Cryptography and Communications最新文献

Cyclic codes are an important subclass of linear codes, they not only have good algebraic structure, but also are easy to be encoded and decoded. At present, researchers have constructed many optimal ternary cyclic codes, but the study on quinary cyclic codes is less developed. In this paper, by analyzing the solutions of certain equations over (mathbb {F}_{5^m}), we construct some optimal quinary cyclic codes with three zeros and with parameters ([5^m-1, 5^m-2-2m, 4]), ([5^m-1, 5^m-2-frac{3m}{2}, 4]). Moreover, the weight distributions of two classes of their duals are also provided.

This paper presents a direct construction of novel type cross Z-complementary sequence sets (CZCSSs), whose aperiodic correlation sums exhibit zero correlation zones at both the front-end and tail-end shifts. CZCSS can be regarded as an extension of the symmetrical Z-complementary code set (SZCCS). The available construction of SZCCS has a limitation on the set size, with a maximum set size of 8. The proposed generalized Boolean function-based construction can generate CZCSS/SZCCS of length in the form of a non-power-of-two with variable set size (2^{n+1}), where each code has (2^{n+1}) constituent sequences. The proposed construction also yields cross Z-complementary pairs and cross Z-complementary sets with a larger number of constituent sequences compared to the existing work.

Linear complementary dual (LCD) codes are linear codes which intersect their dual codes trivially, which have been of interest and extensively studied due to their practical applications in computational complexity and information protection. In this paper, we give some methods for constructing LCD codes over small finite fields by modifying some typical methods for constructing linear codes. We show that all odd-like binary Euclidean LCD codes, ternary Euclidean LCD codes and quaternary Hermitian LCD codes can be constructed using the modified methods. Our results improve the known lower bounds on the largest minimum distances of LCD codes. Furthermore, we give two counterexamples to disprove the conjecture proposed by Bouyuklieva (Des. Codes Cryptogr. 89(11), 2445–2461 2021).

Abstract

As a particular subclass of cyclic codes, BCH codes have wide applications in storage devices, communication systems, consumer electronics and other fields. However, parameters of BCH codes are unknown in general. In this paper, we investigate parameters of BCH codes of length (frac{q^m+1}{lambda }) where (lambda mid q+1) .Some new techniques are employed to study the coset leaders. For any odd prime power q and (m=4,8) , or (mge 12) and (mequiv 4~ (textrm{mod}~ 8)) , the second, the third and the fourth largest coset leaders modulo (q^m+1) are determined, and the dimensions of some BCH codes of length (q^m+1) with large designed distances are given. For (1<lambda <q+1) , the first few largest coset leaders and the coset leaders modulo (frac{q^m+1}{lambda }) in the range 1 to ( frac{ q^{lfloor (m+1)/2rfloor }}{lambda }) are studied, and the dimensions of some BCH codes of length (frac{q^m+1}{lambda }) are given as well. The BCH codes presented in this paper are LCD codes and have a sharper lower bound on the minimum distance than the well-known BCH bound.

In this article, we examine Differential Fault Attacks (DFA) targeting two stream ciphers, FLIP and FiLIP. We explore the fault model where an adversary flips a single bit of the key at an unknown position. Our analysis involves establishing complexity bounds for these attacks, contingent upon the cryptographic parameters of the Boolean functions employed as filters and the key size. Initially, we demonstrate how the concept of sensitivity enables the detection of the fault position using only a few keystream bits. This represents an enhancement over previous DFA methodologies applied to these ciphers. Subsequently, we leverage the properties of the filter’s derivatives to execute attacks. This approach is universally applicable to any filter, and we delineate specific attack strategies for the two function families previously implemented in these ciphers.

Recently nonlinear feedback shift registers (NFSRs) have frequently been used as basic building blocks for stream ciphers. A major problem concerning NFSRs is to construct NFSRs with large periods. In this paper, a new NFSR structure whose period could be theoretically analyzed is proposed and studied, called GL-S-NFSR. A GL-S-NFSR is a selective cascade connection of a primitive Galois LFSR into a standard Galois NFSR with a linear simplified feedback function, where standard Galois NFSRs with linear simplified feedback functions are very useful in stream ciphers, e.g., Trivium. It is proved that the periods of the output sequences of a GL-S-NFSR are lower bounded by the product of all the Zsigmondy primes of ( 2^n-1 ) with a probability close to 1 under a weak assumption, and particularly, if n is a prime, then (2^n-1) divides the periods of the output sequences with a high probability, where n is the stage of the Galois LFSR. Besides, it is also proved that there are several registers satisfying that the periods are multiples of Zsigmondy primes without any assumption. Note that the main building block of Kreyvium consists of a standard Galois NFSR with a linear simplified feedback function and two pure cycling registers (PCRs). Periodic results on GL-S-NFSR are applied to Kreyvium by modifying one PCR to a primitive LFSR and the modified building block of Kreyvium is called M-Kreyvium. It is shown that the sequences involved in M-Kreyvium could have large periods with high probabilities.

A repairable ramp scheme is a ramp scheme in which a player can securely reconstruct a lost share with the help from a subset of players. This will take place without the participation of the dealer who set up the scheme. The repairing protocol should not compromise the security of the ramp scheme. Distribution designs were introduced by Stinson and Wei (Des. Codes Cryptogr. 86, 195–210 2018) and can be used to construct repairable ramp schemes. In this paper, we first give the definitions of a (varvec{(tau _{1},tau _{2},l_{1},l_{2})})-distribution design and a repairable ramp scheme. And we use anti-Pasch Steiner triple systems as distribution designs to construct repairable ramp schemes. We determine the existence of an anti-Pasch Steiner triple system (QFSTS(varvec{(v)})) with a minimum basic repairing set for (varvec{vequiv 1,3pmod 6}), (varvec{vgeqslant 9}) and (varvec{vne 13}). Then we obtain a (varvec{(2,4,n,3)})-repairable ramp scheme containing (varvec{n}) players with (varvec{lceil frac{2v}{3}rceil leqslant nleqslant frac{v(v-1)}{6}}).

The exclusion basis system is a combinatorial formulation of group key management that provides long-term and flexible protection for wireless sensor networks while allowing for reasonable adjustment of the number of keys per node and the number of re-key messages. In this paper, we extend the work of Karst and Wicker to near-resolvable design, symmetric balanced incomplete block designs, and balanced incomplete block designs with the repetition count of a distinct pair of elements equal to one, and it is observed that near-resolvable design provides minimal re-keying compared to symmetric balanced incomplete block designs and balanced incomplete block designs. Also, near-resolvable design and exclusion basis system have the same re-keying size when the number of keys is (n-1).

In this paper, we study a class of binary sequences with two-valued non-zero periodic autocorrelation sum and good periodic crosscorrelation sum as well as balanced properties. We make use of the sequences obtained in (No, J. et al., IEEE Trans. Inform. Theory 44(3), 1278-1282 2001) and adopt the extraction method similar to (Lüke, H. IEEE Trans. Inform. Theory 43(1) 1997). The new sequences are proven to be balanced or almost balanced. Based on these correlation and balanced properties, an important application is to construct Hadamard matrices of order (p+1) for (pequiv 3~()mod 4) and (2p+2) for (pequiv 1~()mod 4). Some examples are shown to verify the theoretical results.