Cryptography and Communications

Publisher: Springer Verlag


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Springer Verlag

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Publications in this journal

  • [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).
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    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).
  • Cryptography and Communications 03/2014; 6(1).
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    ABSTRACT: Cross-bifix-free sets are sets of bifix-free sequences with the property that no prefix of any sequence is a suffix of any other sequence. This paper presents a general construction method for cross-bifix-free sequences based on kernels. The cardinality of cross-bifix-free sets follows the Fibonacci progression. A simplified method, applicable to a limited number of so-called “regular kernel sets”, is proposed as well. Properties of such sequences with an outline for further research are discussed.
    Cryptography and Communications 03/2014; 6(1).
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    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).
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    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;
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    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;
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    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).
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    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;
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    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).
  • [show abstract] [hide abstract]
    ABSTRACT: In this paper, we first present some new results about the Welch-Gong (WG) transformations, followed by a description of the WG stream cipher family which is built upon an LFSR and a WG transformation over an extension field. The randomness properties of keystreams produced by a decimated WG cipher are derived based on the new results. We also discuss the selection criteria for choosing the optimal parameters for a WG cipher in order to achieve the maximum level of security. Finally, we present the optimal parameters for the WG transformations over GF(2m); 7 <=m<=16 based on the proposed criteria.
    2013 13th Canadian Workshop on Information Theory (CWIT'13); 06/2013
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    ABSTRACT: We examine the security of the 64-bit lightweight block cipher PRESENT-80 against related-key differential attacks. With a computer search we are able to prove that for any related-key differential characteristic on full-round PRESENT-80, the probability of the characteristic only in the 64-bit state is not higher than 2−64. To overcome the exponential (in the state and key sizes) computational complexity of the search we use truncated differences, however as the key schedule is not nibble oriented, we switch to actual differences and apply early abort techniques to prune the tree-based search. With a new method called extended split approach we are able to make the whole search feasible and we implement and run it in real time. Our approach targets the PRESENT-80 cipher however,with small modifications can be reused for other lightweight ciphers as well.
    Cryptography and Communications 01/2013;
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    ABSTRACT: In this paper we give the second weight codewords of the generalized Reed-Muller code of order r and length $q^m$.
    Cryptography and Communications 03/2012;
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    ABSTRACT: Linear cryptanalysis and linear approximation methods in general are among the most important cryptanalysis methods of symmetric ciphers and their components. Recently, these methods have been extended to efficiently exploit multiple linear approximations simultaneously. It is known that high nonlinearity of Boolean functions and S-boxes is a desirable property and that the bent functions offer the strongest resistance against cryptanalysis using single linear approximations. The goal of this paper is to investigate to which extent resistance against the multidimensional extension of the linear cryptanalysis method can be achieved. For this purpose some common highly nonlinear Boolean functions as well as a basic LFSR based key stream generator using a nonlinear filter function are investigated.
    Cryptography and Communications 01/2012; 4:47-64.
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    ABSTRACT: In this paper the possibilities of an iterative concatenation method towards construction of Boolean functions resistant to algebraic cryptanalysis are investigated. The notion of $\mathcal{AAR}$ (Algebraic Attack Resistant) function is introduced as a unified measure of protection against classical algebraic attacks as well as fast algebraic attacks. Then, it is shown that functions that posses the highest resistance to fast algebraic attacks are necessarily of maximum algebraic immunity, thus opposing a maximum resistance to algebraic cryptanalysis in general. The developed theoretical framework allows us to iteratively construct functions with maximum $\mathcal{AI}$ , and of almost optimized resistance to fast algebraic cryptanalysis. This infinite class for the first time, apart from almost optimal resistance to algebraic cryptanalysis, in addition generates functions that allow an extremely efficient hardware implementation, possess high nonlinearity and maximum algebraic degree; thus unifying most of the relevant cryptographic criteria.
    Cryptography and Communications 01/2012; 4:25-45.
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    ABSTRACT: In this paper we give a new construction of highly nonlinear vectorial Boolean functions. This construction is based on coding theory, more precisely we use concatenation to construct Boolean functions from codes over containing a first-order generalized Reed–Muller code. As it turns out this construction has a very compact description in terms of Boolean functions, which is of independent interest. The construction allows one to design functions with better nonlinearities than known before.
    Cryptography and Communications 01/2012; 4:65-77.
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    ABSTRACT: To date, the basic idea for implementing stream ciphers has been confined to individual standalone designs. In this paper, we introduce the notion of integrated implementation of multiple stream ciphers within a single architecture, where the goal is to achieve area and throughput efficiency by exploiting the structural similarities of the ciphers at an algorithmic level. We present two case studies to support our idea. First, we propose the merger of SNOW 3G and ZUC stream ciphers, which constitute a part of the 3GPP LTE-Advanced security suite. We propose HiPAcc-LTE, a high performance integrated design that combines the two ciphers in hardware, based on their structural similarities. The integrated architecture reduces the area overhead significantly compared to two distinct cores, and also provides almost double throughput in terms of keystream generation, compared with the state-of-the-art implementations of the individual ciphers. As our second case study, we present IntAcc-RCHC, an integrated accelerator for the stream ciphers RC4 and HC-128. We show that the integrated accelerator achieves a slight reduction in area without any loss in throughput compared to our standalone implementations. We also achieve at least 1.5 times better throughput compared to general purpose processors. Long term vision of this hardware integration approach for cryptographic primitives is to build a flexible core supporting multiple designs having similar algorithmic structures.
    Cryptography and Communications 01/2012; 2012:48.
  • [show abstract] [hide abstract]
    ABSTRACT: We prove a necessary condition for some polynomials of degree 4e (e an odd number) to be APN over for large n, and we investigate the polynomials f of degree 12.
    Cryptography and Communications 01/2011; 3:227-240.

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