1 / 19

Constructing a Self-Dual Normal Basis in Odd Characteristic Extension Fields

This paper presents a method for constructing self-dual normal bases (SDN) within odd characteristic extension fields. It explores the relationship between traditional Gauss period normal bases (GNB) and SDN, providing insight into properties and construction techniques essential for applications in public key cryptography and elliptic curve cryptography. The main results include a systematic approach to translating between GNB and SDN, addressing the need for efficient arithmetic operations in cryptographic algorithms. Future works will delve into the adaptability of the constructed SDN within various cryptographic applications.

aviva
Télécharger la présentation

Constructing a Self-Dual Normal Basis in Odd Characteristic Extension Fields

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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

  2. 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

  3. 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

  4. 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

  5. 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

  6. 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)

  7. Preparation Main result Introduction Conclusion Motivation • Bases • Gauss period normal basis (GNB), optimal normal basis • dual basis, self-dual normal basis (SDN)

  8. 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)

  9. Main result Conclusion Trace matrix Preparation Self-dual normal basis • Self-dual normal basis in

  10. 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

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

  12. 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 .

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

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

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

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

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

  18. Conclusion Main result Translation between GNB and SDN TypeII-X NB (GNB) SDN SDN GNBand GNBSDN 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 ?

More Related