Cryptography and Communications最新文献

For an (imaginary) hyperelliptic curve (mathcal {H}) of genus g, with a Weierstrass point (Omega ), taken as the point at infinity, we determine a basis of the Riemann-Roch space (mathcal {L}(Delta + m Omega )), where (Delta ) is of degree zero, directly from the Mumford representation of (Delta ). This provides in turn a generating matrix of a Goppa code.

Differential-linear cryptanalysis is an efficient cryptanalysis method to attack ARX ciphers, which have been used to present the best attacks on many ARX primitives such as Chaskey and Chacha. In this paper, we present the differential-linear cryptanalysis of another ARX-based block cipher SPARX-64/128. We first construct multiple 6-round differential-linear distinguishers based on the structure of SPARX-64/128, and then extend them into 14-round differential-linear distinguishers by adding a 7-round differential characteristic before and a one-round linear approximation after the distinguishers. Then we introduce a new linear approximation of modular addition, and use it to extend one more round after the 14-round differential-linear distinguishers. With the 15-round differential-linear distinguishers, we present a differential-linear attack on 18-round SPARX-64/128.

Bent functions have a number of practical applications in cryptography, coding theory, and other fields. Fourier transform is a key tool to study bent functions on finite abelian groups. Using Fourier transforms, in this paper, we first present two necessary and sufficient conditions on the existence of bent functions via faithful actions of finite abelian groups and then show two constructions of sequences with ideal auto-correlation (SIACs). In addition, we construct a periodic complementary sequence set (PCSS) by rearranging a periodic multiple shift sequence (PMSS) corresponding to a bent function on a finite abelian group. Some concrete constructions of SIACs and PCSSs are provided to illustrate the efficiency of our methods.

This paper studies Abelian and consta-Abelian polyadic codes over rings defined as affine algebras over chain rings. For this purpose, we use the classical construction via splittings and multipliers of the underlying Abelian group. We also derive some results on the structure of the associated polyadic codes and the number of codes under these conditions.

In 1953, Carlitz showed that all permutation polynomials over ({mathbb F}_q), where (q>2) is a power of a prime, are generated by the special permutation polynomials (x^{q-2}) (the inversion) and ( ax+b) (affine functions, where (0ne a, bin {mathbb F}_q)). Recently, Nikova, Nikov and Rijmen (2019) proposed an algorithm (NNR) to find a decomposition of the inverse function in quadratics, and computationally covered all dimensions (nle 16). Petrides (2023) theoretically found a class of integers for which it is easy to decompose the inverse into quadratics, and improved the NNR algorithm, thereby extending the computation up to (nle 32). In this paper, we extend Petrides’ result, as well as we propose a new number theoretical approach, which allows us to easily cover all (surely, odd) exponents up to 250, at least.

Let (mathbb {F}_q) be a finite field with q elements, where q is a power of a prime p. In this paper, we obtain an improvement on Weil bounds for character sums associated to a polynomial f(x) over (mathbb {F}_q ), which extends the results of Wan et al. (Des. Codes Cryptogr. 81, 459–468, 2016) and Wu et al. (Des. Codes Cryptogr. 90, 2813–2821, 2022).

In this paper, we not only give the parity check matrix of the [1, 0]-twisted generalized Reed-Solomon (in short, TGRS) code, but also determine the weight distribution. Especially, we show that the [1, 0]-TGRS code is not GRS or EGRS. Furthermore, we present a sufficient and necessary condition for any punctured code of the [1, 0]-TGRS code to be self-orthogonal, and then construct several classes of self-dual or almost self-dual [1, 0]-TGRS codes. Finally, on the basis of these self-dual or almost self-dual [1, 0]-TGRS codes, we obtain some LCD [1, 0]-TGRS codes.

The sequence pairs of length (2^{m}) projected from Type-II and Type-III/II complementary array pairs of size (2times 2times cdots times 2) (m-times) form Type-II and Type-III complementary sequence pairs, respectively. An exhaustive search for binary Type-II and Type-III complementary sequence pairs of small lengths (2^{m}) ((m=1,2,3,4)) shows that they are all projected from the aforementioned complementary array pairs, whose algebraic normal forms satisfy specified expressions. It’s natural to ask whether the conclusion holds for all m. In this paper, we proved that these expressions of algebraic normal forms determine all the binary Type-II and Type-III/II complementary array pairs of size (2times 2times cdots times 2).

In this paper, we address an open problem posed by Bai and Xia in [2]. We study polynomials of the form (f(x)=x^{4q+1}+lambda _1x^{5q}+lambda _2x^{q+4}) over the finite field ({mathbb F}_{5^{k}}), which are not quasi-multiplicative equivalent to any of the known permutation polynomials in the literature. We find necessary and sufficient conditions on (lambda _1, lambda _2 in {mathbb F}_{5^{k}}) so that f(x) is a permutation monomial, binomial, or trinomial of ({mathbb F}_{5^{2k}}).