# Cryptography and Communications

Publisher: Springer Verlag

## Description

- Impact factor0.00
- 5-year impact0.00
- Cited half-life0.00
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- ISSN1936-2447
- OCLC85825471
- Material typePeriodical, Internet resource
- Document typeJournal / Magazine / Newspaper, Internet Resource

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- Classification green

## Publications in this journal

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**ABSTRACT:**We study the relationship between the Walsh Transform of a Boolean function and its Algebraic Normal Form(ANF), and present algorithms that compute the Walsh coefficients at a small set of points in terms of certain parameters derived from the ANF of a Boolean function. In the first part of this paper, based on the previous result by Gupta and Sarkar, we investigate the formula in Gupta-Sarkar’s algorithm in a novel iterative method and obtain a recurrence relation for the Walsh Transform of a Boolean function. The second part is devoted to applying this formula to algorithms to evaluate it. Experimental result shows that for the specified classes of Boolean functions, our algorithms can perform better than Gupta-Sarkar’s algorithm. For example, the proposed algorithm “ComputeWalsh” is able to compute the Walsh coefficients of the functions for which the complexity of Gupta-Sarkar’s algorithm is impractical. Besides, for functions acting on high number of variables (m>30) and having low number of monomials, the proposed algorithms are advantageous over the Fast Walsh Transform which is a standard method of computing the Walsh Transform with a complexity of O(m2m ) operations.Cryptography and Communications 12/2014; 6(4). - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper investigates a new framework to analyze symmetric ciphers by guessing intermediate states and dividing algorithms into consecutive sub-ciphers. It is suitable for lightweight ciphers with simple key schedules and block sizes smaller than key lengths. New attacks on the block cipher family KATAN are proposed by adopting this framework. Our new attacks can recover the master keys of 175-round KATAN32, 130-round KATAN48 and 112-round KATAN64 faster than exhaustive search, and thus reach many more rounds than previous attacks. We also provide new attacks on 115-round KATAN32 and 100-round KATAN48 in order to demonstrate this new kind of attacks can be more time-efficient and memory-efficient than existing attacks.Cryptography and Communications 12/2014; 6(4). - [Show abstract] [Hide abstract]

**ABSTRACT:**A set of words with the property that no prefix of any word is the suffix of any other word is called cross-bifix-free set. We provide an efficient generating algorithm producing Gray codes for a remarkable family of cross-bifix-free sets.Cryptography and Communications 12/2014; 6(4). - [Show abstract] [Hide abstract]

**ABSTRACT:**Iterated attacks are comprised of iterating adversaries who can make d plaintext queries, in each iteration to compute a bit, and are trying to distinguish between a random cipher C and the perfect cipher C ∗ based on all bits. Vaudenay showed that a 2d-decorrelated cipher resists to iterated attacks of order d when iterations have almost no common queries. Then, he first asked what the necessary conditions are for a cipher to resist a non-adaptive iterated attack of order d. I.e., whether decorrelation of order 2d − 1 could be sufficient. Secondly, he speculated that repeating a plaintext query in different iterations does not provide any advantage to a non-adaptive distinguisher. We close here these two long-standing open problems negatively. For those questions, we provide two counter-intuitive examples.W e also deal with adaptive iterated adversaries who can make both plaintext and ciphertext queries in which the future queries are dependent on the past queries. We show that decorrelation of order 2d protects against these attacks of order d. We also study the generalization of these distinguishers for iterations making non-binary outcomes. Finally, we measure the resistance against two well-known statistical distinguishers, namely, differential-linear and boomerang distinguishers and show that 4-decorrelation degree protects against these attacks.Cryptography and Communications 12/2014; 6(4). - [Show abstract] [Hide abstract]

**ABSTRACT:**Hitag2 is a widely applied lightweight stream cipher with a traditional structure containing linear shift feedback and nonlinear filtering. It uses a Boolean function of 20 variables as its nonlinear filter. For easy implementation, this function is constructed by a two-layer composition of one 5-variable Boolean function and five 4-variable Boolean functions. In this paper, the concept of nested function is extracted from the construction of the two-layer Boolean function in Hitag2. Then we study some general properties of nested functions, such as balancedness, algebraic degree, Walsh spectra and algebraic immunity. We prove that the Walsh spectra of a nested function can be split into a product of the Walsh spectra of its subfunctions and generating function when the subfunctions are all balanced. Moreover, two upper bounds on algebraic immunity of nested functions are proposed. By using a hybrid approach of logical reasoning and computer computation, we obtain the precise value of the algebraic immunity of the filter function used in Hitag2, which is equal to 6.Cryptography and Communications 09/2014; 6(3). - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the access structure and multiplicativity of linear secret sharing schemes based on codes from complete graphs. First, we describe the access structure of the schemes based on cut-set and cycle codes. Second, we show that the class of access structures based on odd cycles cannot be realized by ideal multiplicative linear secret sharing schemes over any finite field. This can be seen as a contribution to the characterization of access structures of ideal multiplicative schemes. The access structure based on odd cycles corresponds to the scheme based on the dual of the extended cycle code. Finally, we show that we can obtain ideal multiplicative linear secret sharing scheme based on the dual of an augmented extended cycle code.Cryptography and Communications 06/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**The nonlinearity of a Boolean function $F: \mathbb{F}_{2}^{m}\rightarrow \mathbb{F}_{2}$ is the minimum Hamming distance between f and all affine functions. The nonlinearity of a S-box $f: \mathbb{F}_{2}^{m}\rightarrow \mathbb{F}_{2}^{n}$ is the minimum nonlinearity of its component (Boolean) functions $v\cdot f,\, v\in \mathbb{F}_{2}^{n}\,\backslash \{0\}$ . This notion quantifies the level of resistance of the S-box to the linear attack. In this paper, the distribution of the nonlinearity of (m, n)-functions is investigated. When n = 1, it is known that asymptotically, almost all m-variable Boolean functions have high nonlinearities. We extend this result to (m, n)-functions.Cryptography and Communications 06/2014; 6(2). - [Show abstract] [Hide abstract]

**ABSTRACT:**Let G be a simple, undirected graph with vertex set V. For v ∈ V and r ≥ 1, we denote by B G,r (v) the ball of radius r and centre v. A set ${\cal C} \subseteq V$ is said to be an r-identifying code in G if the sets $B_{G,r}(v)\cap {\cal C}$ , v ∈ V, are all nonempty and distinct. A graph G admitting an r-identifying code is called r-twin-free, and in this case the size of a smallest r-identifying code in G is denoted by γ r (G). We study the following structural problem: let G be an r-twin-free graph, and G * be a graph obtained from G by adding or deleting a vertex. If G * is still r-twin-free, we compare the behaviours of γ r (G) and $\gamma_r(G^*)$ , establishing results on their possible differences and ratios.Cryptography and Communications 06/2014; 5(2). - [Show abstract] [Hide abstract]

**ABSTRACT:**We show the existence of perfect arrays, of unbounded sizes, over the basic quaternions {1, − 1,i, − i,j, − j,k, − k}. We translate the algorithm of Arasu and de Launey, to inflate perfect arrays over the four roots of unity, from a polynomial, into a simple matrix approach. Then, we modify this algorithm to inflate perfect arrays over the basic quaternions {1, − 1,i, − i,j, − j,k, − k}. We show that all modified Lee Sequences (in the sense of Barrera Acevedo and Hall, Lect Notes Comput Sci 159–167, 2012) of length m = p + 1 ≡ 2 (mod 4), where p is a prime number, can be folded into a perfect two-dimensional array (with only one occurrence of the element j) of size $2\times \frac{m}{2}$ , with $GCD(2,\frac{m}{2})=1$ . Then, each of these arrays can be inflated into perfect arrays of sizes $2p\times \frac{m}{2}p$ (previously unknown sizes), with a random appearance of all the elements 1, − 1,i, − i,j, − j,k, − k.Cryptography and Communications 03/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**This paper presents a new method of construction of near perfect sequences of even length N = 2mn where m is an odd prime number and n = (2J + 1), J is an even number. We use a shift sequence associated with a primitive polynomial of degree 2J over a finite field GF(2), together with a pair of completely orthogonal sequences of length m to construct near perfect sequences of odd lengths. We concatenate two near perfect sequences of same odd lengths under certain conditions to obtain new near perfect sequences of even lengths. These near perfect sequences also exist for unbounded lengths over m th roots of unity.Cryptography and Communications 03/2014; 6(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**We propose a construction for complementary sets of arrays that exploits a set of mutually-unbiased bases (a MUB). In particular we present, in detail, the construction for complementary pairs that is seeded by a MUB of dimension 2, where we enumerate ...Cryptography and Communications 03/2014; 6(1). - [Show abstract] [Hide abstract]

**ABSTRACT:**We describe a systematic framework for using a stream cipher supporting an initialisation vector (IV) to perform various tasks of authentication and authenticated encryption. These include message authentication code (MAC), authenticated encryption (AE), authenticated encryption with associated data (AEAD) and deterministic authenticated encryption (DAE) with associated data. Several schemes are presented and rigourously analysed. A major component of the constructions is a keyed hash function having provably low collision and differential probabilities. Methods are described to efficiently extend such hash functions to take multiple inputs. In particular, double-input hash functions are required for the construction of AEAD schemes. An important practical aspect of our work is that a designer can combine off-the-shelf stream ciphers with off-the-shelf hash functions to obtain secure primitives for MAC, AE, AEAD and DAE(AD).Cryptography and Communications 01/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**We give easy proofs of some recent results concerning threshold gaps in ramp schemes. We then generalise a construction method for ramp schemes employing error-correcting codes so that it can be applied using nonlinear (as well as linear) codes. Finally, as an immediate consequence of these results, we provide a new explicit bound on the minimum length of a code having a specified distance and dual distance.Cryptography and Communications 12/2013; - [Show abstract] [Hide abstract]

**ABSTRACT:**The stream cipher WG-7 is a lightweight variant of the well-known Welch- Gong (WG) stream cipher family, targeted to resource-constrained devices like RFID tags, smart cards, and wireless sensor nodes. Recently, a distinguishing attack was discovered against the stream cipher WG-7 by Orumiehchiha, Pieprzyk and Steinfeld. In this paper, we extend their work to a general distinguishing attack and suggest criteria to protect the WG stream cipher family from this attack. Our analysis shows that by properly choosing the minimal polynomial of the linear feedback shift register for a WG stream cipher, the general distinguishing attack can be easily thwarted.Cryptography and Communications 12/2013; 5(4). -
##### Article: Block weighing matrices

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**ABSTRACT:**We define a special type of weighing matrix called block weighing matrices. Motivated by questions arising in the context of optical quantum computing, we prove that infinite families of anticirculant block weighing matrices can be obtained from generic weighing matrices. The classification problem is left open.Cryptography and Communications 09/2013; 5(3). - [Show abstract] [Hide abstract]

**ABSTRACT:**The algebraic immunity of cryptographic Boolean functions with odd number of variables is studied in this paper. Proper modifications of functions with maximum algebraic immunity are proved that yield new functions whose algebraic immunity is also maximum. Several results are provided for both the multivariate and univariate representation, and their applicability is shown on known classes of Boolean functions. Moreover, new efficient algorithms to produce functions of guaranteed maximum algebraic immunity are developed, which further extend and generalize well-known constructions in this area. It is shown that high nonlinearity as well as good behavior against fast algebraic attacks are also achievable in several cases.Cryptography and Communications 09/2013; 5(3). - [Show abstract] [Hide abstract]

**ABSTRACT:**We present a construction for complementary pairs of arrays that exploits a set of mutually-unbiased bases, and enumerate these arrays as well as the corresponding set of complementary sequences obtained from the arrays by projection. We also sketch an algorithm to uniquely generate these sequences. The pairwise squared inner-product of members of the sequence set is shown to be $\frac{1}{2}$. Moreover, a subset of the set can be viewed as a codebook that asymptotically achieves $\sqrt{\frac{3}{2}}$ times the Welch bound.Cryptography and Communications 08/2013; 6(1).

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