Theoretical and Practical Possibilities of Elliptic Curves : From Elliptic Curve Cryptosystems to Post-Quantum Cryptosystems

DOI Web Site 8 References
  • MIYAJI Atsuko
    Graduate School of Engineering, Osaka University Japan Advanced Institute of Science and Technology

Bibliographic Information

Other Title
  • 楕円曲線の理論的及び実用的可能性
  • ―楕円曲線暗号から耐量子暗号まで―

Abstract

<p>In 1985, Miller and Koblitz independently introduced elliptic curve cryptosystems, a type of public key cryptosystem. Elliptic curve cryptosystems use the fact that elliptic curves become a group to realize an ID-based cryptosystem for the first time, by applying a bilinear map on an elliptic curve. Furthermore, in recent years, isogenies on elliptic curves have been used to realize post-quantum cryptosystems. Elliptic curves are indeed treasures for solving various cryptographic problems. Elliptic curves have been applied to resolve many theoretical problems and are merely a theoretical breakthrough. The charm of elliptic curves is that they are highly practical. To verify the correctness of a blockchain, the elliptic curve DSA signature (ECDSA) is used, since the signature size of ECDSA is very short. Furthermore, the elliptic curve realizes a post-quantum cryptosystem. In this paper, we discuss various breakthroughs achieved by using elliptic curves as well as international standardization related to elliptic curves.</p>

Journal

  • IEICE ESS Fundamentals Review

    IEICE ESS Fundamentals Review 14 (4), 329-336, 2021-04-01

    The Institute of Electronics, Information and Communication Engineers

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