Cryptography and Communications最新文献

This article introduces the concept of (mathcal {S}_0)-equivalence class, i.e. , n-variable Boolean functions up to the addition of a symmetric function null in (0_n) and (1_n), and investigates its application to study weightwise perfectly balanced functions. On the one hand, we show that weightwise properties, such as being weightwise perfectly balanced, the weightwise nonlinearity and weightwise algebraic immunity, are invariants of these equivalence classes. On the other hand, we analyze the variation of global parameters inside the same class, and prove, for example, that there is always a function with high degree, algebraic immunity, or nonlinearity in the (mathcal {S}_0)-equivalence class of a function. Finally, we discuss how these results can be extended to other equivalence relations and their applications in cryptography.

DNA sequences are prone to creating secondary structures by folding back on themselves by non-specific hybridization of its nucleotides. The formation of large stem-length secondary structures makes the sequences chemically inactive towards synthesis and sequencing processes. Furthermore, in DNA computing, other constraints like homopolymer run length also introduce complications. In this paper, our goal is to tackle the problems due to the creation of secondary structures in DNA sequences along with constraints such as not having a large homopolymer run length. This paper presents families of DNA codes with secondary structures of stem length at most two and homopolymer run length at most four. We identified (mathbb {Z}_{11}) as an ideal structure to construct DNA codes to avoid the above problems. By mapping the error-correcting codes over (mathbb {Z}_{11}) to DNA nucleotides, we obtained DNA codes with rates 0.5765 times the corresponding code rate over (mathbb {Z}_{11}), including some new secondary structure-free and better-performing codes for DNA-based data storage and DNA computing purposes.

Code-based cryptography received attention after the NIST started the post-quantum cryptography standardization process in 2016. A central NP-hard problem is the binary syndrome decoding problem, on which the security of many code-based cryptosystems lies. The best known methods to solve this problem all stem from the information-set decoding strategy, first introduced by Prange in 1962. A recent line of work considers augmented versions of this strategy, with hints typically provided by side-channel information. In this work, we consider the integer syndrome decoding problem, where the integer syndrome is available but might be noisy. We study how the performance of the decoder is affected by the noise. First we identify the noise model as being close to a centered in zero binomial distribution. Second we model the probability of success of the ISD-score decoder in presence of a binomial noise. Third, we demonstrate that with high probability our algorithm finds the solution as long as the noise parameter d is linear in t (the Hamming weight of the solution) and t is sub-linear in the code-length. We provide experimental results on cryptographic parameters for the BIKE and Classic McEliece cryptosystems, which are both candidates for the fourth round of the NIST standardization process.

Additive codes have a wide range of applications. A classical nice and generic way to construct linear codes is via trace functions. In this paper, first, we generalize this method to construct additive codes. Then, we use this method to get some explicit additive codes. Computing Weil-like sums, we obtain parameters of these codes such as the length and weight distribution. We show that our codes have few weights.

In recent years, zero-correlation zone (ZCZ) sequences have been studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, in a cognitive radio (CR) network, it is desirable to design ZCZ sequences having spectrally-null-constrained (SNC) property to achieve a low spectral density profile. This paper focuses on the construction of SNC-ZCZ sequences having flexible support, where support refers to a collection of indices corresponding to non-zero entries in the sequence. The proposed SNC-ZCZ sequences are reduced to traditional ZCZ sequences when the support size is equal to the length of the sequence. To obtain ZCZ sequences, we first propose a construction of traditional/SNC-complete complementary codes (SNC-CCCs) using a class of extended Boolean functions (EBFs). With the help of this class, we propose another class of EBFs that generates asymptotically optimal traditional/SNC-ZCZ sequences of prime-power lengths with respect to Tang-Fan-Matsufuzi bound. Furthermore, a relation between the second-order cosets of first-order generalized Reed-Muller (GRM) code and the proposed traditional ZCZ sequences is also established. The enumeration of traditional ZCZ sequences within a GRM code is also established. This enumeration is achieved by tallying the distinct second-order cosets of the first-order GRM code and quantifying the number of ZCZ sequences residing within a particular coset. Moreover, the Hamming distance of the proposed traditional ZCZ sequences is also computed.

V. Levenshtein first proposed the sequence reconstruction problem in 2001. This problem studies the same sequence from some set is transmitted over multiple channels, and the decoder receives the different outputs. Assume that the transmitted sequence is at distance d from some code and there are at most r errors in every channel. Then the sequence reconstruction problem is to find the minimum number of channels required to recover exactly the transmitted sequence that has to be greater than the maximum intersection between two metric balls of radius r, where the distance between their centers is at least d. In this paper, we study the sequence reconstruction problem of permutations under the Hamming distance. In this model we define a Cayley graph over the symmetric group, study its properties and find the exact value of the largest intersection of its two metric balls for (d=2r). Moreover, we give a lower bound on the largest intersection of two metric balls for (d=2r-1).

Additive codes have gained importance in algebraic coding theory due to their applications in quantum error correction and quantum computing. The article begins by developing some properties of Additive Complementary Dual (ACD) codes with respect to arbitrary dualities over finite abelian groups. Further, we introduce a subclass of non-symmetric dualities referred to as the skew-symmetric dualities. Then, we precisely count symmetric and skew-symmetric dualities over finite fields. Two conditions have been obtained: one is a necessary and sufficient condition, and the other is a necessary condition. The necessary and sufficient condition is for an additive code to be an ACD code over arbitrary dualities. The necessary condition is on a generator matrix of an ACD code over skew-symmetric dualities. We provide bounds for the highest possible minimum distance of ACD codes over skew-symmetric dualities. Finally, we find some new quaternary ACD codes over non-symmetric dualities with better parameters than the symmetric ones.

Many modern cryptographic primitives for hashing and (authenticated) encryption make use of constructions that are instantiated with an iterated cryptographic permutation that operates on a fixed-width state consisting of an array of bits. Often, such permutations are the repeated application of a relatively simple round function consisting of a linear layer and a non-linear layer. These constructions do not require that the underlying function is a permutation and they can plausibly be based on a non-invertible transformation. Recently, Grassi proposed the use of non-invertible mappings operating on arrays of digits that are elements of a finite field of odd characteristic for so-called MPC-/FHE-/ZK-friendly symmetric cryptographic primitives. In this work, we consider a mapping that we call (gamma ) that has a simple expression and is based on squaring. We discuss, for the first time, the differential and linear propagation properties of (gamma ) and observe that these follow the same rules up to a relabeling of the digits. This is an intriguing property that, as far as we know, only exists for (gamma ) and the binary mapping (chi _{_{3}}) that is used in the cryptographic permutation Xoodoo. Moreover, we study the implications of its non-invertibility on differentials with zero output difference and on biases at the output of the (gamma ) mapping and show that they are as small as they can possibly be.

We describe the computer-aided classification of equitable partitions of the 12-cube with quotient matrix [[2, 10], [6, 6]], or, equivalently, simple orthogonal arrays OA(1536, 12, 2, 7), or order-7 correlation-immune Boolean functions in 12 arguments with 1536 ones (which completes the classification of unbalanced order-7 correlation-immune Boolean functions in 12 arguments and, as derived objects, unbalanced order-6 correlation-immune Boolean functions in 11 arguments). We find that there are 103 equivalence classes of the considered objects, and there are only two almost-OA(1536, 12, 2, 8) among them. Additionally, we find that there are 40 equivalence classes of pairs of disjoint simple OA(1536, 12, 2, 7) (equivalently, equitable partitions of the 12-cube with quotient matrix [[2, 6, 4], [6, 2, 4], [6, 6, 0]]) and discuss the existence of a non-simple OA(1536, 12, 2, 7).

This paper presents a class of integer codes that are suitable for use in various optical networks. The presented codes are generated with the help of a computer and have the ability to correct l-bit burst errors corrupting one b-bit byte (1 ≤ l < b) and single errors corrupting two b-bit bytes. To evaluate the performance of the presented codes, we analyze their probabilities of incorrect decoding for two types of channels. In addition, the paper shows that the proposed codes can be interleaved without using an interleaver, which allows the decoder to correct all l-bit burst errors as well as many random errors.