Henk D. L. Hollmann

On Codes with the Identifiable Parent Property

IfCis aq-ary code of lengthnandaandbare two codewords, thencis called a descendant ofaandbifci?{ai, bi} fori=1, ?, n. We are interested in codesCwith the property that, given any descendantc, one can always identify at least one of the “parent” codewords inC. We study bounds onF(n, q), the maximal cardinality of a codeCwith this property, which we call theidentifiable parent property. Such codes play a role in schemes that protect against piracy of software.

XOR-based Visual Cryptography Schemes

A recent publication introduced a Visual Crypto (VC) system, based on the polarisation of light. This VC system has goodresolution, contrast and colour properties.Mathematically, the VC system is described by the XOR operation (modulo two addition). In this paper we investigate Threshold Visual Secret Sharing schemes associated to XOR-based VC systems. Firstly, we show that n out of n schemes with optimal resolution and contrast exist, and that (2,n) schemes are equivalent to binary codes. It turns out that these schemes have much better resolution than their OR-based counterparts. Secondly, we provide two explicit constructions for general k out of n schemes. Finally, we derive bounds on the contrast and resolution of XOR-based schemes. It follows from these bounds that for k<n, the contrast is strictly smaller than one. Moreover, the bounds imply that XOR-based k out of n schemes for even k are fundamentally different from those for odd k.

Cryptanalysis of a Generic Class of White-Box Implementations

A white-box implementation of a block cipher is a software implementation from which it is difficult for an attacker to extract the cryptographic key. Chow et al. published white-box implementations for AES and DES. These implementations are based on ideas that can be used to derive white-box implementations for other block ciphers as well. In particular, the ideas can be used to derive a white-box implementation for any substitution linear-transformation (SLT) cipher. Although the white-box implementations of AES and DES have been cryptanalyzed, the cryptanalyses published use typical properties of AES and DES. It is therefore an open question whether an SLT cipher exists for which the techniques of Chow et al. result in a secure white-box implementation. In this paper we largely settle this question by presenting an algorithm that is able to extract the key from such an implementation under a mild condition on the diffusion matrix. The condition is, for instance, satisfied by all MDS matrices. Our result can serve as a basis to design block ciphers and to develop white-box techniques that result in secure white-box implementations.

Proofs of Two Conjectures on Ternary Weakly Regular Bent Functions

In this paper, we study ternary monomial functions of the form <i>f</i>(<i>x</i>) = Tr<i>n</i>(<i>axd</i>), where <i>x</i> isin \BBF ₃ <i>n</i> and <i>Trn</i>: \BBF ₃ <i>n</i>rarr \BBF ₃ is the absolute trace function. Using a lemma of Hou, Stickelbergers theorem on Gauss sums, and certain ternary weight inequalities, we show that certain ternary monomial functions arising in the 2006 <b>IEEE Transactions on Information Theory</b> paper (vol. 52, pp. 2018-2032, 2006) are weakly regular bent, thus settling a conjecture of Helleseth and Kholosha. We also prove that the Coulter-Matthews bent functions are weakly regular.

On the realizability of biorthogonal, m-dimensional two-band filter banks

We show an algebraic approach for the design of ladder structures for causal biorthogonal filter banks. The key ingredient of the approach is known in literature as Euclids algorithm. Using this algorithm we derive some strong result on the design freedom for ladder structures. In particular we show that the dimensionality of the problem plays an important role. We end by with some conjectures concerning the extensions to multichannel and noncausal filter banks. >

A relation between Levenshtein-type distances and insertion-and-deletion correcting capabilities of codes

A code is a collection of words or strings, not necessarily all of the same length, over come fixed alphabet. A relation is established between the insertion-and-deletion correcting capability of a code and its minimum distance for suitable Levenshtein-type distance measures. >

Minimizing pattern count for interconnect test under a ground bounce constraint

When testing the interconnect structures on a board, test programmers sometimes ask, How can I control the test pattern generation process to avoid ground bounce problems during Extest mode? Those wishing to satisfy a simultaneously-switching-outputs constraint will find several new solutions in this article.

Generic erasure correcting sets: bounds and constructions

A generic (r, m)-erasure correcting set generates for each binary linear code of codimension r a collection of parity check equations that enables iterative decoding of all potentially correctable erasure patterns of size at most m. As we have shown earlier, such a set essentially is just a parity check collection with this property for the Hamming code of codimension r.We prove non-constructively that for fixed m the minimum size F(r, m) of a generic (r, m)-erasure correcting set is linear in r. Moreover, we show constructively that F(r, 3) ≤ 3(r - 1)log23 + 1, which is a major improvement on a previous construction showing that F(r, 3) ≤ 1 + 1/2;r(r - 1).In the course of this work we encountered the following problem that may be of independent interest: what is the smallest size of a collection C ⊆ F2n such that, given any set of s independent vectors in F2n, there is a vector c ∈ C that has inner product 1 with all of these vectors? We show non-constructively that, for fixed s, this number is linear in n.

On Binary Cyclic Codes With Few Weights

Let \( {C_{{{t_{0}}}}}{,_{{{t_{1}}...,{t_{r}}}}} \) denote the binary cyclic code of length n = 2 m − 1 with defining zeros \( {\alpha ^{{{t_{0}}}}},{\alpha ^{{{t_{1}}}}}...,{a^{{{t_{r}}}}} \), where α is a primitive element of GF(2 m ). Using the method in [8], we determine the weight distribution of the following cyclic codes. (i) \( {C_{{1,{t_{1}},{t_{2}}}}}, \), where m = 2r + 1, t 1 = 2r + 1, t 2 = 2 r−1 + 1. (This code appeared in Research Problem 9.7 of MacWilhams and Sloane [14].) (ii) \( {C_{{1,t,{t^{2}}}}}, \) where m = 2r + l, t = l + 22r+1 (This code appeared in a conjecture of Chang, Gaal, Golomb, Gong, and Kumar [5].) (iii) Several cyclic codes in the paper of Van Lint and Wilson [12]. (iv) C 1,t, where \( m = 2r,t = \sum\nolimits_{{i = 0}}^{r} {{2^{{ik}}}} \), gcd(m, k) = 1.

Performance of efficient balanced codes

The problem of appraising the spectral performance of codes based on a new algorithm for generating zero-disparity codewords presented by D.E. Knuth (1986) is addressed. In order to get some insight into the efficiency of Knuths construction technique, the authors evaluate the spectral properties of its code streams. The structure of Knuth codes allows the derivation a simple expression for (an approximation to) the sum of variance of these codes. This quantity plays a key role in the spectral performance characterization of DC-balanced codes. The authors evaluate this expression and compare the sum variance of Knuth codes with the sum variance of the polarity bit codes for fixed redundancy. Under the premise that the sum variance can serve as a quantity to judge the width of the spectral notch, the authors conclude that codes based on Knuths algorithm offer less spectral suppression than polarity bit codes with the same redundancy. >