A new notion of bent sequence related to Hadamard matrices was introduced recently,motivated by a security application(Solé,et al.,2021).The authors study the self-dual class in length at most 196.The authors use...A new notion of bent sequence related to Hadamard matrices was introduced recently,motivated by a security application(Solé,et al.,2021).The authors study the self-dual class in length at most 196.The authors use three competing methods of generation:Exhaustion,Linear Algebra and Gr?bner bases.Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples.The authors conjecture that if v is an even perfect square,a self-dual bent sequence of length v always exists.The authors introduce the strong automorphism group of Hadamard matrices,which acts on their associated self-dual bent sequences.The authors give an efficient algorithm to compute that group.展开更多
Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-e...Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-essary condition is derived to determine whether the sum of the combinations of Gold functions,tr1^(n)(x^(2+1)),1≤i≤n−1,over finite fields 2n F(n be even)in addition to another term tr1^(n/2)(x^(2n/2+1))is a Bent function.Similar to the result presented by Khoo et al.,the condition can be verified by polynominal greatest common divisor(GCD)computation.A similar result also holds in the case n pF(n be even,p be odd prime).Using the constructed Bent functions and Niho type Bent functions given by Dobbertin et al.,many new generalized binary Bent sequences are obtained.展开更多
Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardwa...Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardware circuit and the soflware program flow chart of the SW/SFH PN code generator are also given,which is based on generalized Bent function sequence generator by using a single chip mlcrocomputer.展开更多
This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the res...This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties:nl(f)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6展开更多
基金supported in part by the National Natural Science Foundation of China under Grant No.12071001The work of Dean Crnkovi?is supported by Croatian Science Foundation under the project 6732。
文摘A new notion of bent sequence related to Hadamard matrices was introduced recently,motivated by a security application(Solé,et al.,2021).The authors study the self-dual class in length at most 196.The authors use three competing methods of generation:Exhaustion,Linear Algebra and Gr?bner bases.Regular Hadamard matrices and Bush-type Hadamard matrices provide many examples.The authors conjecture that if v is an even perfect square,a self-dual bent sequence of length v always exists.The authors introduce the strong automorphism group of Hadamard matrices,which acts on their associated self-dual bent sequences.The authors give an efficient algorithm to compute that group.
基金supported by the National Natural Science Foundation of China(No.60373059)the National Research Foundation for the Doctoral Program of Higher Education of China(No.20040013007)the Research Foundation of the State Key Laboratory of Information Security.
文摘Bent functions in trace forms play an important role in the constructions of generalized binary Bent se-quences.Trace representation of some degree two Bent functions are presented in this paper.A sufficient and nec-essary condition is derived to determine whether the sum of the combinations of Gold functions,tr1^(n)(x^(2+1)),1≤i≤n−1,over finite fields 2n F(n be even)in addition to another term tr1^(n/2)(x^(2n/2+1))is a Bent function.Similar to the result presented by Khoo et al.,the condition can be verified by polynominal greatest common divisor(GCD)computation.A similar result also holds in the case n pF(n be even,p be odd prime).Using the constructed Bent functions and Niho type Bent functions given by Dobbertin et al.,many new generalized binary Bent sequences are obtained.
文摘Generalized Bent function and generalized Bent function sequences are introduced in this paper.The main performance or these sequences used as SW/SFH(Short Wave/Slow Frequency Hopping) code are studied. And the hardware circuit and the soflware program flow chart of the SW/SFH PN code generator are also given,which is based on generalized Bent function sequence generator by using a single chip mlcrocomputer.
文摘This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties:nl(f)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6
