collision resistant hash function
Merkle and Damgard
1989
Cryptographic hash function received more attention
1990s
MD4 Cryptanalysis
Dobbertin
1995
A huge step in hash function cryptanalysis
Wang et al.
2004

6. Cryptographic Hash Function
Introduction
Input: m (variable length)
Output: H (fixed length)
ℎ 𝑚 =𝐻
Cryptographic hash function
Collision resistance
𝑚 1 ≠ 𝑚 2 ↛h 𝑚 1 =ℎ( 𝑚 2 )
Pre-image resistance
ℎ 𝑚 =𝐻 ,H↛𝑚
Second pre-image resistance
ℎ 𝑚 1 =𝐻 , 𝑚 1 ≠ 𝑚 2 ↛ℎ 𝑚 2 =𝐻

7. Cryptographic Hash Function (cont’d)
Two different types
Modification Detection Code (MDC)
Message Authentication Code(MAC)
Message
Hash function
MAC function
Hash
MAC
Key

8. Cryptographic Hash Function (cont’d)
A Taxonomy
MDC
One Way Hash Functions (OWHF)
Collision Resistant Hash Functions (CRHF)
Universal One Way Hash Functions (UOWHF)
MAC
Application
Based on speed/resistance
Some usual applications
Store passwords
Digital Signature
Zero-Knowledge proof
Use as a PRNG
etc.

9. Cryptographic Hash Function (cont’d)
ARX-Design hash functions
Use only three operations
modular Addition
Rotation
Xor
Modular addition provides nonlinearity
Rotation prevents the balance
XOR complicates the function
ARX operations are functionally complete
Security is a common belief and has not been proven.

10. Cryptographic Hash Function (cont’d)
ShA-3 competition finalists
BLAKE (Aumasson et al.)
Grøstl (Knudsen et al.)
JH (Hongjun Wu)
Keccak (Keccak team, Daemen et al.)
Skein (Schneier et al.)
Let’s take a look at BLAKE hash function

11. Cryptographic Hash Function (cont’d)
BLAKE hash function
Designed to compete in SHA-3
Did pass to final round
ARX-Design
ℎ, the compression function
Inputs:
ℎ= ℎ 0 ,…, ℎ 7
𝑚= 𝑚 0 ,…, 𝑚 15
𝑠= 𝑠 0 ,…, 𝑠 3
𝑡= 𝑡 0 , 𝑡 1
Output:
ℎ′= ℎ′ 0 ,…, ℎ′ 7

12. Cryptographic Hash Function (cont’d)
BLAKE hash function
Using 𝐺 in compression function (ℎ)

13. Cryptographic Hash Function (cont’d)
BLAKE hash function
Column step and diagonal step

14. Cryptographic Hash Function (cont’d)
BLAKE hash function
Final round
Iterative algorithm

15. Hash Functions’ Cryptanalysis
Purpose
Pre-image
Second pre-image
Collision
Others
Pseudo collision
Length extension
Birthday paradox
Range: q
The number of input data: k
1− 𝑒 −𝑘(𝑘−1)/2𝑞

16. Hash Functions’ Cryptanalysis (cont’d)
Cryptanalysis of hash functions
Differential cryptanalysis
Reflection cryptanalysis
Boomerang attack
Linear cryptanalysis
Rotational cryptanalysis
Cube attack
Algebraic cryptanalysis
Statistical
Sophisticated
High data complexity
Algebraic
Newer
Low data complexity

17. Noteworthy cryptanalysis
MD5 differential cryptanalysis
2005, Wang et al.
A huge step
Cube attack on MD6
2009, Aumasson et al.
Rotational cryptanalysis on ARX-Design
2010, Khovratovich and Nikolic
Linear cryptanalysis of CubeHash
2011, Ashur and Dukelman
Algebraic cryptanalysis on Keccak
2013, Morawiecki and Srebrny

18. Noteworthy cryptanalysis (cont’d)
Some results
Algebraic cryptanalysis of Keccak

19. Conclusion Talked about cryptographic hash functions Cryptanalysis
History
Application
A taxonomy
ARX-Design hash function
An example
Cryptanalysis
Hash functions’ cryptanalysis
Purpose of cryptanalysis
Some results

20. Any Question?