In this paper, by using the properties of the cyclic Hadamard matrices of order 4t, an infinite class of (4t-1)-variable 2-resilient rotation symmetric Boolean functions is constructed, and the nonlinearity of the constructed functions are also studied. To the best of our knowledge, this is the first class of direct constructions of 2-resilient rotation symmetric Boolean functions. The spirit of this method is different from the known methods depending on the solutions of an equation system proposed by Du Jiao, et al. Several situations are examined, as the direct corollaries, three classes of (4t-1)-variable 2-resilient rotation symmetric Boolean functions are proposed based on the corresponding sequences, such as m sequences, Legendre sequences, and twin primes sequences respectively.

Cloud computing enables computational resource-limited devices to economically outsource much computations to the cloud. Modular exponentiation is one of the most expensive operations in public key cryptographic protocols, and such operation may be a heavy burden for the resource-constraint devices. Previous works for secure outsourcing modular exponentiation which use one or two untrusted cloud server model or have a relatively large computational overhead, or do not support the 100% possibility for the checkability. In this letter, we propose a new efficient and verifiable algorithm for securely outsourcing modular exponentiation in the two untrusted cloud server model. The algorithm improves efficiency by generating random pairs based on EBPV generators, and the algorithm has 100% probability for the checkability while preserving the data privacy.

In this paper, we study partial key exposure attacks on RSA where the number of unexposed blocks of the private key is greater than or equal to one. This situation, called generalized framework of partial key exposure attack, was first shown by Sarkar [22] in 2011. Under a certain condition for the values of exposed bits, we present a new attack which needs fewer exposed bits and thus improves the result in [22]. Our work is a generalization of [28], and the approach is based on Coppersmith's method and the technique of unravelled linearization.

Semi-bent functions have very high nonlinearity and hence they have many applications in symmetric-key cryptography, binary sequence design for communications, and combinatorics. In this paper, we focus on studying the additive autocorrelation of semi-bent functions. We provide a lower bound on the maximum additive autocorrelation absolute value of semi-bent functions with three-level additive autocorrelation. Semi-bent functions with three-level additive autocorrelation achieving this bound with equality are said to have perfect three-level additive autocorrelation. We present two classes of balanced semi-bent functions with optimal algebraic degree and perfect three-level additive autocorrelation.

In this paper, we study the problem of a Boolean function can be represented as the sum of two bent functions. This problem was recently presented by N. Tokareva when studying the number of bent functions [27]. Firstly, several classes of functions, such as quadratic Boolean functions, Maiorana-MacFarland bent functions, many partial spread functions etc, are proved to be able to be represented as the sum of two bent functions. Secondly, methods to construct such functions from low dimension ones are also introduced. N. Tokareva's main hypothesis is proved for n≤6. Moreover, two hypotheses which are equivalent to N. Tokareva's main hypothesis are presented. These hypotheses may lead to new ideas or methods to solve this problem. Finally, necessary and sufficient conditions on the problem when the sum of several bent functions is again a bent function are given.

Because of the algebraic attacks, a high algebraic immunity is now an important criteria for Boolean functions used in stream ciphers. In 2011, X.Y. Zeng et al. proposed three constructions of balanced Boolean functions with maximum algebraic immunity, the constructions are based on univariate polynomial representation of Boolean functions. In this paper, we will improve X.Y. Zeng et al.' constructions to obtain more even-variable Boolean functions with maximum algebraic immunity. It is checked that, our new functions can have as high nonlinearity as X.Y. Zeng et al.' functions.

In this comment, an inequality of algebraic immunity of the sum of two Boolean functions is pointed out to be generally incorrect. Then we present some results on how to impose conditions such that the inequality is true. Finally, complete proofs of two existing results are given.

T-function is a kind of cryptographic function which is shown to be useful in various applications. It is known that any function f on F2n or Z2n automatically deduces a unique polynomial fF ∈ F2n[x] with degree ≤ 2n-1. In this letter, we study an algebraic property of fF while f is a T-function. We prove that for a single cycle T-function f on F2n or Z2n, deg fF=2n-2 which is optimal for a permutation. We also consider a kind of widely used T-function in many cryptographic algorithms, namely the modular addition function Ab(x)=x+b ∈ Z2n[x]. We demonstrate how to calculate deg Ab F from the constant value b. These results can facilitate us to evaluate the immunity of the T-function based cryptosystem against some known attacks such as interpolation attack and integral attack.

Constructing degree-optimized resilient Boolean functions with high nonlinearity is a significant study area in Boolean functions. In this letter, we provide a construction of degree-optimized n-variable (n odd and n ≥ 35) resilient Boolean functions, and it is shown that the resultant functions achieve the currently best known nonlinearity.

Rotation symmetric Boolean functions (RSBFs) that are invariant under circular translation of indices have been used as components of different cryptosystems. In this paper, odd-variable balanced RSBFs with maximum algebraic immunity (AI) are investigated. We provide a construction of n-variable (n=2k+1 odd and n ≥ 13) RSBFs with maximum AI and nonlinearity ≥ 2n-1-¥binom{n-1}{k}+2k+2k-2-k, which have nonlinearities significantly higher than the previous nonlinearity of RSBFs with maximum AI.

Remote data possession checking for cloud storage is very important, since data owners can check the integrity of outsourced data without downloading a copy to their local computers. In a previous work, Chen proposed a remote data possession checking protocol using algebraic signature and showed that it can resist against various known attacks. In this paper, we find serious security flaws in Chen's protocol, and shows that it is vulnerable to replay attack by a malicious cloud server. Finally, we propose an improved version of the protocol to guarantee secure data storage for data owners.

In this paper, we investigate the security property of RSA when some middle bits of the private key d are known to an attacker. Using the technique of unravelled linearization, we present a new attack on RSA with known middle bits, which improves a previous result under certain circumstance. Our approach is based on Coppersmith's method for finding small roots of modular polynomial equations.

In a previous work [1], Wang et al. proposed a privacy-preserving outsourcing scheme for biometric identification in cloud computing, namely CloudBI. The author claimed that it can resist against various known attacks. However, there exist serious security flaws in their scheme, and it can be completely broken through a small number of constructed identification requests. In this letter, we modify the encryption scheme and propose an improved version of the privacy-preserving biometric identification design which can resist such attack and can provide a much higher level of security.