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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.

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Presentation on theme: "Introduction PreparationMain result Conclusion A Method for Constructing A Self-Dual Normal Basis in Odd Characteristic Extension Field Department of Communication."— Presentation transcript:

1 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

2 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

3 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

4 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

5 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.

6 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)

7 Introduction Motivation PreparationMain result Conclusion  Bases Gauss period normal basis (GNB), optimal normal basis dual basis, self-dual normal basis (SDN)

8 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)

9 Self-dual normal basis Preparation Main resultConclusion  Self-dual normal basis in Trace matrix

10 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

11 Main result Conclusion TypeII-X NB in an SDN in

12 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.

13 How to construct SDN Main result Conclusion In order to satisfy and need to satisfy

14 How to construct SDN Main result Conclusion In addition, in order to satisfy needs to satisfy

15 How to construct SDN Main result Conclusion The most important is Changing parameter such that except for the case, it is always found.

16 Translation between GNB and SDN Main result Conclusion TypeII-X NB in an SDN in basis translation

17 Translation between GNB and SDN Main result Conclusion TypeII-X NB (GNB) SDN

18 Translation between GNB and SDN Main result Conclusion TypeII-X NB (GNB) SDN SDN GNB and GNB SDN require several multiplications and additions in.

19 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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