Study of Linear Codes for Coset Coding with Highest Security

• Project/Area Number: 26289116
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Communication/Network engineering
• Research Institution: Nagoya University (2017); Tokyo Institute of Technology (2014-2016)
• Principal Investigator: Matsumoto Ryutaroh 名古屋大学, 工学研究科, 准教授 (10334517)
• Co-Investigator(Kenkyū-buntansha): 萩原 学 千葉大学, 大学院理学研究院, 准教授 (80415728)
• Research Collaborator: GEIL Olav ; RUANO Diego
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥10,790,000 (Direct Cost: ¥8,300,000、Indirect Cost: ¥2,490,000); Fiscal Year 2016: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000); Fiscal Year 2015: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2014: ¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
• Keywords: 秘密分散 / セキュアネットワーク符号化 / ネットワーク符号化 / 量子計算 / 量子情報 / 線形符号 / コセット符号化 / 量子秘密分散 / 情報理論 / 符号理論 / 情報セキュリティ / 相対一般化ハミング重み / ハミング重み / 一般相対化ハミング重み / 一般相対化ランク重み

Outline of Final Research Achievements

Coset coding is a representative method for securing messages in an information theoretic secure way, and it usually consists of a pair of linear codes. Coset coding with linear codes is useful for secret sharing and secure network coding. But it had been unknown which linear codes are suitable. In this project, we clarified which linear codes are suitable for secret sharing and secure network coding, respectively. Moreover, we also proposed explicit constructions of suitable linear codes. As another application, we also clarified the relationship between quantum secret sharing and suitable pairs of linear codes for it.

Research Products

• [Int'l Joint Research] オルボー大学(デンマーク)
• [Int'l Joint Research] オルボー大学/数学科(デンマーク)
• [Int'l Joint Research] Aalborg University/Technical University of Denmark(Denmark)
• [Journal Article] Two Gilbert-Varshamov-type existential bounds for asymmetric quantum error-correcting codes (2017)
  • Author(s): Matsumoto Ryutaroh
  • Journal Title: Quantum Information Processing Volume: 16 Issue: 12 Pages: 285-285
  • DOI: 10.1007/s11128-017-1748-y
  • Peer Reviewed
• [Journal Article] Unitary reconstruction of secret for stabilizer-based quantum secret sharing (2017)
  • Author(s): Matsumoto Ryutaroh
  • Journal Title: Quantum Information Processing Volume: 16 Issue: 8 Pages: 202-202
  • DOI: 10.1007/s11128-017-1656-1
  • Peer Reviewed / Open Access
• [Journal Article] Universal Secure Multiplex Network Coding With Dependent and Non-Uniform Messages (2017)
  • Author(s): Matsumoto Ryutaroh、Hayashi Masahito
  • Journal Title: IEEE Transactions on Information Theory Volume: 63 Issue: 6 Pages: 3773-3782
  • DOI: 10.1109/tit.2017.2694012
  • Peer Reviewed
• [Journal Article] On Asymptotically Good Ramp Secret Sharing Schemes (2017)
  • Author(s): Olav GEIL, Stefano MARTIN, Umberto MARTINEZ-PENAS, Ryutaroh MATSUMOTO, Diego RUANO
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E100.A Issue: 12 Pages: 2699-2708
  • DOI: 10.1587/transfun.E100.A.2699
  • NAID: 130006236514
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Quantum Stabilizer Codes Can Realize Access Structures Impossible by Classical Secret Sharing (2017)
  • Author(s): Ryutaroh Matsumoto
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E100.A Issue: 12 Pages: 2738-2739
  • DOI: 10.1587/transfun.E100.A.2738
  • NAID: 130006236509
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed
• [Journal Article] Quantum Optimal Multiple Assignment Scheme for Realizing General Access Structure of Secret Sharing (2017)
  • Author(s): Ryutaroh Matsumoto
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E100.A Issue: 2 Pages: 726-728
  • DOI: 10.1587/transfun.E100.A.726
  • NAID: 130005305986
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] A short proof for the multi-deletion error correction property of Helberg codes (2016)
  • Author(s): Manabu Hagiwara
  • Journal Title: IEICE Communications Express Volume: 5 Issue: 2 Pages: 49-51
  • DOI: 10.1587/comex.2015XBL0182
  • NAID: 130005125260
  • ISSN: 2187-0136
  • Peer Reviewed / Open Access / Acknowledgement Compliant
• [Journal Article] Relative Generalized Rank Weight of Linear Codes and Its Applications to Network Coding (2015)
  • Author(s): J. Kurihara, R. Matsumoto, and T. Uyematsu
  • Journal Title: IEEE Transactions on Information Theory Volume: 61 Issue: 7 Pages: 3912-3936
  • DOI: 10.1109/tit.2015.2429713
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Strong Security of the Strongly Multiplicative Ramp Secret Sharing Based on Algebraic Curves (2015)
  • Author(s): R. Matsumoto
  • Journal Title: IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences Volume: E98.A Issue: 7 Pages: 1576-1578
  • DOI: 10.1587/transfun.E98.A.1576
  • NAID: 130005085807
  • ISSN: 0916-8508, 1745-1337
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Optimal multiple assignment scheme for strongly secure ramp secret sharing schemes with general access structures (2015)
  • Author(s): R. Matsumoto
  • Journal Title: IEICE Communications Express Volume: 4 Issue: 11 Pages: 317-320
  • DOI: 10.1587/comex.4.317
  • NAID: 130005108345
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Quantum strongly secure ramp secret sharing (2015)
  • Author(s): P. Zhang and R. Matsumoto
  • Journal Title: Quantum Information Processing Volume: 14 Issue: 2 Pages: 715-729
  • DOI: 10.1007/s11128-014-0863-2
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Relative Generalized Hamming Weights of One-Point Algebraic Geometric Codes (2014)
  • Author(s): O.Geil, S. Martin, R. Matsumoto, D. Ruano, Y. Luo
  • Journal Title: IEEE Transactions on Information Theory Volume: 60 Issue: 10 Pages: 5938-5949
  • DOI: 10.1109/tit.2014.2345375
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Perfect codes for single balanced adjacent deletions (2017)
  • Author(s): Manabu Hagiwara
  • Organizer: 2017 IEEE International Symposium on Information Theory
  • Int'l Joint Research
• [Presentation] Multipermutation Ulam sphere analysis toward characterizing maximal code size (2017)
  • Author(s): Justin Kong, Manabu Hagiwara
  • Organizer: 2017 IEEE International Symposium on Information Theory
  • Int'l Joint Research
• [Presentation] バランス隣接挿入／削除誤りの性質 (2017)
  • Author(s): 萩原学
  • Organizer: 2017情報理論とその応用シンポジウム
• [Presentation] Binary Multipermutation Ulam Sphere Analysis (2017)
  • Author(s): Justin Kong, Manabu Hagiwara
  • Organizer: 2017情報理論とその応用シンポジウム
• [Presentation] Unifying notions of generalized weights for universal security on wire-tap networks (2016)
  • Author(s): Umberto Martinez-Penas, Ryutaroh Matsumoto
  • Organizer: 2016 54th Annual Allerton Conference on Communication, Control, and Computing
  • Place of Presentation: Monticello, Illinois, USA
  • Year and Date: 2016-09-27
  • Int'l Joint Research
• [Presentation] 順序のある代数系上の挿入削除誤り訂正符号 (2015)
  • Author(s): 萩原学
  • Organizer: 情報理論とその応用シンポジウム予稿集
  • Place of Presentation: 岡山県倉敷市
  • Year and Date: 2015-11-24
• [Presentation] On the Primitive Polynomial as the Characteristic Polynomial of a Symmetric Companion Matrix (2014)
  • Author(s): Manabu Hagiwara and Takaaki Sasaki
  • Organizer: International Symposium on Information Theory and its Applications
  • Place of Presentation: Melborne, Australia
  • Year and Date: 2014-10-26 – 2014-10-29
• [Presentation] New Asymptotic Metrics for Relative Generalized Hamming Weight (2014)
  • Author(s): Ryutaroh Matsumoto
  • Organizer: 2014 IEEE International Symposium on Information Theory
  • Place of Presentation: Hawaii, USA
  • Year and Date: 2014-06-29 – 2014-07-04
• [Remarks] Reliable and Secure Communication
  • URL: http://matcom.math.aau.dk/
• [Remarks] How secret is a secret?
  • URL: http://matcom.math.aau.dk/DFF2014-2017/