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学者姓名：刘倩
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Abstract ：
Recently, a new concept called multiplicative differential was introduced by Ellingsen et al. [7]. As an extension of the differential uniformity, it is theoretically appealing to determine the properties of c-differential uniformity and the corresponding c-differential spectrum. In this paper, based on certain quadratic character sums and two special elliptic curves over F-p, the (-1)-differential spectra of the following two classes of power functions over F-p(n) is completely determined: (1) f(1)(x)=x(pn+3/2), where p>3 and p equivalent to 3(mod4); (2) f(2)(x)=x(pn)-3, where p>3. The obtained result shows that the (-1)-differential spectra of f(1)(x) and f(2)(x) can be expressed explicitly in terms of n. Moreover, an upper bound of the c-differential uniformity of f(2)(x) is given.
Keyword ：
c-differential spectrum c-differential spectrum c-differential uniformity c-differential uniformity Elliptic curve Elliptic curve Power function Power function Quadratic character sum Quadratic character sum
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| GB/T 7714 | Liu, Qian , Huang, Zhiwei , Chen, Zhixiong et al. On the (-1)-differential spectra of two classes of power functions over finite fields [J]. | APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING , 2025 . |
| MLA | Liu, Qian et al. "On the (-1)-differential spectra of two classes of power functions over finite fields" . | APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING (2025) . |
| APA | Liu, Qian , Huang, Zhiwei , Chen, Zhixiong , Jiang, Rong , Zhang, Liupiao . On the (-1)-differential spectra of two classes of power functions over finite fields . | APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING , 2025 . |
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Cyclic codes constitute a significant subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, by analyzing the solutions of certain equations over F5m\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{5<^>m}$$\end{document} and using the multivariate method, we propose eight classes of optimal quinary cyclic codes C(1,e,5m-12)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}_{(1, e, \frac{5<^>m-1}{2})}$$\end{document} and prove that our new optimal quinary cyclic codes are inequivalent to the known ones. Moreover, we show that the quinary cyclic codes C(5m+12,5m-12+e,5m-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}_{(\frac{5<^>m+1}{2}, \frac{5<^>m-1}{2}+e, 5<^>m-1)}$$\end{document} and C(1,e,5m-12)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}_{(1, e, \frac{5<^>m-1}{2})}$$\end{document} have the same optimality. As a result, we can get new optimal quinary cyclic codes from known ones. In addition, we reveal the quinary cyclic codes C(5m+12,5m-12+e,5m-12)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}_{(\frac{5<^>m+1}{2}, \frac{5<^>m-1}{2}+e, \frac{5<^>m-1}{2})}$$\end{document} and C(1,e,5m-12)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {C}_{(1,e,\frac{5<^>m-1}{2})}$$\end{document} have the same parameters for e equivalent to 3(mod4)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$e\equiv 3\pmod 4$$\end{document}.
Keyword ：
Cyclic code Cyclic code Optimal code Optimal code Quinary code. Quinary code.
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| GB/T 7714 | Liu, Qian , Huang, Junhao , Zheng, Dabin et al. Several classes of optimal quinary cyclic codes with minimum distance four [J]. | CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES , 2025 . |
| MLA | Liu, Qian et al. "Several classes of optimal quinary cyclic codes with minimum distance four" . | CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES (2025) . |
| APA | Liu, Qian , Huang, Junhao , Zheng, Dabin , Jiang, Rong , Zhang, Liupiao . Several classes of optimal quinary cyclic codes with minimum distance four . | CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES , 2025 . |
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Permutation polynomials with low c-differential uniformity had wide applications in cryptography and design theory. In this paper, by utilizing the Weil sums technique and solving some certain equations over Fp2m, we concentrate on characterizing five classes of perfect c-nonlinear (PcN) permutation polynomials of the form (xpm-x+delta)s+x over finite fields with odd characteristic. Firstly, two classes of PcN permutation polynomials are obtained over F3n. Secondly, we characterize the permutation property of a class of polynomials with aforementioned form by using the AGW criterion. Finally, three classes of PcN permutation polynomials are determined over Fp2m with odd characteristic.
Keyword ：
C-differential uniformity C-differential uniformity Perfect c-nonlinear function Perfect c-nonlinear function Permutation polynomial Permutation polynomial
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| GB/T 7714 | Liu, Qian , Chen, Guifeng , Zheng, Dabin . Five classes of PcN permutation polynomials with the form (xpm-x plus δ)s+x over Fp2m [J]. | COMPUTATIONAL & APPLIED MATHEMATICS , 2025 , 44 (7) . |
| MLA | Liu, Qian et al. "Five classes of PcN permutation polynomials with the form (xpm-x plus δ)s+x over Fp2m" . | COMPUTATIONAL & APPLIED MATHEMATICS 44 . 7 (2025) . |
| APA | Liu, Qian , Chen, Guifeng , Zheng, Dabin . Five classes of PcN permutation polynomials with the form (xpm-x plus δ)s+x over Fp2m . | COMPUTATIONAL & APPLIED MATHEMATICS , 2025 , 44 (7) . |
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Permutation polynomials with low boomerang uniformity have wide applications in cryptography. In this paper, by utilizing the Weil sums technique and solving some certain equations over F-2n, we determine the boomerang uniformity of these permutation polynomials: (1) f(1)(x) = (x(2m) + x + delta)(22m)+1 + x, where n = 3m, delta is an element of F-2n with Tr-m(n)(delta) = 1; (2) f(2)(x) = (x(2m) + x + delta)(22m-1)+2(m-)1 + x, where n = 3m, delta is an element of F-2n with Tr-m(n)(delta) = 0; (3) f(3)(x) = (x(2m) + x + delta)2(3m-1)+2(m-1) + x, where n = 3m, delta is an element of F-2n with Tr-m(n)(delta) = 0. The results show that the boomerang uniformity of f(1)(x), f(2)(x) and f(3)(x) can attain 2(n).
Keyword ：
boomerang uniformity boomerang uniformity Finite field Finite field permutation polynomial permutation polynomial Weil sum Weil sum
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| GB/T 7714 | Liu, Qian , Chen, Zhixiong , Liu, Ximeng . The boomerang uniformity of three classes of permutation polynomials over F2n [J]. | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2024 , 24 (12) . |
| MLA | Liu, Qian et al. "The boomerang uniformity of three classes of permutation polynomials over F2n" . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS 24 . 12 (2024) . |
| APA | Liu, Qian , Chen, Zhixiong , Liu, Ximeng . The boomerang uniformity of three classes of permutation polynomials over F2n . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2024 , 24 (12) . |
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In this paper, we present some new key-recovery attacks on Misty L-KF, Misty R-KF, and generalized Feistel schemes. Firstly, we propose a new 5-round distinguisher on Misty L-KF structure. Based on our new distinguisher attack, we propose a new6-round Demiric-Sel & ccedil;uk meet-in-the-middle attack (DS-MITM attack) against Misty L-KF structure. Secondly, we extend our classical DS-MITM attack to a new quantum DS-MITM attack on Misty L-KF structure by using the quantum claw finding algorithm. In addition, we apply the above method to attack Misty R-KF and generalized Feistel schemes. To sum up, we construct our classical key-recovery attacks on the 6-round Misty L-KF structure and Misty R-KF structure with O(2(3n/4)) time and O(2(n/2)) memory cost. By using a quantum computer, our new quantum key-recovery attacks on the 6-round Misty L-KF structures and Misty R-KF structures can be constructed with O(2n/2) time and O(2n/2) memory cost. Furthermore, we can construct our new quantum (5d-4)-round key-recovery attacks on the d-branch contracting Feistels with O(2(d-1)n/d) time and O(2(d-1)n/d) memory cost. In the end, we can construct our new quantum(4d-3)-round and (5d-4)-round key-recovery attacks on the two types of d-branch expanding Feistels with O(2(d-1)n/d) time and O(2(d-1)n/d) memory cost.
Keyword ：
Cryptanalysis Cryptanalysis Generalized Feistel scheme Generalized Feistel scheme Misty structure Misty structure Quantum DS-MITM attack Quantum DS-MITM attack
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| GB/T 7714 | Zou, Jian , Huang, Kairong , Zhu, Min et al. New Demiric-Selcuk meet-in-the-middle attacks on Misty and Feistel schemes [J]. | QUANTUM INFORMATION PROCESSING , 2024 , 23 (4) . |
| MLA | Zou, Jian et al. "New Demiric-Selcuk meet-in-the-middle attacks on Misty and Feistel schemes" . | QUANTUM INFORMATION PROCESSING 23 . 4 (2024) . |
| APA | Zou, Jian , Huang, Kairong , Zhu, Min , Zou, Hongkai , Luo, Yiyuan , Liu, Qian . New Demiric-Selcuk meet-in-the-middle attacks on Misty and Feistel schemes . | QUANTUM INFORMATION PROCESSING , 2024 , 23 (4) . |
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Cryptographic bent functions are maximally nonlinear Boolean functions with an even number of variables. They are not only closely related to some interesting combinatorial objects, but also have important applications in coding, sequence design, cryptography and cyber security. In this paper, we firstly investigate the Walsh transform of two families of functions via Maiorana-MacFarland's class. Secondly, we present new infinite families of permutations. We show that those families have nice property that one can select three elements among them which can be used to construct bent functions. Finally, by using two linear translators, we construct bent functions from the class of Maiorana-MacFarland. © 2023 IEEE.
Keyword ：
Boolean functions Boolean functions Cryptography Cryptography Cybersecurity Cybersecurity Walsh transforms Walsh transforms
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| GB/T 7714 | Liu, Qian , Chen, Yan , Chen, Zhixiong et al. New Cryptographic Bent Functions from Permutations and Linear Translator in Cyber Security [C] . 2023 : 515-522 . |
| MLA | Liu, Qian et al. "New Cryptographic Bent Functions from Permutations and Linear Translator in Cyber Security" . (2023) : 515-522 . |
| APA | Liu, Qian , Chen, Yan , Chen, Zhixiong , Liu, Ximeng , Lin, Hui . New Cryptographic Bent Functions from Permutations and Linear Translator in Cyber Security . (2023) : 515-522 . |
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Cryptographic functions with low differential uniformity have wide applications in cryptography and cyber security. In this paper, we further investigate c-differential uniformity proposed by Ellingsen et al. (IEEE Transactions on Information Theory. 2020, 66(9): 5781-5789). Specifically, two classes of power functions with low (1)-differential uniformity over finite fields with odd characteristic are obtained. In addition, a class of permutation polynomials and P1N or AP1N functions over F3n are proposed. These functions with low c-differential uniformity are utilized to resist against c-differential attacks in cyberspace from those with the usual low differential uniformity. © 2023 IEEE.
Keyword ：
Cryptography Cryptography Cybersecurity Cybersecurity Information theory Information theory Polynomials Polynomials
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| GB/T 7714 | Liu, Qian , Dong, Xiaobei , Chen, Zhixiong et al. Some Classes of Cryptographic Power Functions and Permutation Polynomials with Low (-1)-Differential Uniformity in Cyber Security [C] . 2023 : 109-115 . |
| MLA | Liu, Qian et al. "Some Classes of Cryptographic Power Functions and Permutation Polynomials with Low (-1)-Differential Uniformity in Cyber Security" . (2023) : 109-115 . |
| APA | Liu, Qian , Dong, Xiaobei , Chen, Zhixiong , Liu, Ximeng , Xu, Li . Some Classes of Cryptographic Power Functions and Permutation Polynomials with Low (-1)-Differential Uniformity in Cyber Security . (2023) : 109-115 . |
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In this paper, we study the permutation property of pentanomials with the form xrh(xpm-1) over Fp2m , where p is an element of {2, 3}. More precisely, based on some seventh-degree and eighth-degree irreducible pentanomials over F2, we present eight classes of permutation pentanomials over F22m by determining the solutions of some equations with low degrees. In addition, based on the investigation of algebraic curves associated with fractional polynomials over finite fields, eight classes of permutation pentanomials over F32m are discovered by choosing some seventh-degree irreducible pentanomials over F3. Finally, several classes of permutation pentanomials and heptanomials over F22m and F32m are derived from known permutation polynomials on mu 2m+1 and mu 3m+1, respectively, where mu d is the set of d-th roots of unity.(c) 2023 Elsevier Inc. All rights reserved.
Keyword ：
Finite fields Finite fields Permutation heptanomial Permutation heptanomial Permutation pentanomial Permutation pentanomial Permutation polynomial Permutation polynomial
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| GB/T 7714 | Liu, Qian , Chen, Guifeng , Liu, Ximeng et al. Several classes of permutation pentanomials with the form xrh(xpm-1) over Fp2m [J]. | FINITE FIELDS AND THEIR APPLICATIONS , 2023 , 92 . |
| MLA | Liu, Qian et al. "Several classes of permutation pentanomials with the form xrh(xpm-1) over Fp2m" . | FINITE FIELDS AND THEIR APPLICATIONS 92 (2023) . |
| APA | Liu, Qian , Chen, Guifeng , Liu, Ximeng , Zou, Jian . Several classes of permutation pentanomials with the form xrh(xpm-1) over Fp2m . | FINITE FIELDS AND THEIR APPLICATIONS , 2023 , 92 . |
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Permutation polynomials with low c-differential uniformity and boomerang uniformity have wide applications in cryptography. In this paper, by utilizing the Weil sums technique and solving some certain equations over F-2n, we determine the c-differential uniformity and boomerang uniformity of these permutation polynomials: (1) f1(x) = x + Tr-1(n)( x(2k+1)+1+ x(3)+ x + ux), where n = 2k+ 1, u is an element of F-2n with Tr-1(n)(u) = 1; (2) f(2)(x) = x + Tr-1(n)( x(2k+3)+( x + 1)(2k)+3), where n = 2k+ 1; (3) f(3)(x) = x(-1)+ Tr-1(n)(( x(-1)+ 1)(d)+ x(-d)), where nis even and dis a positive integer. The results show that the involutions f(1)(x) and f(2)(x) are APcN functions for c is an element of F(2)n\{0, 1}. Moreover, the boomerang uniformity of f(1)(x) and f(2)(x) can attain 2(n). Furthermore, we generalize some previous works and derive the upper bounds on the c-differential uniformity and boomerang uniformity of f(3)(x). (c) 2023 Elsevier Inc. All rights reserved.
Keyword ：
Boomerang uniformity Boomerang uniformity C-differential uniformity C-differential uniformity Permutation polynomial Permutation polynomial
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| GB/T 7714 | Liu, Qian , Huang, Zhiwei , Xie, Jianrui et al. The c-differential uniformity and boomerang uniformity of three classes of permutation polynomials over F-2(n) [J]. | FINITE FIELDS AND THEIR APPLICATIONS , 2023 , 89 . |
| MLA | Liu, Qian et al. "The c-differential uniformity and boomerang uniformity of three classes of permutation polynomials over F-2(n)" . | FINITE FIELDS AND THEIR APPLICATIONS 89 (2023) . |
| APA | Liu, Qian , Huang, Zhiwei , Xie, Jianrui , Liu, Ximeng , Zou, Jian . The c-differential uniformity and boomerang uniformity of three classes of permutation polynomials over F-2(n) . | FINITE FIELDS AND THEIR APPLICATIONS , 2023 , 89 . |
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Functions with low differential uniformity have wide applications in cryptography. In this paper, by using the quadratic character of F-pn*, we further investigate the (-1)-differential uniformity of these functions in odd characteristic: (1) f(1)(x) = x(d), where d = - p(n)-1/2 + p(k) + 1, n and k are two positive integers satisfying n/gcd(n,k) is odd; (2) f(2)(x) = (x(pm) - x)(pn-1/2) (+1) + x + x(pm), where n = 3m; (3) f(3)(x) = (x(3m) - x) 3(n-1/2 +1) + (x(3m) - x) 3(n-1/2) +3(m) + x, where n = 3m. The results show that the upper bounds on the (-1)-differential uniformity of the power function f(1)(x) are derived. Furthermore, we determine the (-1) -differential uniformity of two classes of permutation polynomials f(2)(x) and f(3)(x) over F-pn and F-3n, respectively. Specifically, a class of permutation polynomial f(3)(x) that is of P-1N or AP(-1)N function over F-3n is obtained.
Keyword ：
C-differential uniformity C-differential uniformity Differential uniformity Differential uniformity Perfect and almost perfect c-nonlinear functions Perfect and almost perfect c-nonlinear functions
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| GB/T 7714 | Liu, Qian , Liu, Ximeng , Chen, Meixiang et al. Further results on the (-1)-differential uniformity of some functions over finite fields with odd characteristic [J]. | APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING , 2023 , 36 (4) : 681-697 . |
| MLA | Liu, Qian et al. "Further results on the (-1)-differential uniformity of some functions over finite fields with odd characteristic" . | APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 36 . 4 (2023) : 681-697 . |
| APA | Liu, Qian , Liu, Ximeng , Chen, Meixiang , Zou, Jian , Huang, Zhiwei . Further results on the (-1)-differential uniformity of some functions over finite fields with odd characteristic . | APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING , 2023 , 36 (4) , 681-697 . |
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