Guozhen Xiao

On the global avalanche characteristics between two Boolean functions and the higher order nonlinearity

The criterion for the global avalanche characteristics (GAC) of cryptographic functions is an important property. To measure the correlation between two arbitrary Boolean functions, we propose two new criteria called the sum-of-squares indicator and the absolute indicator of the cross-correlation between two Boolean functions. The two indicators generalize the GAC criterion. Based on the properties of the cross-correlation function, we deduce the rough lower and the rough upper bounds on the two indicators by hamming weights of two Boolean functions, and generalize some properties between the Walsh spectrum and the cross-correlation function. Furthermore, we give the tight upper and the tight lower bounds on the two indicators. Finally, we show some relationships between the upper bounds on the two indicators and the higher order nonlinearity.

The linear complexity of new generalized cyclotomic binary sequences of order four

Whiteman generalized cyclotomic sequences are proven to exhibit a number of good randomness properties. In this paper we determine the linear complexity of some newly generalized cyclotomic sequences, of order four with period pq which are defined by Ding and Helleseth. The results show that all of these sequences have high linear complexity.

Linear complexity of binary Whiteman generalized cyclotomic sequences of order 2k

In this correspondence, we obtain the linear complexity and minimal polynomials of binary Whiteman generalized cyclotomic sequences of order 2^k, where k>1. Our result shows that all of these sequences possess large linear complexity.

Efficient elliptic curve scalar multiplication algorithms resistant to power analysis

This paper presents four algorithms for securing elliptic curve scalar multiplication against power analysis. The highest-weight binary form (HBF) of scalars and randomization are applied to resist power analysis. By using a special method to recode the scalars, the proposed algorithms do not suffer from simple power analysis (SPA). With the randomization of the secret scalar or base point, three of the four algorithms are secure against differential power analysis (DPA), refined power analysis (RPA) and zero-value point attacks (ZPA). The countermeasures are also immune to the doubling attack. Fast Shamirs method is used in order to improve the efficiency of parallel scalar multiplication. Compared with previous countermeasures, the new countermeasures achieve higher security and do not impact overall performance.

Cryptographic properties of some binary generalized cyclotomic sequences with the length p2

Herein, the cryptographic properties of some generalized cyclotomic sequences, with the period p^2, are investigated. Results show that these sequences always possess good balance and linear complexity (larger than half the period). Their autocorrelation functions are shown to be three-valued if p=3(mod4), and five-valued otherwise. Moreover, the distribution of patterns of length 2 are discussed.

Trace representation of some generalized cyclotomic sequences of length pq

This paper contributes to trace representation of some generalized cyclotomic sequences of length pq(p,qprime), which are defined by Ding and Helleseth. From the relations between these sequences and the Legendre sequence, we firstly confirm the defining pairs of these sequences of arbitrary order. Then, we obtain their trace representation, from which we give their linear complexity using Keys method. It can be seen that Bai et al.s conclusion is a special case of our result when the order is two. Finally, an example is given to illustrate the validity of our result.