Pub Date : 2023-09-01DOI: 10.1587/transfun.2022dmp0001
Ren ISHIBASHI, Kazuki YONEYAMA
Authenticated Key Exchange (AKE) is a cryptographic protocol to share a common session key among multiple parties. Usually, PKI-based AKE schemes are designed to guarantee secrecy of the session key and mutual authentication. However, in practice, there are many cases where mutual authentication is undesirable such as in anonymous networks like Tor and Riffle, or difficult to achieve due to the certificate management at the user level such as the Internet. Goldberg et al. formulated a model of anonymous one-sided AKE which guarantees the anonymity of the client by allowing only the client to authenticate the server, and proposed a concrete scheme. However, existing anonymous one-sided AKE schemes are only known to be secure in the random oracle model. In this paper, we propose generic constructions of anonymous one-sided AKE in the random oracle model and in the standard model, respectively. Our constructions allow us to construct the first post-quantum anonymous one-sided AKE scheme from isogenies in the standard model.
{"title":"Post-Quantum Anonymous One-Sided Authenticated Key Exchange without Random Oracles","authors":"Ren ISHIBASHI, Kazuki YONEYAMA","doi":"10.1587/transfun.2022dmp0001","DOIUrl":"https://doi.org/10.1587/transfun.2022dmp0001","url":null,"abstract":"Authenticated Key Exchange (AKE) is a cryptographic protocol to share a common session key among multiple parties. Usually, PKI-based AKE schemes are designed to guarantee secrecy of the session key and mutual authentication. However, in practice, there are many cases where mutual authentication is undesirable such as in anonymous networks like Tor and Riffle, or difficult to achieve due to the certificate management at the user level such as the Internet. Goldberg et al. formulated a model of anonymous one-sided AKE which guarantees the anonymity of the client by allowing only the client to authenticate the server, and proposed a concrete scheme. However, existing anonymous one-sided AKE schemes are only known to be secure in the random oracle model. In this paper, we propose generic constructions of anonymous one-sided AKE in the random oracle model and in the standard model, respectively. Our constructions allow us to construct the first post-quantum anonymous one-sided AKE scheme from isogenies in the standard model.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"82 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135944506","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}
Pub Date : 2023-05-01DOI: 10.1587/transfun.2022map0010
Sho OBATA, Koichi KOBAYASHI, Yuh YAMASHITA
In a power network, it is important to detect a cyber attack. In this paper, we propose a method for detecting false data injection (FDI) attacks in distributed state estimation. An FDI attack is well known as one of the typical cyber attacks in a power network. As a method of FDI attack detection, we consider calculating the residual (i.e., the difference between the observed and estimated values). In the proposed detection method, the tentative residual (estimated error) in ADMM (Alternating Direction Method of Multipliers), which is one of the powerful methods in distributed optimization, is applied. First, the effect of an FDI attack is analyzed. Next, based on the analysis result, a detection parameter is introduced based on the residual. A detection method using this parameter is then proposed. Finally, the proposed method is demonstrated through a numerical example on the IEEE 14-bus system.
{"title":"Detection of False Data Injection Attacks in Distributed State Estimation of Power Networks","authors":"Sho OBATA, Koichi KOBAYASHI, Yuh YAMASHITA","doi":"10.1587/transfun.2022map0010","DOIUrl":"https://doi.org/10.1587/transfun.2022map0010","url":null,"abstract":"In a power network, it is important to detect a cyber attack. In this paper, we propose a method for detecting false data injection (FDI) attacks in distributed state estimation. An FDI attack is well known as one of the typical cyber attacks in a power network. As a method of FDI attack detection, we consider calculating the residual (i.e., the difference between the observed and estimated values). In the proposed detection method, the tentative residual (estimated error) in ADMM (Alternating Direction Method of Multipliers), which is one of the powerful methods in distributed optimization, is applied. First, the effect of an FDI attack is analyzed. Next, based on the analysis result, a detection parameter is introduced based on the residual. A detection method using this parameter is then proposed. Finally, the proposed method is demonstrated through a numerical example on the IEEE 14-bus system.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135752370","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}
Pub Date : 2023-03-01DOI: 10.1587/transfun.2022vlp0005
Lingxiao HOU, Yutaka MASUDA, Tohru ISHIHARA
The approximate logarithmic multiplier proposed by Mitchell provides an efficient alternative for processing dense multiplication or multiply-accumulate operations in applications such as image processing and real-time robotics. It offers the advantages of small area, high energy efficiency and is suitable for applications that do not necessarily achieve high accuracy. However, its maximum error of 11.1% makes it challenging to deploy in applications requiring relatively high accuracy. This paper proposes a novel operand decomposition method (OD) that decomposes one multiplication into the sum of multiple approximate logarithmic multiplications to widely reduce Mitchell multiplier errors while taking full advantage of its area savings. Based on the proposed OD method, this paper also proposes an accuracy reconfigurable multiply-accumulate (MAC) unit that provides multiple reconfigurable accuracies with high parallelism. Compared to a MAC unit consisting of accurate multipliers, the area is significantly reduced to less than half, improving the hardware parallelism while satisfying the required accuracy for various scenarios. The experimental results show the excellent applicability of our proposed MAC unit in image smoothing and robot localization and mapping application. We have also designed a prototype processor that integrates the minimum functionality of this MAC unit as a vector accelerator and have implemented a software-level accuracy reconfiguration in the form of an instruction set extension. We experimentally confirmed the correct operation of the proposed vector accelerator, which provides the different degrees of accuracy and parallelism at the software level.
{"title":"An Accuracy Reconfigurable Vector Accelerator based on Approximate Logarithmic Multipliers for Energy-Efficient Computing","authors":"Lingxiao HOU, Yutaka MASUDA, Tohru ISHIHARA","doi":"10.1587/transfun.2022vlp0005","DOIUrl":"https://doi.org/10.1587/transfun.2022vlp0005","url":null,"abstract":"The approximate logarithmic multiplier proposed by Mitchell provides an efficient alternative for processing dense multiplication or multiply-accumulate operations in applications such as image processing and real-time robotics. It offers the advantages of small area, high energy efficiency and is suitable for applications that do not necessarily achieve high accuracy. However, its maximum error of 11.1% makes it challenging to deploy in applications requiring relatively high accuracy. This paper proposes a novel operand decomposition method (OD) that decomposes one multiplication into the sum of multiple approximate logarithmic multiplications to widely reduce Mitchell multiplier errors while taking full advantage of its area savings. Based on the proposed OD method, this paper also proposes an accuracy reconfigurable multiply-accumulate (MAC) unit that provides multiple reconfigurable accuracies with high parallelism. Compared to a MAC unit consisting of accurate multipliers, the area is significantly reduced to less than half, improving the hardware parallelism while satisfying the required accuracy for various scenarios. The experimental results show the excellent applicability of our proposed MAC unit in image smoothing and robot localization and mapping application. We have also designed a prototype processor that integrates the minimum functionality of this MAC unit as a vector accelerator and have implemented a software-level accuracy reconfiguration in the form of an instruction set extension. We experimentally confirmed the correct operation of the proposed vector accelerator, which provides the different degrees of accuracy and parallelism at the software level.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135907374","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}
Pub Date : 2023-03-01DOI: 10.1587/transfun.2022cip0002
Yasufumi Hashimoto
The problem of Isomorphism of Polynomials (IP problem) is known to be important to study the security of multivariate public key cryptosystems, one of the major candidates of post-quantum cryptography, against key recovery attacks. In these years, several schemes based on the IP problem itself or its generalization have been proposed. At PQCrypto 2020, Santoso introduced a generalization of the problem of Isomorphism of Polynomials, called the problem of Blockwise Isomorphism of Polynomials (BIP problem), and proposed a new Diffie-Hellman type encryption scheme based on this problem with Circulant matrices (BIPC problem). Quite recently, Ikematsu et al. proposed an attack called the linear stack attack to recover an equivalent key of Santoso's encryption scheme. While this attack reduced the security of the scheme, it does not contribute to solving the BIPC problem itself. In the present paper, we describe how to solve the BIPC problem directly by simplifying the BIPC problem due to the conjugation property of circulant matrices. In fact, we experimentally solved the BIPC problem with the parameter, which has 256 bit security by Santoso's security analysis and has 72.7bit security against the linear stack attack, by about 10 minutes.
{"title":"Solving the Problem of Blockwise Isomorphism of Polynomials with Circulant Matrices","authors":"Yasufumi Hashimoto","doi":"10.1587/transfun.2022cip0002","DOIUrl":"https://doi.org/10.1587/transfun.2022cip0002","url":null,"abstract":"The problem of Isomorphism of Polynomials (IP problem) is known to be important to study the security of multivariate public key cryptosystems, one of the major candidates of post-quantum cryptography, against key recovery attacks. In these years, several schemes based on the IP problem itself or its generalization have been proposed. At PQCrypto 2020, Santoso introduced a generalization of the problem of Isomorphism of Polynomials, called the problem of Blockwise Isomorphism of Polynomials (BIP problem), and proposed a new Diffie-Hellman type encryption scheme based on this problem with Circulant matrices (BIPC problem). Quite recently, Ikematsu et al. proposed an attack called the linear stack attack to recover an equivalent key of Santoso's encryption scheme. While this attack reduced the security of the scheme, it does not contribute to solving the BIPC problem itself. In the present paper, we describe how to solve the BIPC problem directly by simplifying the BIPC problem due to the conjugation property of circulant matrices. In fact, we experimentally solved the BIPC problem with the parameter, which has 256 bit security by Santoso's security analysis and has 72.7bit security against the linear stack attack, by about 10 minutes.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136131356","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}
Pub Date : 2023-01-01DOI: 10.1587/transfun.2023eal2084
Changhui CHEN, Haibin KAN, Jie PENG, Li WANG
Permutation polynomials have important applications in cryptography, coding theory and combinatorial designs. In this letter, we construct four classes of permutation polynomials over 𝔽2n × 𝔽2n , where 𝔽2n is the finite field with 2n elements.
{"title":"Four classes of bivariate permutation polynomials over finite fields of even characteristic","authors":"Changhui CHEN, Haibin KAN, Jie PENG, Li WANG","doi":"10.1587/transfun.2023eal2084","DOIUrl":"https://doi.org/10.1587/transfun.2023eal2084","url":null,"abstract":"Permutation polynomials have important applications in cryptography, coding theory and combinatorial designs. In this letter, we construct four classes of permutation polynomials over 𝔽2n × 𝔽2n , where 𝔽2n is the finite field with 2n elements.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136374318","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}
Pub Date : 2023-01-01DOI: 10.1587/transfun.2023eap1019
Yuto ARIMURA, Shigeru YAMASHITA
{"title":"Efficient Realization of an SC Circuit with Feedback and Its Applications","authors":"Yuto ARIMURA, Shigeru YAMASHITA","doi":"10.1587/transfun.2023eap1019","DOIUrl":"https://doi.org/10.1587/transfun.2023eap1019","url":null,"abstract":"","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134979823","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}
Pub Date : 2023-01-01DOI: 10.1587/transfun.2023eap1085
Zelin LIU, Fangmin XU
{"title":"Joint AP Selection and Grey Wolf Optimization Based Pilot Design for Cell-Free Massive MIMO Systems","authors":"Zelin LIU, Fangmin XU","doi":"10.1587/transfun.2023eap1085","DOIUrl":"https://doi.org/10.1587/transfun.2023eap1085","url":null,"abstract":"","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"266 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134980020","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}
Pub Date : 2023-01-01DOI: 10.1587/transfun.2023eap1064
Yingzhong ZHANG, Xiaoni DU, Wengang JIN, Xingbin QIAO
Boolean functions with a few Walsh spectral values have important applications in sequence ciphers and coding theory. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra by using the secondary construction of Boolean functions, in particular, plateaued functions are included. Then, we construct three classes of Boolean functions with five-valued Walsh spectra using Kasami functions and investigate the Walsh spectrum distributions of the new functions. Finally, three classes of minimal linear codes with five-weights are obtained, which can be used to design secret sharing scheme with good access structures.
{"title":"Constructions of Boolean functions with five-valued Walsh spectra and their applications","authors":"Yingzhong ZHANG, Xiaoni DU, Wengang JIN, Xingbin QIAO","doi":"10.1587/transfun.2023eap1064","DOIUrl":"https://doi.org/10.1587/transfun.2023eap1064","url":null,"abstract":"Boolean functions with a few Walsh spectral values have important applications in sequence ciphers and coding theory. In this paper, we first construct a class of Boolean functions with at most five-valued Walsh spectra by using the secondary construction of Boolean functions, in particular, plateaued functions are included. Then, we construct three classes of Boolean functions with five-valued Walsh spectra using Kasami functions and investigate the Walsh spectrum distributions of the new functions. Finally, three classes of minimal linear codes with five-weights are obtained, which can be used to design secret sharing scheme with good access structures.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135260755","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}
Pub Date : 2023-01-01DOI: 10.1587/transfun.2023cip0019
Yasuhiko IKEMATSU, Tsunekazu SAITO
Multivariate public key cryptosystems (MPKC) are constructed based on the problem of solving multivariate quadratic equations (MQ problem). Among various multivariate schemes, UOV is an important signature scheme since it is underlying some signature schemes such as MAYO, QR-UOV, and Rainbow which was a finalist of NIST PQC standardization project. To analyze the security of a multivariate scheme, it is necessary to analyze the first fall degree or solving degree for the system of polynomial equations used in specific attacks. It is known that the first fall degree or solving degree often relates to the Hilbert series of the ideal generated by the system. In this paper, we study the Hilbert series of the UOV scheme, and more specifically, we study the Hilbert series of ideals generated by quadratic polynomials used in the central map of UOV. In particular, we derive a prediction formula of the Hilbert series by using some experimental results. Moreover, we apply it to the analysis of the reconciliation attack for MAYO.
{"title":"Hilbert series for systems of UOV polynomials","authors":"Yasuhiko IKEMATSU, Tsunekazu SAITO","doi":"10.1587/transfun.2023cip0019","DOIUrl":"https://doi.org/10.1587/transfun.2023cip0019","url":null,"abstract":"Multivariate public key cryptosystems (MPKC) are constructed based on the problem of solving multivariate quadratic equations (MQ problem). Among various multivariate schemes, UOV is an important signature scheme since it is underlying some signature schemes such as MAYO, QR-UOV, and Rainbow which was a finalist of NIST PQC standardization project. To analyze the security of a multivariate scheme, it is necessary to analyze the first fall degree or solving degree for the system of polynomial equations used in specific attacks. It is known that the first fall degree or solving degree often relates to the Hilbert series of the ideal generated by the system. In this paper, we study the Hilbert series of the UOV scheme, and more specifically, we study the Hilbert series of ideals generated by quadratic polynomials used in the central map of UOV. In particular, we derive a prediction formula of the Hilbert series by using some experimental results. Moreover, we apply it to the analysis of the reconciliation attack for MAYO.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135357289","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}
Pub Date : 2023-01-01DOI: 10.1587/transfun.2023vlp0002
Sohei SHIMOMAI, Kei UEDA, Shinji KIMURA
Recently, Quantum Annealing (QA) has attracted attention as an efficient algorithm for combinatorial optimization problems. In QA, the input data size becomes large and its reduction is important for accelerating by the hardware emulation since the usable memory size and its bandwidth are limited. The paper proposes the compression method of input sparse matrices for QA emulator. The proposed method uses the sparseness of the coefficient matrix and the reappearance of the same values. An independent table is introduced and data are compressed by the search and registration method of two consecutive data in the value table. The proposed method is applied to Traveling Salesman Problem (TSP) with 32, 64 and 96 cities and Nurse Scheduling Problem (NSP). The proposed method could reduce the amount of data by 1/40 for 96 city TSP and could manage 96 city TSP on the hardware emulator. When applied to NSP, we confirmed the effectiveness of the proposed method by the compression ratio ranging from 1/4 to 1/11.8. The data reduction is also useful for the simulation/emulation performance when using the compressed data directly and 1.9 times faster speed can be found on 96 city TSP than the CSR-based method.
{"title":"Input Data Format for Sparse Matrix in Quantum Annealing Emulator","authors":"Sohei SHIMOMAI, Kei UEDA, Shinji KIMURA","doi":"10.1587/transfun.2023vlp0002","DOIUrl":"https://doi.org/10.1587/transfun.2023vlp0002","url":null,"abstract":"Recently, Quantum Annealing (QA) has attracted attention as an efficient algorithm for combinatorial optimization problems. In QA, the input data size becomes large and its reduction is important for accelerating by the hardware emulation since the usable memory size and its bandwidth are limited. The paper proposes the compression method of input sparse matrices for QA emulator. The proposed method uses the sparseness of the coefficient matrix and the reappearance of the same values. An independent table is introduced and data are compressed by the search and registration method of two consecutive data in the value table. The proposed method is applied to Traveling Salesman Problem (TSP) with 32, 64 and 96 cities and Nurse Scheduling Problem (NSP). The proposed method could reduce the amount of data by 1/40 for 96 city TSP and could manage 96 city TSP on the hardware emulator. When applied to NSP, we confirmed the effectiveness of the proposed method by the compression ratio ranging from 1/4 to 1/11.8. The data reduction is also useful for the simulation/emulation performance when using the compressed data directly and 1.9 times faster speed can be found on 96 city TSP than the CSR-based method.","PeriodicalId":55003,"journal":{"name":"Ieice Transactions on Fundamentals of Electronics Communications and Computer Sciences","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135699270","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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