Designs, Codes and Cryptography最新文献

An orientable sequence of order n over an alphabet({0,1,ldots , k{-}1}) is a cyclic sequence such that each length-n substring appears at most once in either direction. When (k= 2), efficient algorithms are known to construct binary orientable sequences, with asymptotically optimal length, by applying the classic cycle-joining technique. The key to the construction is the definition of a parent rule to construct a cycle-joining tree of asymmetric bracelets. Unfortunately, the parent rule does not generalize to larger alphabets. Furthermore, unlike the binary case, a cycle-joining tree does not immediately lead to a simple successor-rule when (k ge 3) unless the tree has certain properties. In this paper, we derive a parent rule to derive a cycle-joining tree of k-ary asymmetric bracelets. This leads to a successor rule that constructs asymptotically optimal k-ary orientable sequences in O(n) time per symbol using O(n) space. In the special case when (n=2), we provide a simple construction of k-ary orientable sequences of maximal length.

SCARF, an ultra low-latency tweakable block cipher, is the first cipher designed for cache randomization. The block cipher design is significantly different from other common tweakable block ciphers; with a block size of only 10 bits, and yet the input key size is a whopping 240 bits. Notably, the majority of the round key in its round function is absorbed into the data path through AND operations, rather than the typical XOR operations. In this paper, we present a key-recovery attack on a round-reduced version of SCARF with 4 + 4 rounds under the single pair-of-tweaks setting. Our attack is essentially a Meet-in-the-Middle (MitM) attack, where the matching phase is represented by a system of linear equations. Unlike the cryptanalysis conducted by the designers, our attack is effective under both security requirements they have outlined. The data complexity of our attack is (2^{10}) plaintexts, with a time complexity of approximately (2^{60.63}) 4-round of SCARF encryptions. It is important to note that our attack does not threaten the overall security of SCARF.

Let p be any prime number such that (pequiv 1 pmod 4), and let ({mathbb {F}}_p) be the finite field of p elements. In this paper, we first construct a new AMDS symbol-pair cyclic code of length 4p and of symbol-pair distance 9 by examining its generator polynomial. We then use the generator polynomial to obtain a family of ((p-1)/2) AMDS symbol-pair constacyclic codes of the same length and of the same symbol-pair distance.

In 1999, Xing, Niederreiter and Lam introduced a generalization of AG codes (GAG codes) using the evaluation at non-rational places of a function field. In this paper, we show that one can obtain a locality parameter r in such codes by using only non-rational places of degree at most r. This is, up to the author’s knowledge, a new way to construct locally recoverable codes (LRCs). We give an example of such a code reaching the Singleton-like bound for LRCs, and show the parameters obtained for some longer codes over (mathbb F_3). We then investigate similarities with some concatenated codes. Contrary to previous methods, our construction allows one to obtain directly codes whose dimension is not a multiple of the locality. Finally, we give an asymptotic study using the Garcia–Stichtenoth tower of function fields, for both our construction with GAG codes and a construction of concatenated codes. We give explicit infinite families of LRCs with locality 2 over any finite field of cardinality greater than 3 following our approach with GAG codes.

Symbol-pair codes introduced by Cassuto and Blaum in 2010 are designed to protect against pair errors in symbol-pair read channels. This special channel structure is motivated by the limitations of the reading process in high density data storage systems, where it is no longer possible to read individual symbols. In this work, we study bounds and constructions of codes in symbol-pair metric. By using some combinatorial structures, we give constructions of optimal q-ary symbol-pair codes with constant pair-weight (w_p) and pair-distance (2w_p-1) for some length n, and some optimal q-ary codes with pair-weight (w_p=3,4) for all pair-distance between 3 and (2w_p-1).

Two-dimensional multilength optical orthogonal codes (2D MLOOCs) were proposed as a means of simultaneously reducing the chip rate and accommodating multimedia services with multiple bit rates and quality of service (QoS) requirements in OCDMA networks. This paper considers two-dimensional multilength optical orthogonal codes with inter-cross-correlation of (lambda =2). New upper bounds on the size of 2D MLOOCs are presented under certain constraints. In order to construct optimal 2D MLOOCs, a compatible mixed difference packing (CMDP) set system is introduced. By using both direct constructions and recursive constructions, several series of 2D MLOOCs are obtained which are optimal with respect to the new upper bounds.

Anemoi is a family of compression and hash functions over finite fields (mathbb {F}_q) for efficient Zero-Knowledge applications. Its round function is based on a novel permutation (mathcal {H}: mathbb {F}_q^2 rightarrow mathbb {F}_q^2), called the open Flystel, which is parametrized by a permutation (E: mathbb {F}_q rightarrow mathbb {F}_q) and two functions (Q_gamma , Q_delta : mathbb {F}_q rightarrow mathbb {F}_q). Over a prime field (mathbb {F}_p) with E a power permutation and (Q_gamma ), (Q_delta ) quadratic functions with identical leading coefficient, the Anemoi designers conjectured for the absolute value of the Walsh transform that (max _{textbf{a} in mathbb {F}_p^2, textbf{b} in mathbb {F}_p^2 {setminus } { textbf{0} }} left| mathcal {W}_mathcal {H} (psi , textbf{a}, textbf{b}) right| le p cdot log left( p right) ). By exploiting that the open Flystel is CCZ-equivalent to the closed Flystel, we prove in this note that (max _{textbf{a} in mathbb {F}_p^2, textbf{b} in mathbb {F}_p^2 {setminus } { textbf{0} }} left| mathcal {W}_mathcal {H} (psi , textbf{a}, textbf{b}) right| le (d - 1) cdot p), where (d = deg left( E right) ).

Non-overlapping codes over a given alphabet are defined as a set of words satisfying the property that no prefix of any length of any word is a suffix of any word in the set, including itself. When the word lengths are variable, it is additionally required that no word is contained as a subword within any other word. In this paper, we present a new construction of variable-length non-overlapping codes that generalizes the construction by Bilotta. Subsequently, we derive the generating function and an enumerative formula for our constructed code, and establish upper bound on their cardinalities. A comparison with the bound provided by Bilotta shows that the newly constructed code offers improved performance in the code size.

In a previous paper, the authors determined the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Hoffman coclique. As a counterpart of this result, in the present paper we determine the parameters of all strongly regular graphs that can be decomposed into a divisible design graph and a Delsarte clique. In particular, an infinite family of strongly regular graphs with the required decomposition and a new infinite family of divisible design graphs are found.

Complete permutations in addition over finite fields have attracted many scholars’ attention due to their wide applications in combinatorics, cryptography, sequences, and so on. In 2020, Tu et al. introduced the concept of the complete permutation in the sense of multiplication (CPM for short). In this paper, we further study the constructions and applications of CPMs. We mainly construct many classes of CPMs through three different approaches, i.e., index, self-inverse binomial, which is a new concept proposed in this paper, and linearized polynomial. Particularly, we provide a modular algorithm to produce all CPMs with a given index and determine all CPMs with index 3. Many infinite classes of complete self-inverse binomials are proposed, which explain most of the experimental results about complete self-inverse binomials over ({mathbb {F}}_{2^n}) with (nle 10). Six classes of linearized CPMs are given by using standard arguments from fast symbolic computations and a general method is proposed by the AGW criterion. Finally, two applications of CPMs in cryptography are discussed.