ISSN:

1930-5346

eISSN:

1930-5338

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## Advances in Mathematics of Communications

February 2019 , Volume 13 , Issue 1

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**Abstract:**

The first construction of strongly secure quantum ramp secret sharing by Zhang and Matsumoto had an undesirable feature that the dimension of quantum shares must be larger than the number of shares. By using algebraic curves over finite fields, we propose a new construction in which the number of shares can become arbitrarily large for fixed dimension of shares.

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**Abstract:**

We consider a communication scenario in which the channel undergoes two different classes of attacks at the same time: a passive eavesdropper and an active jammer. This scenario is modelled by the concept of *arbitrarily varying wiretap channels* (AVWCs). In this paper, we derive a full characterization of the list secrecy capacity of the AVWC, showing that the list secrecy capacity is equivalent to the correlated random secrecy capacity if the list size *L* is greater than the order of symmetrizability of the AVC between the transmitter and the legitimate receiver. Otherwise, it is zero. Our result indicates that for a sufficiently large list size *L*, list codes can overcome the drawbacks of correlated and uncorrelated codes and provide a stable secrecy capacity for AVWCs. Furthermore, we investigate the effect of relaxing the reliability and secrecy constraints by allowing a non-vanishing error probability and information leakage on the list size *L*. We found that we can construct a list code whose rate is close to the correlated secrecy capacity using a finite list size *L* that only depends on the average error probability requested. Finally, we point out that our capacity characterization is an important step in investigating the analytical properties of the capacity function such as: the continuity behavior, Turing computability and super-activation of parallel AVWCs.

*+*[Abstract](2851)

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**Abstract:**

Scalar multiplication on suitable Legendre form elliptic curves can be speeded up in two ways. One can perform the bulk of the computation either on the associated Kummer line or on an appropriate twisted Edwards form elliptic curve. This paper provides details of moving to and from between Legendre form elliptic curves and associated Kummer line and moving to and from between Legendre form elliptic curves and related twisted Edwards form elliptic curves. Further, concrete twisted Edwards form elliptic curves are identified which correspond to known Kummer lines at the 128-bit security level which provide very fast scalar multiplication on modern architectures supporting SIMD operations.

*+*[Abstract](2234)

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**Abstract:**

Round functions used as building blocks for iterated block ciphers, both in the case of Substitution-Permutation Networks (SPN) and Feistel Networks (FN), are often obtained as the composition of different layers. The bijectivity of any encryption function is guaranteed by the use of invertible layers or by the Feistel structure. In this work a new family of ciphers, called *wave ciphers*, is introduced. In wave ciphers, round functions feature *wave functions*, which are vectorial Boolean functions obtained as the composition of *non-invertible* layers, where the confusion layer enlarges the message which returns to its original size after the diffusion layer is applied. Efficient decryption is guaranteed by the use of wave functions in FNs. It is shown how to avoid that the group generated by the round functions acts imprimitively, a serious flaw for the cipher. The primitivity is a consequence of a more general result, which reduce the problem of proving that a given FN generates a primitive group to proving that an SPN, directly related to the given FN, generates a primitive group. Finally, a concrete instance of real-world size wave cipher is proposed as an example, and its resistance against differential and linear cryptanalyses is also established.

*+*[Abstract](2879)

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**Abstract:**

One of the basic problems in secret sharing is to determine the exact values of the information ratio of the access structures. This task is important from the practical point of view, since the security of any system degrades as the amount of secret information increases.

A Dutch windmill graph consists of the edge-disjoint cycles such that all of them meet in one vertex. In this paper, we determine the exact information ratio of secret sharing schemes on the Dutch windmill graphs. Furthermore, we determine the exact ratio of some related graph families.

*+*[Abstract](2856)

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**Abstract:**

In the recent work [

*+*[Abstract](2978)

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**Abstract:**

We revisit the factoring with known bits problem on RSA moduli. In 1996, Coppersmith showed that the RSA modulus

*+*[Abstract](2987)

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**Abstract:**

Cyclic codes over finite field have been studied for decades due to their wide applications in communication and storage systems. However their weight distributions are known only in a few cases. In this paper, we investigate a class of

*+*[Abstract](2937)

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**Abstract:**

In this paper, we construct cyclic DNA codes over the ring

*+*[Abstract](2445)

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**Abstract:**

Based on the existence of designs for the derived and residual parameters of admissible parameter sets of designs over finite fields we obtain a new infinite series of designs over finite fields for arbitrary prime powers

*+*[Abstract](2831)

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**Abstract:**

This paper investigates the existence, enumeration, and asymptotic performance of self-dual and LCD double circulant codes over Galois rings of characteristic

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**Abstract:**

We identify a flaw in the security proof and a flaw in the concrete security analysis of the WOTS-PRF variant of the Winternitz one-time signature scheme, and discuss the implications to its concrete security.

*+*[Abstract](3177)

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**Abstract:**

Let

where

In this paper, we will present the weight enumerators of the linear codes

1.

2.

It is shown that

2018 Impact Factor: 0.879

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