{"title":"A class of constacyclic BCH codes with length $ frac{q^{m}+1}{2} $","authors":"Huilian Zhu, Jin Li, Shan Huang","doi":"10.3934/amc.2023015","DOIUrl":"https://doi.org/10.3934/amc.2023015","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88191666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present paper, we introduce a new attack on NTRU-HPS cryptosystem using lattice theory and Babai's Nearest Plane Algorithm. This attack generalizes the classic CVP attack on NTRU. We present numerical data in support of the validity of our result.
{"title":"Message recovery attack on NTRU using a lattice independent from the public key","authors":"Marios Adamoudis, Konstantinos A. Draziotis","doi":"10.3934/amc.2023040","DOIUrl":"https://doi.org/10.3934/amc.2023040","url":null,"abstract":"In the present paper, we introduce a new attack on NTRU-HPS cryptosystem using lattice theory and Babai's Nearest Plane Algorithm. This attack generalizes the classic CVP attack on NTRU. We present numerical data in support of the validity of our result.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135009480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Key assignment and key maintenance in encrypted networks of {resource-limited} devices may be a challenging task, due to the permanent need of replacing out-of-service devices with new ones and to the consequent need of updating the key information. Recently, Aragona et al. proposed a new cryptographic scheme, ECTAKS, which provides a solution to this design problem by means of a Diffie-Hellman-like key establishment protocol based on elliptic curves and on a prime field. Even if the authors proved some results related to the security of the scheme, the latter still lacks a formal security analysis. In this paper, we address this issue by providing a security proof for ECTAKS in the setting of computational security, assuming that no adversary can solve the underlying discrete logarithm problems with non-negligible success probability.
{"title":"Formal security proof for a scheme on a topological network","authors":"Roberto Civino, Riccardo Longo","doi":"10.3934/AMC.2021009","DOIUrl":"https://doi.org/10.3934/AMC.2021009","url":null,"abstract":"Key assignment and key maintenance in encrypted networks of {resource-limited} devices may be a challenging task, due to the permanent need of replacing out-of-service devices with new ones and to the consequent need of updating the key information. Recently, Aragona et al. proposed a new cryptographic scheme, ECTAKS, which provides a solution to this design problem by means of a Diffie-Hellman-like key establishment protocol based on elliptic curves and on a prime field. Even if the authors proved some results related to the security of the scheme, the latter still lacks a formal security analysis. In this paper, we address this issue by providing a security proof for ECTAKS in the setting of computational security, assuming that no adversary can solve the underlying discrete logarithm problems with non-negligible success probability.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73776558","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, Borello and Jamous have investigated some lower bounds on the dimension and minimum distance for dihedral codes, in analogy with the theory of BCH codes. In this paper, we extend some of their results to split metacyclic codes, that is, codes over semidirect products of cyclic groups.
{"title":"On BCH split metacyclic codes","authors":"Angelot Behajaina","doi":"10.3934/amc.2021045","DOIUrl":"https://doi.org/10.3934/amc.2021045","url":null,"abstract":"<p style='text-indent:20px;'>Recently, Borello and Jamous have investigated some lower bounds on the dimension and minimum distance for dihedral codes, in analogy with the theory of BCH codes. In this paper, we extend some of their results to split metacyclic codes, that is, codes over semidirect products of cyclic groups.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82160454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Based on solutions of certain equations over finite yields, a necessary and sufficient condition for the quinary negacyclic codes with parameters begin{document}$ [frac{5^m-1}{2},frac{5^m-1}{2}-2m,4] $end{document} to have generator polynomial begin{document}$ m_{alpha^3}(x)m_{alpha^e}(x) $end{document} is provided. Several classes of new optimal quinary negacyclic codes with the same parameters are constructed by analyzing irreducible factors of certain polynomials over finite fields. Moreover, several classes of new optimal quinary negacyclic codes with these parameters and generator polynomial begin{document}$ m_{alpha}(x)m_{alpha^e}(x) $end{document} are also presented.
Based on solutions of certain equations over finite yields, a necessary and sufficient condition for the quinary negacyclic codes with parameters begin{document}$ [frac{5^m-1}{2},frac{5^m-1}{2}-2m,4] $end{document} to have generator polynomial begin{document}$ m_{alpha^3}(x)m_{alpha^e}(x) $end{document} is provided. Several classes of new optimal quinary negacyclic codes with the same parameters are constructed by analyzing irreducible factors of certain polynomials over finite fields. Moreover, several classes of new optimal quinary negacyclic codes with these parameters and generator polynomial begin{document}$ m_{alpha}(x)m_{alpha^e}(x) $end{document} are also presented.
{"title":"Optimal quinary negacyclic codes with minimum distance four","authors":"Jinmei Fan, Yanhai Zhang","doi":"10.3934/amc.2021043","DOIUrl":"https://doi.org/10.3934/amc.2021043","url":null,"abstract":"<p style='text-indent:20px;'>Based on solutions of certain equations over finite yields, a necessary and sufficient condition for the quinary negacyclic codes with parameters <inline-formula><tex-math id=\"M1\">begin{document}$ [frac{5^m-1}{2},frac{5^m-1}{2}-2m,4] $end{document}</tex-math></inline-formula> to have generator polynomial <inline-formula><tex-math id=\"M2\">begin{document}$ m_{alpha^3}(x)m_{alpha^e}(x) $end{document}</tex-math></inline-formula> is provided. Several classes of new optimal quinary negacyclic codes with the same parameters are constructed by analyzing irreducible factors of certain polynomials over finite fields. Moreover, several classes of new optimal quinary negacyclic codes with these parameters and generator polynomial <inline-formula><tex-math id=\"M3\">begin{document}$ m_{alpha}(x)m_{alpha^e}(x) $end{document}</tex-math></inline-formula> are also presented.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80307954","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose cryptanalytic results on two lightweight stream ciphers: Fountain v1 and Lizard. The main results of this paper are the followings: begin{document}$ - $end{document} We propose a zero-sum distinguisher on reduced round Fountain v1. In this context, we study the non-randomness of the cipher with a careful selection of cube variables. Our obtained cube provides a zero-sum on Fountain v1 till begin{document}$ 188 $end{document} initialization rounds and significant non-randomness till begin{document}$ 189 $end{document} rounds. This results in a distinguishing attack on Fountain v1 with begin{document}$ 189 $end{document} initialization rounds. begin{document}$ - $end{document} Further, we find that the same cipher has a weakness against conditional Time-Memory-Data-Tradeoff (TMDTO). We show that TMDTO attack using sampling resistance has online complexity begin{document}$ 2^{110} $end{document} and offline complexity begin{document}$ 2^{146} $end{document} . begin{document}$ - $end{document} Finally, we revisit the Time-Memory-Data-Tradeoff attack on Lizard by Maitra et al. (IEEE Transactions on Computers, 2018) and provide our observations on their work. We show that instead of choosing any random string, some particular strings would provide better results in their proposed attack technique.
In this paper, we propose cryptanalytic results on two lightweight stream ciphers: Fountain v1 and Lizard. The main results of this paper are the followings: begin{document}$ - $end{document} We propose a zero-sum distinguisher on reduced round Fountain v1. In this context, we study the non-randomness of the cipher with a careful selection of cube variables. Our obtained cube provides a zero-sum on Fountain v1 till begin{document}$ 188 $end{document} initialization rounds and significant non-randomness till begin{document}$ 189 $end{document} rounds. This results in a distinguishing attack on Fountain v1 with begin{document}$ 189 $end{document} initialization rounds. begin{document}$ - $end{document} Further, we find that the same cipher has a weakness against conditional Time-Memory-Data-Tradeoff (TMDTO). We show that TMDTO attack using sampling resistance has online complexity begin{document}$ 2^{110} $end{document} and offline complexity begin{document}$ 2^{146} $end{document} . begin{document}$ - $end{document} Finally, we revisit the Time-Memory-Data-Tradeoff attack on Lizard by Maitra et al. (IEEE Transactions on Computers, 2018) and provide our observations on their work. We show that instead of choosing any random string, some particular strings would provide better results in their proposed attack technique.
{"title":"Some results on lightweight stream ciphers Fountain v1 & Lizard","authors":"Ravi Anand, Dibyendu Roy, Santanu Sarkar","doi":"10.3934/amc.2020128","DOIUrl":"https://doi.org/10.3934/amc.2020128","url":null,"abstract":"In this paper, we propose cryptanalytic results on two lightweight stream ciphers: Fountain v1 and Lizard. The main results of this paper are the followings: begin{document}$ - $end{document} We propose a zero-sum distinguisher on reduced round Fountain v1. In this context, we study the non-randomness of the cipher with a careful selection of cube variables. Our obtained cube provides a zero-sum on Fountain v1 till begin{document}$ 188 $end{document} initialization rounds and significant non-randomness till begin{document}$ 189 $end{document} rounds. This results in a distinguishing attack on Fountain v1 with begin{document}$ 189 $end{document} initialization rounds. begin{document}$ - $end{document} Further, we find that the same cipher has a weakness against conditional Time-Memory-Data-Tradeoff (TMDTO). We show that TMDTO attack using sampling resistance has online complexity begin{document}$ 2^{110} $end{document} and offline complexity begin{document}$ 2^{146} $end{document} . begin{document}$ - $end{document} Finally, we revisit the Time-Memory-Data-Tradeoff attack on Lizard by Maitra et al. (IEEE Transactions on Computers, 2018) and provide our observations on their work. We show that instead of choosing any random string, some particular strings would provide better results in their proposed attack technique.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88879279","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We focus on exploring more potential of Longa and Sica's algorithm (ASIACRYPT 2012), which is an elaborate iterated Cornacchia algorithm that can compute short bases for 4-GLV decompositions. The algorithm consists of two sub-algorithms, the first one in the ring of integers begin{document}$ mathbb{Z} $end{document} and the second one in the Gaussian integer ring begin{document}$ mathbb{Z}[i] $end{document}. We observe that begin{document}$ mathbb{Z}[i] $end{document} in the second sub-algorithm can be replaced by another Euclidean domain begin{document}$ mathbb{Z}[omega] $end{document}begin{document}$ (omega = frac{-1+sqrt{-3}}{2}) $end{document}. As a consequence, we design a new twofold Cornacchia-type algorithm with a theoretic upper bound of output begin{document}$ Ccdot n^{1/4} $end{document}, where begin{document}$ C = frac{3+sqrt{3}}{2}sqrt{1+|r|+|s|} $end{document} with small values begin{document}$ r, s $end{document} given by the curves.
The new twofold algorithm can be used to compute begin{document}$ 4 $end{document}-GLV decompositions on two classes of curves. First it gives a new and unified method to compute all begin{document}$ 4 $end{document}-GLV decompositions on begin{document}$ j $end{document}-invariant begin{document}$ 0 $end{document} elliptic curves over begin{document}$ mathbb{F}_{p^2} $end{document}. Second it can be used to compute the begin{document}$ 4 $end{document}-GLV decomposition on the Jacobian of the hyperelliptic curve defined as begin{document}$ mathcal{C}/mathbb{F}_{p}:y^{2} = x^{6}+ax^{3}+b $end{document}, which has an endomorphism begin{document}$ phi $end{document} with the characteristic equation begin{document}$ phi^2+phi+1 = 0 $end{document} (hence begin{document}$ mathbb{Z}[phi] = mathbb{Z}[omega] $end{document}). As far as we know, no
We focus on exploring more potential of Longa and Sica's algorithm (ASIACRYPT 2012), which is an elaborate iterated Cornacchia algorithm that can compute short bases for 4-GLV decompositions. The algorithm consists of two sub-algorithms, the first one in the ring of integers begin{document}$ mathbb{Z} $end{document} and the second one in the Gaussian integer ring begin{document}$ mathbb{Z}[i] $end{document}. We observe that begin{document}$ mathbb{Z}[i] $end{document} in the second sub-algorithm can be replaced by another Euclidean domain begin{document}$ mathbb{Z}[omega] $end{document} begin{document}$ (omega = frac{-1+sqrt{-3}}{2}) $end{document}. As a consequence, we design a new twofold Cornacchia-type algorithm with a theoretic upper bound of output begin{document}$ Ccdot n^{1/4} $end{document}, where begin{document}$ C = frac{3+sqrt{3}}{2}sqrt{1+|r|+|s|} $end{document} with small values begin{document}$ r, s $end{document} given by the curves.The new twofold algorithm can be used to compute begin{document}$ 4 $end{document}-GLV decompositions on two classes of curves. First it gives a new and unified method to compute all begin{document}$ 4 $end{document}-GLV decompositions on begin{document}$ j $end{document}-invariant begin{document}$ 0 $end{document} elliptic curves over begin{document}$ mathbb{F}_{p^2} $end{document}. Second it can be used to compute the begin{document}$ 4 $end{document}-GLV decomposition on the Jacobian of the hyperelliptic curve defined as begin{document}$ mathcal{C}/mathbb{F}_{p}:y^{2} = x^{6}+ax^{3}+b $end{document}, which has an endomorphism begin{document}$ phi $end{document} with the characteristic equation begin{document}$ phi^2+phi+1 = 0 $end{document} (hence begin{document}$ mathbb{Z}[phi] = mathbb{Z}[omega] $end{document}). As far as we know, none of the previous algorithms can be used to compute the begin{document}$ 4 $end{document}-GLV decomposition on the latter class of curves.
{"title":"A new twofold Cornacchia-type algorithm and its applications","authors":"Bei Wang, Ouyang Yi, Songsong Li, Honggang Hu","doi":"10.3934/amc.2021026","DOIUrl":"https://doi.org/10.3934/amc.2021026","url":null,"abstract":"<p style='text-indent:20px;'>We focus on exploring more potential of Longa and Sica's algorithm (ASIACRYPT 2012), which is an elaborate iterated Cornacchia algorithm that can compute short bases for 4-GLV decompositions. The algorithm consists of two sub-algorithms, the first one in the ring of integers <inline-formula><tex-math id=\"M1\">begin{document}$ mathbb{Z} $end{document}</tex-math></inline-formula> and the second one in the Gaussian integer ring <inline-formula><tex-math id=\"M2\">begin{document}$ mathbb{Z}[i] $end{document}</tex-math></inline-formula>. We observe that <inline-formula><tex-math id=\"M3\">begin{document}$ mathbb{Z}[i] $end{document}</tex-math></inline-formula> in the second sub-algorithm can be replaced by another Euclidean domain <inline-formula><tex-math id=\"M4\">begin{document}$ mathbb{Z}[omega] $end{document}</tex-math></inline-formula> <inline-formula><tex-math id=\"M5\">begin{document}$ (omega = frac{-1+sqrt{-3}}{2}) $end{document}</tex-math></inline-formula>. As a consequence, we design a new twofold Cornacchia-type algorithm with a theoretic upper bound of output <inline-formula><tex-math id=\"M6\">begin{document}$ Ccdot n^{1/4} $end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id=\"M7\">begin{document}$ C = frac{3+sqrt{3}}{2}sqrt{1+|r|+|s|} $end{document}</tex-math></inline-formula> with small values <inline-formula><tex-math id=\"M8\">begin{document}$ r, s $end{document}</tex-math></inline-formula> given by the curves.</p><p style='text-indent:20px;'>The new twofold algorithm can be used to compute <inline-formula><tex-math id=\"M9\">begin{document}$ 4 $end{document}</tex-math></inline-formula>-GLV decompositions on two classes of curves. First it gives a new and unified method to compute all <inline-formula><tex-math id=\"M10\">begin{document}$ 4 $end{document}</tex-math></inline-formula>-GLV decompositions on <inline-formula><tex-math id=\"M11\">begin{document}$ j $end{document}</tex-math></inline-formula>-invariant <inline-formula><tex-math id=\"M12\">begin{document}$ 0 $end{document}</tex-math></inline-formula> elliptic curves over <inline-formula><tex-math id=\"M13\">begin{document}$ mathbb{F}_{p^2} $end{document}</tex-math></inline-formula>. Second it can be used to compute the <inline-formula><tex-math id=\"M14\">begin{document}$ 4 $end{document}</tex-math></inline-formula>-GLV decomposition on the Jacobian of the hyperelliptic curve defined as <inline-formula><tex-math id=\"M15\">begin{document}$ mathcal{C}/mathbb{F}_{p}:y^{2} = x^{6}+ax^{3}+b $end{document}</tex-math></inline-formula>, which has an endomorphism <inline-formula><tex-math id=\"M16\">begin{document}$ phi $end{document}</tex-math></inline-formula> with the characteristic equation <inline-formula><tex-math id=\"M17\">begin{document}$ phi^2+phi+1 = 0 $end{document}</tex-math></inline-formula> (hence <inline-formula><tex-math id=\"M18\">begin{document}$ mathbb{Z}[phi] = mathbb{Z}[omega] $end{document}</tex-math></inline-formula>). As far as we know, no","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76145006","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, by calculating the lower bounds on the nonlinearity of the derivatives of the following three classes of Boolean functions, we provide the tight lower bounds on the second-order nonlinearity of these Boolean functions: (1) begin{document}$ f_1(x) = Tr_1^n(x^{2^{r+1}+2^r+1}) $end{document} , where begin{document}$ n = 2r+2 $end{document} with even begin{document}$ r $end{document} ; (2) begin{document}$ f_2(x) = Tr_1^n(lambda x^{2^{2r}+2^{r+1}+1}) $end{document} , where begin{document}$ lambda in mathbb{F}_{2^r}^* $end{document} and begin{document}$ n = 4r $end{document} with even begin{document}$ r $end{document} ; (3) begin{document}$ f_3(x,y) = yTr_1^n(x^{2^r+1})+Tr_1^n(x^{2^r+3}) $end{document} , where begin{document}$ (x, y)in mathbb{F}_{2^n}times mathbb{F}_2 $end{document} , begin{document}$ n = 2r $end{document} with odd begin{document}$ r $end{document} . The results show that our bounds are better than previously known lower bounds in some cases.
In this paper, by calculating the lower bounds on the nonlinearity of the derivatives of the following three classes of Boolean functions, we provide the tight lower bounds on the second-order nonlinearity of these Boolean functions: (1) begin{document}$ f_1(x) = Tr_1^n(x^{2^{r+1}+2^r+1}) $end{document} , where begin{document}$ n = 2r+2 $end{document} with even begin{document}$ r $end{document} ; (2) begin{document}$ f_2(x) = Tr_1^n(lambda x^{2^{2r}+2^{r+1}+1}) $end{document} , where begin{document}$ lambda in mathbb{F}_{2^r}^* $end{document} and begin{document}$ n = 4r $end{document} with even begin{document}$ r $end{document} ; (3) begin{document}$ f_3(x,y) = yTr_1^n(x^{2^r+1})+Tr_1^n(x^{2^r+3}) $end{document} , where begin{document}$ (x, y)in mathbb{F}_{2^n}times mathbb{F}_2 $end{document} , begin{document}$ n = 2r $end{document} with odd begin{document}$ r $end{document} . The results show that our bounds are better than previously known lower bounds in some cases.
{"title":"The lower bounds on the second-order nonlinearity of three classes of Boolean functions","authors":"Qian Liu","doi":"10.3934/AMC.2020136","DOIUrl":"https://doi.org/10.3934/AMC.2020136","url":null,"abstract":"In this paper, by calculating the lower bounds on the nonlinearity of the derivatives of the following three classes of Boolean functions, we provide the tight lower bounds on the second-order nonlinearity of these Boolean functions: (1) begin{document}$ f_1(x) = Tr_1^n(x^{2^{r+1}+2^r+1}) $end{document} , where begin{document}$ n = 2r+2 $end{document} with even begin{document}$ r $end{document} ; (2) begin{document}$ f_2(x) = Tr_1^n(lambda x^{2^{2r}+2^{r+1}+1}) $end{document} , where begin{document}$ lambda in mathbb{F}_{2^r}^* $end{document} and begin{document}$ n = 4r $end{document} with even begin{document}$ r $end{document} ; (3) begin{document}$ f_3(x,y) = yTr_1^n(x^{2^r+1})+Tr_1^n(x^{2^r+3}) $end{document} , where begin{document}$ (x, y)in mathbb{F}_{2^n}times mathbb{F}_2 $end{document} , begin{document}$ n = 2r $end{document} with odd begin{document}$ r $end{document} . The results show that our bounds are better than previously known lower bounds in some cases.","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81095436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jean-François Biasse, C. Fieker, Tommy Hofmann, William Youmans
{"title":"An algorithm for solving the principal ideal problem with subfields","authors":"Jean-François Biasse, C. Fieker, Tommy Hofmann, William Youmans","doi":"10.3934/amc.2023021","DOIUrl":"https://doi.org/10.3934/amc.2023021","url":null,"abstract":"","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77261405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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