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Published byDaisy Stanley Modified over 9 years ago
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Introduction PreparationMain result Conclusion A Method for Constructing A Self-Dual Normal Basis in Odd Characteristic Extension Field Department of Communication Network Engineering, Faculty of Engineering, Okayama University, Japan Hiroaki Nasu, Yasuyuki Nogami, Ryo Namba, and Yoshitaka Morikawa
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Introduction Layout PreparationMain result Conclusion Introduction Background Motivation Preparation Self-dual normal basis (SDN) A special class of Gauss period normal bases Main result How to construct SDN Translation between GNB and SDN Conclusion
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Introduction Background PreparationMain result Conclusion Public key cryptography elliptic curve cryptography pairing-based cryptographic applications ID-based cryptography, Group signature Finite field prime field extension field
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Introduction Background PreparationMain result Conclusion Public key cryptography elliptic curve cryptography pairing-based cryptographic applications ID-based cryptography, Group signature Finite field prime field extension field
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Introduction Background PreparationMain result Conclusion Public key cryptography elliptic curve cryptography pairing-based cryptographic applications : 160-bit prime number : 3,4,5,6,…12,15,… Arithmetic operations in are needed.
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Introduction Background PreparationMain result Conclusion Public key cryptography elliptic curve cryptography pairing-based cryptographic applications ID-based cryptography, Group signature Finite field prime field extension field Bases Gauss period normal basis (GNB), optimal normal basis dual basis, self-dual normal basis (SDN)
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Introduction Motivation PreparationMain result Conclusion Bases Gauss period normal basis (GNB), optimal normal basis dual basis, self-dual normal basis (SDN)
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Introduction Motivation PreparationMain result Conclusion Bases Gauss period normal basis (GNB), optimal normal basis dual basis, self-dual normal basis (SDN) Gauss period normal basis (GNB) self-dual normal basis (SDN)
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Self-dual normal basis Preparation Main resultConclusion Self-dual normal basis in Trace matrix
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A special class of GNBs Preparation Main resultConclusion TypeII-X normal basis (TypeII-X NB) TypeII ONB in TypeII-X NB in Normal basis (NB) in NB GNB
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Main result Conclusion TypeII-X NB in an SDN in
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Property of TypeII-X NB Main result Conclusion TypeII-X NB in By the way, it is well-known that GNB is SDN when is divisible by characteristic.
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How to construct SDN Main result Conclusion In order to satisfy and need to satisfy
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How to construct SDN Main result Conclusion In addition, in order to satisfy needs to satisfy
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How to construct SDN Main result Conclusion The most important is Changing parameter such that except for the case, it is always found.
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Translation between GNB and SDN Main result Conclusion TypeII-X NB in an SDN in basis translation
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Translation between GNB and SDN Main result Conclusion TypeII-X NB (GNB) SDN
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Translation between GNB and SDN Main result Conclusion TypeII-X NB (GNB) SDN SDN GNB and GNB SDN require several multiplications and additions in.
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Conclusion Conclusion Main result How to construct SDN from GNB Translation between GNB and SDN Future work Is the obtained SDN one of GNBs in ?
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