Shaojing Fu

Balanced rotation symmetric boolean functions with maximum algebraic immunity

Rotation symmetric Boolean functions (RSBFs) that are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, even-variable-balanced RSBFs with maximum algebraic immunity (AI) are investigated. At first, we give an original construction of 2 m -variable-balanced RSBFs with maximum AI. Then we improve the construction to obtain more 2 m -variable-balanced RSBFs with maximum AI, and these new RSBFs have higher non-linearity than all previously obtained RSBFs. Further, we generalise our construction of 2 m -variable RSBFs to a new construction that can generate any even-variable RSBFs.

Construction of Rotation Symmetric Boolean Functions with Maximum Algebraic Immunity

Rotation symmetric Boolean functions (RSBFs) which are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, we study the construction of RSBFs with maximum algebraic immunity. First, a new construction of RSBFs on odd number of variables with maximum possible Algebraic Immunity is given. Then by using the relationship between some flats and support of a n -variables Boolean function f , we prove that a construction of RSBFs on even number of variables has maximum possible Algebraic Immunity. Furthermore, we study the nonlinearity of functions by our construction.

Securing the cloud storage audit service: defending against frame and collude attacks of third party auditor

Cloud computing has been envisioned as the next generation architecture of the IT enterprise, but there exist many security problems. A significant problem encountered in the context of cloud storage is whether there exists some potential vulnerabilities towards cloud storage system after introducing third parties. Public verification enables a third party auditor (TPA), on behalf of users who lack the resources and expertise, to verify the integrity of the stored data. Many existing auditing schemes always assume TPA is reliable and independent. This work studies the problem what if certain TPAs are semi-trusted or even potentially malicious in some situations. Actually, the authors consider the task of allowing such a TPA to involve in the audit scheme. They propose a feedback-based audit scheme via which users are relaxed from interacting with cloud service provider (CSP) and can check the integrity of stored data by themselves instead of TPA yet. Specifically, TPA generates the feedback through processing the proof from CSP and returns it to user which is yet unforgeable to TPA and checked exclusively by user. Through detailed security and performance analysis, the authors scheme is shown to be more secure and lightweight.

New constructions of semi-bent functions in polynomial forms

Semi-bent functions are a kind of useful functions in cryptography. In this paper we give new constructions of n -variable quadratic semi-bent functions in polynomial forms for both odd and even n , and we also present many n -variable semi-bent functions with few trace terms when n is even.

Construction of even-variable rotation symmetric Boolean functions with maximum algebraic immunity

Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. In this paper, we investigate n-variable (n even and n ⩾ 12) RSBFs to achieve maximum algebraic immunity (AI), and provide a construction of RSBFs with maximum AI and nonlinearity. These functions have higher nonlinearity than the previously known nonlinearity of RSBFs with maximum AI. We also prove that our construction provides high algebraic degree in some case.

Balanced 2p-variable rotation symmetric Boolean functions with maximum algebraic immunity

Abstract In this paper, we study the construction of Rotation Symmetric Boolean Functions (RSBFs) which achieve a maximum algebraic immunity (AI). For the first time, a construction of balanced 2 p -variable ( p is an odd prime) RSBFs with maximum AI was provided, and the nonlinearity of the constructed RSBFs is not less than 2 2 p − 1 − ( 2 p − 1 p ) + ( p − 2 ) ( p − 3 ) + 2 ; this nonlinearity result is significantly higher than the previously best known nonlinearity of RSBFs with maximum AI.

On the number of rotation symmetric Boolean functions

Rotation symmetric Boolean functions (RSBFs) have been used as components of different cryptosystems. This class of functions are invariant under circular translation of indices. In this paper, we investigated balanced RSBFs and 1st order correlation immune RSBFs. Based on constructive techniques, we give an accurate enumeration formula for n-variable balanced RSBFs when n is a power of a prime. Furthermore, an original and efficient method to enumerate all n-variable (n prime) 1st order correlation-immune functions is presented. The exact number of 1st order correlation immune RSBFs with 11 variables is 6925047156550478825225250374129764511077684773805520800 and the number of 13 variables has 189 digits. Then for more variables, we also provide a significant lower bound on the number of 1st order correlation immune RSBFs.

Efficient, secure and non-iterative outsourcing of large-scale systems of linear equations

Solving large-scale systems of linear equations (L-SLE) is a common scientific and engineering computational task. But such problem involves enormous computing resources, which is burdensome for the resource-limited clients. Cloud computing enables computational resource-limited clients to economically outsource such problems to the cloud server. However, outsourcing LSLE to the cloud brings great security concerns and challenges since the LSLE usually contains sensitive information. Previous works for secure outsourcing LSLE are mainly based on iterative methods which cause heavy computation cost for the client side. And they usually neglect to protect the number and position privacy of zero elements in the coefficient matrix, which is not secure enough for many applications. In this paper, with a series of disguise-based techniques, we propose a new efficient and non-iterative algorithm for securely outsourcing LSLE. Our algorithm only requires two rounds of communication between the client and cloud. Furthermore, the number and positions of zero elements in coefficient matrix can be hidden from the cloud with low computational complexity. Finally, we provide extensive theoretical analysis and experimental evaluation to show its high-efficiency and security compared to the previous works.

Linear complexity of binary sequences with interleaved structure

In this study, the minimal polynomials and the linear complexity of interleaved binary sequences are investigated. Both the linear complexity and the minimal polynomials of low correlation zone sequences constructed by Zhou et al. are completely determined. Besides, an open problem proposed by Li and Tang is discussed. At last, a sufficient condition and a necessary condition are presented about when the linear complexity of the interleaved sequences constructed by Tang et al. attains the maximum.

Construction of highly nonlinear resilient S-boxes with given degree

We provide two new construction methods for nonlinear resilient S-boxes with given degree. The first method is based on the use of linear error correcting codes together with highly nonlinear S-boxes. Given a [u, m, t + 1] linear code where u = n−d−1, d > m, we show that it is possible to construct (n, m, t, d) resilient S-boxes which have currently best known nonlinearity. Our second construction provides highly nonlinear (n, m, t, d) resilient S-boxes which do not have linear structure, then an improved version of this construction is given.