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 ...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.展开更多
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...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.展开更多
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 Par...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.展开更多
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 i...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.展开更多
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 meas...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.展开更多
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 ...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.展开更多
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 i...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.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 61303212 and 61170080)the State Key Program of the National Natural Science of China (Nos. 61332019 and U1135004)the Fundamental Research Funds for the Central Universities, South-Central University for Nationalities (No. CZY14019)
文摘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.
基金supported by the National Basic Research Program of China (2007CB807902, 2007CB807903)the Education Innovation Foundation of Institution and University of Beijing (2004).
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11765016 and 11675113)the Natural Science Foundation of Beijing,China(Grant No.KZ201810028042)Beijing Natural Science Foundation,China(Grant No.Z190005).
文摘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.
基金the National Natural Science Foundation of China (60673072)the Natural Basic Research Program of China (2007CB311201)
文摘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.
文摘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.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10771078, 60973138 and 10971246)Guangzhou Education Bureau Science Foundation (Grant No. 08C017)
文摘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.