Constructing a theory of fixed points assciated with one-way functions

• Project/Area Number: 26330150
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Information security
• Research Institution: Tohoku University
• Principal Investigator: Shizuya Hiroki 東北大学, 教育情報基盤センター, 教授 (50196383)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000); Fiscal Year 2016: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2015: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000); Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 一方向性関数 / 不動点 / 楕円曲線 / 離散対数問題

Outline of Final Research Achievements

It is clear today that the notion of one-way function is essential for us to keep information and information systems secure. The purpose of this research project is to re-investigate one-way functions from a viewpoint of fixed points. Intuitively a fixed point x of a function f is defined as f(x)=x. Since the output is the same as the input, the function looks not to be one-way as far as for the fixed point.
We especially attempted to solve an open question concerning the property of fixed points of an elliptic-curve version of a cryptographic function, and in fact have given a partial solution to the question: among all the elliptic curves, more than a half curves lead to a function that has a trivial fixed point. We have also shown quantitative estimation for non-trivial fixed points.

Research Products

• [Journal Article] Computational Model of Card-Based Cryptographic Protocols and Its Applications (2017)
  • Author(s): Takaaki Mizuki, Hiroki Shizuya
  • Journal Title: IEICE Trans. Fundamentals, Special Section on Cryptography and Information Security Volume: E100-A Pages: 3-11
  • NAID: 130005180847
  • Peer Reviewed / Open Access
• [Journal Article] Computational Model of Card-Based Cryptographic Protocols and Its Applications (2017)
  • Author(s): Takaaki Mizuki and Hiroki Shizuya
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E100.A Issue: 1 Pages: 3-11
  • DOI: 10.1587/transfun.E100.A.3
  • NAID: 130005180847
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A Rigorous Security Proof for the Enhanced Version of Password-Protected Secret Sharing Scheme (2016)
  • Author(s): Shingo Hasegawa, Shuji Isobe, Jun-ya Iwazaki, Eisuke Koizumi, Hiroki Shizuya
  • Journal Title: Interdisciplinary Information Sciences Volume: 22 Pages: 1-26
  • NAID: 130005281206
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] A Strengthened Security Notion for Password-Protected Secrete Sharing Schemes (2015)
  • Author(s): Shingo Hasegawa, Shuji Isobe, Jun-ya Iwazaki, Eisuke Koizumi, Hiroki Shizuya
  • Journal Title: IEICE Trans. Fundamentals, Special Section on Cryptography and Information Security Volume: E98-A Pages: 203-212
  • NAID: 130004770895
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Presentation] A Construction of Attribute-based Aggregate Signatures (2016)
  • Author(s): Shingo Hasegawa, Shuji Isobe, Eisuke Koizumi, Hiroki Shizuya, Ryo Takahashi
  • Organizer: 2016 International Symposium on Information Theory and Its Applications (ISITA 2016)
  • Place of Presentation: Monterey, California, USA
  • Year and Date: 2016-10-30
  • Int'l Joint Research
• [Presentation] 属性ベース集約署名の一構成 (2015)
  • Author(s): 高橋遼，長谷川真吾，磯辺秀司，小泉英介，静谷啓樹
  • Organizer: 電子情報通信学会情報セキュリティ研究会
  • Place of Presentation: 北九州市立大学国際環境工学部ひびきのキャンパス（北九州市若松区）
  • Year and Date: 2015-03-02 – 2015-03-03
• [Presentation] 準同型暗号の安全性証明の限界について (2015)
  • Author(s): 高橋大樹，長谷川真吾，磯辺秀司，小泉英介，静谷啓樹
  • Organizer: 電子情報通信学会情報セキュリティ研究会
  • Place of Presentation: 北九州市立大学国際環境工学部ひびきのキャンパス（北九州市若松区）
  • Year and Date: 2015-03-02 – 2015-03-03
• [Presentation] Password-protected Secret-sharing Schemes without Random Oracles (2014)
  • Author(s): Shingo Hasegawa, Shuji Isobe, Jun-ya Iwazaki, Eisuke Koizumi, Hiroki Shizuya
  • Organizer: Proc. 2014 International Symposium on Information Theory and Its Applications (ISITA 2014)
  • Place of Presentation: Melbourne Convention and Exhibition Center (South Wharf, VIC, Australia)
  • Year and Date: 2014-10-26 – 2014-10-29
• [Presentation] On the Impossibility of Proving Security of Strong-RSA Signatures via the RSA Assumption (2014)
  • Author(s): Masayuki Fukumitsu, Shingo Hasegawa, Shuji Isobe and Hiroki Shizuya
  • Organizer: Proc. 19th Australasian Conference on Information Security and Privacy (ACISP 2014)
  • Place of Presentation: University of Wollongong (Wollongong, NSW, Australia)
  • Year and Date: 2014-07-07 – 2014-07-09