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Preparation. Main result. Introduction. 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
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Preparation Main result Introduction 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
Preparation Main result Introduction Conclusion Layout • 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
Preparation Main result Introduction Conclusion Background • Public key cryptography • elliptic curve cryptography • pairing-based cryptographic applications • ID-based cryptography, Group signature • Finite field • prime field • extension field
Preparation Main result Introduction Conclusion Background • Public key cryptography • elliptic curve cryptography • pairing-based cryptographic applications • ID-based cryptography, Group signature • Finite field • prime field • extension field
Preparation Main result : 160-bit prime number : 3,4,5,6,…12,15,… Arithmetic operations in are needed. Introduction Conclusion Background • Public key cryptography • elliptic curve cryptography • pairing-based cryptographic applications
Preparation Main result Introduction Conclusion Background • 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)
Preparation Main result Introduction Conclusion Motivation • Bases • Gauss period normal basis (GNB), optimal normal basis • dual basis, self-dual normal basis (SDN)
Preparation Main result Introduction Conclusion Motivation Gauss period normal basis (GNB) self-dual normal basis (SDN) • Bases • Gauss period normal basis (GNB), optimal normal basis • dual basis, self-dual normal basis (SDN)
Main result Conclusion Trace matrix Preparation Self-dual normal basis • Self-dual normal basis in
Main result Conclusion Preparation A special class of GNBs TypeII-X normal basis (TypeII-X NB) • Normal basis (NB) in NB GNB TypeII ONB in TypeII-X NB in
Conclusion Main result Main result TypeII-X NB in an SDN in
Conclusion Main result Property of TypeII-X NB TypeII-X NB in By the way, it is well-known that GNB is SDN when is divisible by characteristic .
Conclusion Main result How to construct SDN In order to satisfy and need to satisfy
Conclusion Main result How to construct SDN In addition, in order to satisfy needs to satisfy
Conclusion Main result How to construct SDN The most important is Changing parameter such that except for the case , it is always found.
Conclusion Main result Translation between GNB and SDN TypeII-X NB in an SDN in basis translation
Conclusion Main result Translation between GNB and SDN TypeII-X NB (GNB) SDN
Conclusion Main result Translation between GNB and SDN TypeII-X NB (GNB) SDN SDN GNBand GNBSDN require several multiplications and additions in .
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 ?
