Low correlation zone (LCZ) sequences are useful in quasi-synchronous code-division multiple access (QS-CDMA) communication systems. In this paper, a generic construction of LCZ sequences based on inter-leaved techniqu...Low correlation zone (LCZ) sequences are useful in quasi-synchronous code-division multiple access (QS-CDMA) communication systems. In this paper, a generic construction of LCZ sequences based on inter-leaved technique is investigated. Firstly, the shift sequence is shown to correspond to two-tuple balanced d-form function essentially, which results in new shift sequence. Secondly, an optimal design of p2-ary sequences over the integer residue class ring Zp2 is proposed, which improves the previous construction when p is an odd prime.展开更多
Trivium is an international standard of lightweight stream ciphers(ISO/IEC 29192-3:2012).In this paper,the Trivium-like NFSRs,a class of Galois NFSRs generalized from the Galois NFSR of Trivium,are studied from the pe...Trivium is an international standard of lightweight stream ciphers(ISO/IEC 29192-3:2012).In this paper,the Trivium-like NFSRs,a class of Galois NFSRs generalized from the Galois NFSR of Trivium,are studied from the perspective of Fibonacci NFSRs.It is shown that an n-stage Trivium-like NFSR cannot be equivalent to an n-stage Fibonacci NFSR,which is proved by showing the existence of“collision initial states”.As an intermediate conclusion,a necessary and sufficient condition for a kind of linear degeneracy of a Trivium-like NFSR is obtained from the persepective of interleaved sequences.Moreover,the smallest stage number of a Fibonacci NFSR that can generate all the output sequences of an n-stage Trivium-like NFSR is shown to be greater than n-7 and this value is no less than 371=287+min{93,84,111}specifically for the 288-stage Galois NFSR used in Trivium.These results contradict the existence of a equivalent Fibonacci model of Trivium NFSR of small stage,which implies that Trivium algorithm possesses a fair degree of immunity against“structure attack”.展开更多
基金supported by the Key grant Project of Chinese Ministry of Education(Grant No.311031)the Innovative Research Team of Sichuan Province(Grant No.2011JTD0007)+1 种基金National Natural Science Foundation of China(Grant No.91218301)the Ministry of Education of Humanities and Social Science Foundation of China(Grant No.11XJCZH002)
文摘Low correlation zone (LCZ) sequences are useful in quasi-synchronous code-division multiple access (QS-CDMA) communication systems. In this paper, a generic construction of LCZ sequences based on inter-leaved technique is investigated. Firstly, the shift sequence is shown to correspond to two-tuple balanced d-form function essentially, which results in new shift sequence. Secondly, an optimal design of p2-ary sequences over the integer residue class ring Zp2 is proposed, which improves the previous construction when p is an odd prime.
基金supported by the National Natural Science Foundation of China under Grant Nos.12371526,61872383,61802430,and 62202494。
文摘Trivium is an international standard of lightweight stream ciphers(ISO/IEC 29192-3:2012).In this paper,the Trivium-like NFSRs,a class of Galois NFSRs generalized from the Galois NFSR of Trivium,are studied from the perspective of Fibonacci NFSRs.It is shown that an n-stage Trivium-like NFSR cannot be equivalent to an n-stage Fibonacci NFSR,which is proved by showing the existence of“collision initial states”.As an intermediate conclusion,a necessary and sufficient condition for a kind of linear degeneracy of a Trivium-like NFSR is obtained from the persepective of interleaved sequences.Moreover,the smallest stage number of a Fibonacci NFSR that can generate all the output sequences of an n-stage Trivium-like NFSR is shown to be greater than n-7 and this value is no less than 371=287+min{93,84,111}specifically for the 288-stage Galois NFSR used in Trivium.These results contradict the existence of a equivalent Fibonacci model of Trivium NFSR of small stage,which implies that Trivium algorithm possesses a fair degree of immunity against“structure attack”.
