A Class of the Hamming Weight Hierarchy of Linear Codes with Dimension 5

The weight hierarchy of a [n, k; q] linear code C over Fq is the sequence （d1,…, dr,… , dk）, where dr is the smallest support weight of an r-dimensional subcode of C. In this paper, by using the finite projective geometry method, we research a class of weight hierarchy of linear codes with dimension 5. We first find some new pre- conditions of this class. Then we divide its weight hierarchies into six subclasses, and research one subclass to determine nearly all the weight hierarchies of this subclass of weight hierarchies of linear codes with dimension 5.

Timing and hamming weight attacks on minimal cost encryption scheme

The timing and Hamming weight attacks on the data encryption standard （DES） cryptosystem for minimal cost encryption scheme is presented in this article. In the attack, timing information on encryption processing is used to select and collect effective plaintexts for attack. Then the collected plaintexts are utilized to infer the expanded key differences of the secret key, from which most bits of the expanded secret key are recovered. The remaining bits of the expanded secret key are deduced by the correlations between Hamming weight values of the input of the S-boxes in the first-round. Finally, from the linear relation of the encryption time and the secret key＇s Hamming weight, the entire 56 bits of the secret key are thoroughly recovered. Using the attack, the minimal cost encryption scheme can be broken with 2^23 known plaintexts and about 2^21 calculations at a success rate a 〉 99%. The attack has lower computing complexity, and the method is more effective than other previous methods.

A Note on m-Weights of Linear Codes

m-weight, as a new generalization of classical Hamming weight, was discussedin this paper. A condition for the existence of linear codes of certain m-weights was given; theSingleton bound, Plotkin bound and Sphere Parking bound of Hamming weight were correspondinglygeneralized to the m-weight.

Tighter constraints of multiqubit entanglement in terms of Renyi-α entropy

Quantum entanglement plays essential roles in quantum information processing.The monogamy and polygamy relations characterize the entanglement distributions in the multipartite systems.We present a class of monogamy inequalities related to theµ-th power of the entanglement measure based on Renyi-αentropy,as well as polygamy relations in terms of theµ-th power of Renyi-αentanglement of assistance.These monogamy and polygamy relations are shown to be tighter than the existing ones.

An Improved Simple Power Attack against Camellia's Key Schedule

This paper presents an improved simple power attack against the key schedule of Camellia. While the original attack required an exact determination of the Hamming weight of intermediate data values based on power measurements, in this paper, two types of the simple power attack are presented and shown to be tolerant of errors that might occur in the Hamming weight determinations. In practical applications of the attack, such errors are likely to occur due to noise and distortion in the power measurements and their mapping to the Hamming weights of the data. To resist these attacks, the required design rationale of key schedules and several practical countermeasures are suggested.

A Proof for the Nonexistence of Some Homogeneous Bent Functions

By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist no homogeneous bent functions ofdegree in in n = 2mvariables for m >3.

A Construction of Maximal Linearly Independent Array

Let M be a subset of r-dimensional vector space Vτ （F2） over a finite field F2, consisting of n nonzero vectors, such that every t vectors of M are linearly independent over F2. Then M is called （n, t）-linearly independent array of length n over Vτ（F2）. The （n, t）-linearly independent array M that has the maximal number of elements is called the maximal （r, t）-linearly independent array, and the maximal number is denoted by M（r, t）. It is an interesting combinatorial structure, which has many applications in cryptography and coding theory. It can be used to construct orthogonal arrays, strong partial balanced designs. It can also be used to design good linear codes, In this paper, we construct a class of maximal （r, t）-linearly independent arrays of length r ＋ 2, and provide some enumerator theorems.