We use symplectic self-dual additive codes over begin{document}$ mathbb{F}_4 $end{document} obtained from metacirculant graphs to construct, for the first time, begin{document}$ left[kern-0.15emleft[ {ell, 0, d} right]kern-0.15emright] $end{document} qubit codes with parameters begin{document}$ (ell,d) in {(78, 20), (90, 21), (91, 22), (93,21),(96,22)} $end{document}. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.
We use symplectic self-dual additive codes over begin{document}$ mathbb{F}_4 $end{document} obtained from metacirculant graphs to construct, for the first time, begin{document}$ left[kern-0.15emleft[ {ell, 0, d} right]kern-0.15emright] $end{document} qubit codes with parameters begin{document}$ (ell,d) in {(78, 20), (90, 21), (91, 22), (93,21),(96,22)} $end{document}. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.
{"title":"New quantum codes from metacirculant graphs via self-dual additive $mathbb{F}_4$-codes","authors":"P. Seneviratne, M. F. Ezerman","doi":"10.3934/amc.2021073","DOIUrl":"https://doi.org/10.3934/amc.2021073","url":null,"abstract":"<p style='text-indent:20px;'>We use symplectic self-dual additive codes over <inline-formula><tex-math id=\"M1\">begin{document}$ mathbb{F}_4 $end{document}</tex-math></inline-formula> obtained from metacirculant graphs to construct, for the first time, <inline-formula><tex-math id=\"M2\">begin{document}$ left[kern-0.15emleft[ {ell, 0, d} right]kern-0.15emright] $end{document}</tex-math></inline-formula> qubit codes with parameters <inline-formula><tex-math id=\"M3\">begin{document}$ (ell,d) in {(78, 20), (90, 21), (91, 22), (93,21),(96,22)} $end{document}</tex-math></inline-formula>. Secondary constructions applied to the qubit codes result in many new qubit codes that perform better than the previous best-known.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76819138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We characterize the connection between begin{document}$ p $end{document} -ary linear codes and Ramanujan Cayley graphs. We explicitly determine an equivalence between begin{document}$ t $end{document} -weight linear codes over the finite field begin{document}$ Bbb F_p $end{document} and Ramanujan Cayley graphs with begin{document}$ t+1 $end{document} eigenvalues. In particular, we get an explicit criterion on the equivalence between two-weight linear codes and Ramanujan strongly regular graphs with explicit parameters. Using this characterization, we construct several families of Ramanujan Cayley graphs with two or three eigenvalues from known linear codes with two or three weights, respectively.
We characterize the connection between begin{document}$ p $end{document} -ary linear codes and Ramanujan Cayley graphs. We explicitly determine an equivalence between begin{document}$ t $end{document} -weight linear codes over the finite field begin{document}$ Bbb F_p $end{document} and Ramanujan Cayley graphs with begin{document}$ t+1 $end{document} eigenvalues. In particular, we get an explicit criterion on the equivalence between two-weight linear codes and Ramanujan strongly regular graphs with explicit parameters. Using this characterization, we construct several families of Ramanujan Cayley graphs with two or three eigenvalues from known linear codes with two or three weights, respectively.
{"title":"Connection of $ p $-ary $ t $-weight linear codes to Ramanujan Cayley graphs with $ t+1 $ eigenvalues","authors":"J. Hyun, Yoonjin Lee, Yansheng Wu","doi":"10.3934/AMC.2020133","DOIUrl":"https://doi.org/10.3934/AMC.2020133","url":null,"abstract":"We characterize the connection between begin{document}$ p $end{document} -ary linear codes and Ramanujan Cayley graphs. We explicitly determine an equivalence between begin{document}$ t $end{document} -weight linear codes over the finite field begin{document}$ Bbb F_p $end{document} and Ramanujan Cayley graphs with begin{document}$ t+1 $end{document} eigenvalues. In particular, we get an explicit criterion on the equivalence between two-weight linear codes and Ramanujan strongly regular graphs with explicit parameters. Using this characterization, we construct several families of Ramanujan Cayley graphs with two or three eigenvalues from known linear codes with two or three weights, respectively.","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":"79555643","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}
Some valuable results over rings have a promising utilization in coding theory and error-correcting code theory. In this paper, we study character sums over a certain non-chain ring and their applications in codebooks. There are two major ingredients in this study. The first ingredient is to investigate Gaussian sums, hyper Eisenstein sums, Jacobi sums over a certain non-chain ring and study the properties of these character sums. For their applications, the second ingredient is to present three classes of asymptotically optimal codebooks with respect to the Welch bound and a family of optimal codebooks with respect to the Levenshtein bound, which are constructed from character sums over a certain non-chain ring.
{"title":"Character sums over a non-chain ring and their applications","authors":"Liqin Qian, X. Cao","doi":"10.3934/AMC.2020134","DOIUrl":"https://doi.org/10.3934/AMC.2020134","url":null,"abstract":"Some valuable results over rings have a promising utilization in coding theory and error-correcting code theory. In this paper, we study character sums over a certain non-chain ring and their applications in codebooks. There are two major ingredients in this study. The first ingredient is to investigate Gaussian sums, hyper Eisenstein sums, Jacobi sums over a certain non-chain ring and study the properties of these character sums. For their applications, the second ingredient is to present three classes of asymptotically optimal codebooks with respect to the Welch bound and a family of optimal codebooks with respect to the Levenshtein bound, which are constructed from character sums over a certain non-chain ring.","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":"72815375","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}
{"title":"Dual transform and projective self-dual codes","authors":"I. Bouyukliev, S. Bouyuklieva","doi":"10.3934/amc.2023032","DOIUrl":"https://doi.org/10.3934/amc.2023032","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":"77469085","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}
{"title":"Several classes of new projective three-weight or four-weight linear codes and their applications in $ s $-sum sets","authors":"","doi":"10.3934/amc.2023013","DOIUrl":"https://doi.org/10.3934/amc.2023013","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":"75814955","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 context of digital signatures, the proxy signature holds a significant role of enabling an original signer to delegate its signing ability to another party (i.e., proxy signer). It has significant practical applications. Particularly it is useful in distributed systems, where delegation of authentication rights is quite common. For example, key sharing protocol, grid computing, and mobile communications. Currently, a large portion of existing proxy signature schemes are based on the hardness of problems like integer factoring, discrete logarithms, and/or elliptic curve discrete logarithms. However, with the rising of quantum computers, the problem of prime factorization and discrete logarithm will be solvable in polynomial-time, due to Shor's algorithm, which dilutes the security features of existing ElGamal, RSA, ECC, and the proxy signature schemes based on these problems. As a consequence, construction of secure and efficient post-quantum proxy signature becomes necessary. In this work, we develop a post-quantum proxy signature scheme Mult-proxy, relying on multivariate public key cryptography (MPKC), which is one of the most promising candidates of post-quantum cryptography. We employ a 5-pass identification protocol to design our proxy signature scheme. Our work attains the usual proxy criterion and a one-more-unforgeability criterion under the hardness of the Multivariate Quadratic polynomial (MQ) problem. It produces optimal size proxy signatures and optimal size proxy shares in the field of MPKC.
{"title":"Delegating signing rights in a multivariate proxy signature scheme","authors":"Sumit Kumar Debnath, Tanmay Choudhury, P. Stănică, Kunal Dey, Nibedita Kundu","doi":"10.3934/AMC.2021016","DOIUrl":"https://doi.org/10.3934/AMC.2021016","url":null,"abstract":"In the context of digital signatures, the proxy signature holds a significant role of enabling an original signer to delegate its signing ability to another party (i.e., proxy signer). It has significant practical applications. Particularly it is useful in distributed systems, where delegation of authentication rights is quite common. For example, key sharing protocol, grid computing, and mobile communications. Currently, a large portion of existing proxy signature schemes are based on the hardness of problems like integer factoring, discrete logarithms, and/or elliptic curve discrete logarithms. However, with the rising of quantum computers, the problem of prime factorization and discrete logarithm will be solvable in polynomial-time, due to Shor's algorithm, which dilutes the security features of existing ElGamal, RSA, ECC, and the proxy signature schemes based on these problems. As a consequence, construction of secure and efficient post-quantum proxy signature becomes necessary. In this work, we develop a post-quantum proxy signature scheme Mult-proxy, relying on multivariate public key cryptography (MPKC), which is one of the most promising candidates of post-quantum cryptography. We employ a 5-pass identification protocol to design our proxy signature scheme. Our work attains the usual proxy criterion and a one-more-unforgeability criterion under the hardness of the Multivariate Quadratic polynomial (MQ) problem. It produces optimal size proxy signatures and optimal size proxy shares in the field of MPKC.","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":"82896646","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}
{"title":"Various structures of cyclic codes over the non-Frobenius ring $mathbb{F}_p[u, v] /leftlangle u^2, v^2, u v, v urightrangle$","authors":"H. Choi, Boran Kim","doi":"10.3934/amc.2023030","DOIUrl":"https://doi.org/10.3934/amc.2023030","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":"73135477","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}
Regev (2005) introduced the learning with errors (LWE) problem and showed a quantum reduction from a worst case lattice problem to LWE. Building on the work of Peikert (2009), a classical reduction from the gap shortest vector problem to LWE was obtained by Brakerski et al. (2013). A concrete security analysis of Regev's reduction by Chatterjee et al. (2016) identified a huge tightness gap. The present work performs a concrete analysis of the tightness gap in the classical reduction of Brakerski et al. It turns out that the tightness gap in the Brakerski et al. classical reduction is even larger than the tightness gap in the quantum reduction of Regev. This casts doubts on the implication of the reduction to security assurance of practical cryptosystems.
{"title":"Classical reduction of gap SVP to LWE: A concrete security analysis","authors":"P. Sarkar, Subhadip Singha","doi":"10.3934/AMC.2021004","DOIUrl":"https://doi.org/10.3934/AMC.2021004","url":null,"abstract":"Regev (2005) introduced the learning with errors (LWE) problem and showed a quantum reduction from a worst case lattice problem to LWE. Building on the work of Peikert (2009), a classical reduction from the gap shortest vector problem to LWE was obtained by Brakerski et al. (2013). A concrete security analysis of Regev's reduction by Chatterjee et al. (2016) identified a huge tightness gap. The present work performs a concrete analysis of the tightness gap in the classical reduction of Brakerski et al. It turns out that the tightness gap in the Brakerski et al. classical reduction is even larger than the tightness gap in the quantum reduction of Regev. This casts doubts on the implication of the reduction to security assurance of practical cryptosystems.","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":"76826893","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}
For an odd prime begin{document}$ p $end{document} and positive integers begin{document}$ m $end{document} and begin{document}$ ell $end{document}, let begin{document}$ mathbb{F}_{p^m} $end{document} be the finite field with begin{document}$ p^{m} $end{document} elements and begin{document}$ R_{ell,m} = mathbb{F}_{p^m}[v_1,v_2,dots,v_{ell}]/langle v^{2}_{i}-1, v_{i}v_{j}-v_{j}v_{i}rangle_{1leq i, jleq ell} $end{document}. Thus begin{document}$ R_{ell,m} $end{document} is a finite commutative non-chain ring of order begin{document}$ p^{2^{ell} m} $end{document} with characteristic begin{document}$ p $end{document}. In this paper, we aim to construct quantum codes from skew constacyclic codes over begin{document}$ R_{ell,m} $end{document}. First, we discuss the structures of skew constacyclic codes and determine their Euclidean dual codes. Then a relation between these codes and their Euclidean duals has been obtained. Finally, with the help of a duality-preserving Gray map and the CSS construction, many MDS and better non-binary quantum codes are obtained as compared to the best-known quantum codes available in the literature.
For an odd prime begin{document}$ p $end{document} and positive integers begin{document}$ m $end{document} and begin{document}$ ell $end{document}, let begin{document}$ mathbb{F}_{p^m} $end{document} be the finite field with begin{document}$ p^{m} $end{document} elements and begin{document}$ R_{ell,m} = mathbb{F}_{p^m}[v_1,v_2,dots,v_{ell}]/langle v^{2}_{i}-1, v_{i}v_{j}-v_{j}v_{i}rangle_{1leq i, jleq ell} $end{document}. Thus begin{document}$ R_{ell,m} $end{document} is a finite commutative non-chain ring of order begin{document}$ p^{2^{ell} m} $end{document} with characteristic begin{document}$ p $end{document}. In this paper, we aim to construct quantum codes from skew constacyclic codes over begin{document}$ R_{ell,m} $end{document}. First, we discuss the structures of skew constacyclic codes and determine their Euclidean dual codes. Then a relation between these codes and their Euclidean duals has been obtained. Finally, with the help of a duality-preserving Gray map and the CSS construction, many MDS and better non-binary quantum codes are obtained as compared to the best-known quantum codes available in the literature.
{"title":"New quantum codes from skew constacyclic codes","authors":"Ram Krishna Verma, O. Prakash, A. Singh, H. Islam","doi":"10.3934/amc.2021028","DOIUrl":"https://doi.org/10.3934/amc.2021028","url":null,"abstract":"<p style='text-indent:20px;'>For an odd prime <inline-formula><tex-math id=\"M1\">begin{document}$ p $end{document}</tex-math></inline-formula> and positive integers <inline-formula><tex-math id=\"M2\">begin{document}$ m $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M3\">begin{document}$ ell $end{document}</tex-math></inline-formula>, let <inline-formula><tex-math id=\"M4\">begin{document}$ mathbb{F}_{p^m} $end{document}</tex-math></inline-formula> be the finite field with <inline-formula><tex-math id=\"M5\">begin{document}$ p^{m} $end{document}</tex-math></inline-formula> elements and <inline-formula><tex-math id=\"M6\">begin{document}$ R_{ell,m} = mathbb{F}_{p^m}[v_1,v_2,dots,v_{ell}]/langle v^{2}_{i}-1, v_{i}v_{j}-v_{j}v_{i}rangle_{1leq i, jleq ell} $end{document}</tex-math></inline-formula>. Thus <inline-formula><tex-math id=\"M7\">begin{document}$ R_{ell,m} $end{document}</tex-math></inline-formula> is a finite commutative non-chain ring of order <inline-formula><tex-math id=\"M8\">begin{document}$ p^{2^{ell} m} $end{document}</tex-math></inline-formula> with characteristic <inline-formula><tex-math id=\"M9\">begin{document}$ p $end{document}</tex-math></inline-formula>. In this paper, we aim to construct quantum codes from skew constacyclic codes over <inline-formula><tex-math id=\"M10\">begin{document}$ R_{ell,m} $end{document}</tex-math></inline-formula>. First, we discuss the structures of skew constacyclic codes and determine their Euclidean dual codes. Then a relation between these codes and their Euclidean duals has been obtained. Finally, with the help of a duality-preserving Gray map and the CSS construction, many MDS and better non-binary quantum codes are obtained as compared to the best-known quantum codes available in the literature.</p>","PeriodicalId":50859,"journal":{"name":"Advances in Mathematics of Communications","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90554973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Recently, Ivanov et al. proposed a new approach to construct code-based cryptosystems, namely the begin{document}$ {sf IKKR} $end{document} public-key encryptions (PKE) in the International Workshop on Code-Based Cryptography (CBCrypto 2020) [ 9 ]. Unlike the usual construction in code-based encryption schemes which has restrictions on the Hamming weight of the error introduced into the ciphertext, the begin{document}$ {sf IKKR} $end{document} approach allows error vectors of arbitrary weight being introduced into the ciphertext. Using this new approach, Ivanov et al. constructed two cryptosystems, namely the modified and the upgraded begin{document}$ {sf IKKR} $end{document} -PKE. This paper aims to discuss the practical security of the begin{document}$ {sf IKKR} $end{document} -PKE. In particular, we describe the weaknesses in the design of the public key used in the begin{document}$ {sf IKKR} $end{document} -PKE. We exploit such weaknesses and propose two attacks to recover the plaintext in the begin{document}$ {sf IKKR} $end{document} -PKE. The approach of our first attack is similar to the LCKN attack [ 12 ], whilst our second attack is more efficient than the LCKN attack. Our experimental results show that we can recover the plaintext from a given ciphertext in less than 176 milliseconds for schemes based on random Goppa codes and BCH codes.
Recently, Ivanov et al. proposed a new approach to construct code-based cryptosystems, namely the begin{document}$ {sf IKKR} $end{document} public-key encryptions (PKE) in the International Workshop on Code-Based Cryptography (CBCrypto 2020) [ 9 ]. Unlike the usual construction in code-based encryption schemes which has restrictions on the Hamming weight of the error introduced into the ciphertext, the begin{document}$ {sf IKKR} $end{document} approach allows error vectors of arbitrary weight being introduced into the ciphertext. Using this new approach, Ivanov et al. constructed two cryptosystems, namely the modified and the upgraded begin{document}$ {sf IKKR} $end{document} -PKE. This paper aims to discuss the practical security of the begin{document}$ {sf IKKR} $end{document} -PKE. In particular, we describe the weaknesses in the design of the public key used in the begin{document}$ {sf IKKR} $end{document} -PKE. We exploit such weaknesses and propose two attacks to recover the plaintext in the begin{document}$ {sf IKKR} $end{document} -PKE. The approach of our first attack is similar to the LCKN attack [ 12 ], whilst our second attack is more efficient than the LCKN attack. Our experimental results show that we can recover the plaintext from a given ciphertext in less than 176 milliseconds for schemes based on random Goppa codes and BCH codes.
{"title":"Polynomial-time plaintext recovery attacks on the IKKR code-based cryptosystems","authors":"T. Lau, C. H. Tan","doi":"10.3934/AMC.2020132","DOIUrl":"https://doi.org/10.3934/AMC.2020132","url":null,"abstract":"Recently, Ivanov et al. proposed a new approach to construct code-based cryptosystems, namely the begin{document}$ {sf IKKR} $end{document} public-key encryptions (PKE) in the International Workshop on Code-Based Cryptography (CBCrypto 2020) [ 9 ]. Unlike the usual construction in code-based encryption schemes which has restrictions on the Hamming weight of the error introduced into the ciphertext, the begin{document}$ {sf IKKR} $end{document} approach allows error vectors of arbitrary weight being introduced into the ciphertext. Using this new approach, Ivanov et al. constructed two cryptosystems, namely the modified and the upgraded begin{document}$ {sf IKKR} $end{document} -PKE. This paper aims to discuss the practical security of the begin{document}$ {sf IKKR} $end{document} -PKE. In particular, we describe the weaknesses in the design of the public key used in the begin{document}$ {sf IKKR} $end{document} -PKE. We exploit such weaknesses and propose two attacks to recover the plaintext in the begin{document}$ {sf IKKR} $end{document} -PKE. The approach of our first attack is similar to the LCKN attack [ 12 ], whilst our second attack is more efficient than the LCKN attack. Our experimental results show that we can recover the plaintext from a given ciphertext in less than 176 milliseconds for schemes based on random Goppa codes and BCH codes.","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":"85433503","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：