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Shanqi PANG Ying WANG Jiao DU Wenju XU
Orthogonal arrays and orthogonal partitions have great significance in communications and coding theory. In this letter, by using a generalized orthogonal partition, Latin squares and orthogonal Latin squares, we present an iterative construction method of orthogonal arrays of strength t and orthogonal partitions. As an application of the method, more orthogonal arrays of strength t and orthogonal partitions than the existing methods can be constructed.
Jiao DU Shaojing FU Longjiang QU Chao LI Tianyin WANG Shanqi PANG
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.
Jiao DU Qiaoyan WEN Jie ZHANG Shanqi PANG
In this letter, a property of the characteristic matrix of the Rotation Symmetric Boolean Functions (RSBFs) is characterized, and a sufficient and necessary condition for RSBFs being 1st correlation-immune (1-CI for simplicity) is obtained. This property is applied to construct resilient RSBFs of order 1 (1-resilient for simplicity) on pq variables, where p and q are both prime consistently in this letter. The results show that construction and counting of 1-resilient RSBFs on pq variables are equivalent to solving an equation system and counting the solutions. At last, the counting of all 1-resilient RSBFs on pq variables is also proposed.
Jiao DU Qiaoyan WEN Jie ZHANG Xin LIAO
Orthogonal arrays have important applications in statistics and computer science, as well as in coding theory. In this letter, a new construction method of symmetric orthogonal arrays of strength t is proposed, which is a concatenation of two orthogonal partitions according to a latin square. As far as we know, this is a new construction of symmetric orthogonal arrays of strength t, where t is a given integer. Based on the different latin squares, we also study the enumeration problem of orthogonal partitions, and a lower bound on the count of orthogonal partitions is derived.
Jiao DU Ziyu CHEN Le DONG Tianyin WANG Shanqi PANG
In this paper, the notion of 2-tuples distribution matrices of the rotation symmetric orbits is proposed, by using the properties of the 2-tuples distribution matrix, a new characterization of 2-resilient rotation symmetric Boolean functions is demonstrated. Based on the new characterization of 2-resilient rotation symmetric Boolean functions, constructions of 2-resilient rotation symmetric Boolean functions (RSBFs) are further studied, and new 2-resilient rotation symmetric Boolean functions with prime variables are constructed.
Shanqi PANG Yajuan WANG Guangzhou CHEN Jiao DU
The orthogonal array is an important object in combinatorial design theory, and it is applied to many fields, such as computer science, coding theory and cryptography etc. This paper mainly studies the existence of the mixed orthogonal arrays of strength two with seven factors and presents some new constructions. Consequently, a few new mixed orthogonal arrays are obtained.
Lu ZHAO Bo XU Tianqing CAO Jiao DU
A unified construction for yielding optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences was proposed by Zeng et al. In this paper, the linear complexity over finite field 𝔽2, 𝔽4 and Galois ring ℤ4 of the quaternary sequences are discussed, respectively. The exact values of linear complexity of sequences obtained by Legendre sequence pair, twin-prime sequence pair and Hall's sextic sequence pair are derived.
Shaojing FU Jiao DU Longjiang QU Chao LI
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.
Le DONG Tianli WANG Jiao DU Shanqi PANG
We present a rebound attack on the 4-branch type-2 generalized Feistel structure with an SPS round function, which is called the type-2 GFN-SPS in this paper. Applying a non-full-active-match technique, we construct a 6-round known-key truncated differential distinguisher, and it can deduce a near-collision attack on compression functions of this structure embedding the MMO or MP modes. Extending the 6-round attack, we build a 7-round truncated differential path to get a known-key differential distinguisher with seven rounds. The results give some evidences that this structure is not stronger than the type-2 GFN with an SP round function and not weaker than that with an SPSP round function against the rebound attack.