In the process of encoding and decoding,erasure codes over binary fields,which just need AND operations and XOR operations and therefore have a high computational efficiency,are widely used in various fields of inform...In the process of encoding and decoding,erasure codes over binary fields,which just need AND operations and XOR operations and therefore have a high computational efficiency,are widely used in various fields of information technology.A matrix decoding method is proposed in this paper.The method is a universal data reconstruction scheme for erasure codes over binary fields.Besides a pre-judgment that whether errors can be recovered,the method can rebuild sectors of loss data on a fault-tolerant storage system constructed by erasure codes for disk errors.Data reconstruction process of the new method has simple and clear steps,so it is beneficial for implementation of computer codes.And more,it can be applied to other non-binary fields easily,so it is expected that the method has an extensive application in the future.展开更多
The mathematical theory for elliptic curve encryption based on optimal normal basis(ONB) over F_2~m is introduced.Then an elliptic curve cryptography(ECC) based encryption scheme isanalyzed and designed.The mechanism ...The mathematical theory for elliptic curve encryption based on optimal normal basis(ONB) over F_2~m is introduced.Then an elliptic curve cryptography(ECC) based encryption scheme isanalyzed and designed.The mechanism for key exchange based on Diffie-Hellman is described in detailsfor further applications.Based on these theoretic foundations,the software based on ECC is developedand an application is provided.The software is characterized by excellent security as well as highefficiency.展开更多
We give a unified treatment of Fast Fourier Transforms for UDMD systems which contains, as special cases, Fast Fourier algorithms for character groups of many subgroups associated with binary fields.
Nowadays most communications are done by utilizing digital transmission mechanisms.The security of this digital information transmitted through different communication systems is quite important.The secrecy of digital...Nowadays most communications are done by utilizing digital transmission mechanisms.The security of this digital information transmitted through different communication systems is quite important.The secrecy of digital data is one of the burning topics of the digitally developed world.There exist many traditional algorithms in the literature to provide methods for robust communication.The most important and recent modern block cipher named the advanced encryption standard(AES)is one of the extensively utilized encryption schemes with binary based.AES is a succession of four fundamental steps:round key,sub-byte,shift row,and mix column.In this work,we will provide an innovative methodology for extending the AES in a Galois fieldwith any characteristic p.All four steps in the fundamental process with binary characteristics will be adjusted because of the new enhancement.By applying double affine transformations,we have enhanced the number of options in our suggested substitution boxes.The reconstruction of the nonlinear confusion component and encryption structure provides robustness in the generalized AES.The increase in the keyspace due to the Galois field generalization implies that we have improved additional confusion abilities and broadened the current notions.The implementation of the proposed structure of AES for image,audio,and video encryption will provide high security for secure communication.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.61501064Sichuan Provincial Science and Technology Project under Grant No.2016GZ0122
文摘In the process of encoding and decoding,erasure codes over binary fields,which just need AND operations and XOR operations and therefore have a high computational efficiency,are widely used in various fields of information technology.A matrix decoding method is proposed in this paper.The method is a universal data reconstruction scheme for erasure codes over binary fields.Besides a pre-judgment that whether errors can be recovered,the method can rebuild sectors of loss data on a fault-tolerant storage system constructed by erasure codes for disk errors.Data reconstruction process of the new method has simple and clear steps,so it is beneficial for implementation of computer codes.And more,it can be applied to other non-binary fields easily,so it is expected that the method has an extensive application in the future.
基金Supported by National 863 Plan Project (No. 2002AA142040)
文摘The mathematical theory for elliptic curve encryption based on optimal normal basis(ONB) over F_2~m is introduced.Then an elliptic curve cryptography(ECC) based encryption scheme isanalyzed and designed.The mechanism for key exchange based on Diffie-Hellman is described in detailsfor further applications.Based on these theoretic foundations,the software based on ECC is developedand an application is provided.The software is characterized by excellent security as well as highefficiency.
文摘We give a unified treatment of Fast Fourier Transforms for UDMD systems which contains, as special cases, Fast Fourier algorithms for character groups of many subgroups associated with binary fields.
基金This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project Number(PNURSP2022R87)Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘Nowadays most communications are done by utilizing digital transmission mechanisms.The security of this digital information transmitted through different communication systems is quite important.The secrecy of digital data is one of the burning topics of the digitally developed world.There exist many traditional algorithms in the literature to provide methods for robust communication.The most important and recent modern block cipher named the advanced encryption standard(AES)is one of the extensively utilized encryption schemes with binary based.AES is a succession of four fundamental steps:round key,sub-byte,shift row,and mix column.In this work,we will provide an innovative methodology for extending the AES in a Galois fieldwith any characteristic p.All four steps in the fundamental process with binary characteristics will be adjusted because of the new enhancement.By applying double affine transformations,we have enhanced the number of options in our suggested substitution boxes.The reconstruction of the nonlinear confusion component and encryption structure provides robustness in the generalized AES.The increase in the keyspace due to the Galois field generalization implies that we have improved additional confusion abilities and broadened the current notions.The implementation of the proposed structure of AES for image,audio,and video encryption will provide high security for secure communication.
