## CryptoDB

### Longjiang Qu

#### Affiliation: National University of Defense Technology

#### Publications

**Year**

**Venue**

**Title**

2008

EPRINT

Enumeration of Balanced Symmetric Functions over GF(p)
Abstract

It is proved that the construction and enumeration of the number of balanced symmetric functions over GF(p) are equivalent to solving an equation system and enumerating the solutions. Furthermore, we give an lower bound on number of balanced symmetric functions over GF(p), and the lower bound provides best known results.

2006

EPRINT

The Design Principle of Hash Function with Merkle-Damg{\aa}rd Construction
Abstract

The paper discusses the security of
hash function with Merkle-Damg{\aa}rd construction and provides
the complexity bound of finding a collision
and primage of hash function based on the condition probability of
compression function $y=F(x,k)$. we make a conclusion that in
Merkle-Damma{\aa}rd construction, the requirement of free start
collision resistant and free start collision resistant on
compression function is not necessary and it is enough if the
compression function with properties of fix start collision
resistant and fix start preimage resistant. However, the condition
probability $P_{Y|X=x}(y)$ and $P_{Y|K=k}(y)$ of compression
function $y=F(x,k)$ have much influence on the security of the hash
function. The best design of compression function should have
properties of that $P_{Y|X=x}(y)$ and $P_{Y|K=k}(y)$ are both
uniformly distributed for all $x$ and $k$. At the end of the paper,
we discussed the block cipher based hash function, point out among
the the 20 schemes, selected by PGV\cite{Re:Preneel} and
BPS\cite{Re:JBlack}, the best scheme is block cipher itself, if the
block cipher with perfect security and perfect key distribution.

2005

EPRINT

On the Boolean functions With Maximum Possible Algebraic Immunity : Construction and A Lower Bound of the Count
Abstract

This paper gives a construction method which can get a large class
of Boolean functions with maximum algebraic immunity(AI) from one
such giving function. Our constructions get more functions than any
previous construction. The cryptographic properties, such as
balance, algebraic degree etc, of those functions are studied. It
shows that we can construct Boolean functions with better
cryptographic properties, which gives the guidance for the design of
Boolean functions to resist algebraic attack, and helps to design
good cryptographic primitives of cryptosystems. From these
constructions, we show that the count of the Boolean functions with
maximum AI is bigger than ${2^{2^{n-1}}}$ for $n$ odd, bigger than
${2^{2^{n-1}+\frac{1}{2}\binom{n}{\frac{n}{2}} }}$ for $n$ even,
which confirms the computer simulation result that such boolean
functions are numerous. As far as we know, this is the first bound
about this count.

#### Coauthors

- Li Chao (1)
- Qingping Dai (1)
- Keqin Feng (1)
- Guozhu Feng (1)
- Shaojing Fu (2)
- Jian Guo (1)
- Duo Lei (1)
- Ping Li (1)
- Chao Li (4)
- Da Lin (1)
- Meicheng Liu (1)
- Vincent Rijmen (1)
- Bing Sun (2)