• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2006 Fiscal Year Final Research Report Summary

Research on the Applications of Short Vector Problem and Lattice Algorithms on Public Key

Research Project

Project/Area Number 16500009
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Fundamental theory of informatics
Research InstitutionThe University of Electro-Communications

Principal Investigator

OHTA Kazuo  The University of Electro-Communications, Department of Information and Communication Engineering, Professor, 電気通信学部, 教授 (80333491)

Co-Investigator(Kenkyū-buntansha) KIDA Masanari  The University of Electro-Communications, Department of Mathematics, Associate Professor, 電気通信学部, 助教授 (20272057)
KUNIHIRO Noboru  The University of Electro-Communications, Department of Information and Communication Engineering, Associate Professor, 電気通信学部, 助教授 (60345436)
KANAYAMA Naoki  University of Tsukuba, Faculty of System Information Engineering, Research Staff of Industry- Academia-Government Collaboration, Research Staff of Industry- Academia- Government Collaboration, システム情報工学研究科, 研究員 (70339696)
Project Period (FY) 2004 – 2006
KeywordsLattice / LLL algorithm / Coppersmith method / Knapsack's cryptosystem
Research Abstract

・We propose a new method for solving the shortest vector problem (SVP) by combing classical and quantum computations.
・We propose an algorithm of factoring any integer N which has k different prime factors with the same bit-length, when ( 1/(k+2) + ε/(k(k-1)) ) log(N) high-order bits of each prime factor are given, based on a new lattice-based algorithm of solving any k-variate polynomial equation over Z
・For RSA, May showed the deterministic polynomial time equivalence of computing d to factoring N (=pq). On the other hand, Takagi showed a variant of RSA such that the decryption algorithm is faster than the standard RSA, where N=p^rq while ed= 1 mod (pΓ/1)(qΓ1). We show that the deterministic polynomial time equivalence also holds in this variant.
・Many knapsack cryptosystems are vulnerable to low density attack. However, there are several proposed schemes which are strong to this attack. The density of these schemes becomes high by reducing the Hamming weight of a message. In Asiacrypt 2005, Nguyen and Stern introduced pseudo-density and showed that if the pseudo-density is low enough, the knapsack scheme can be broken by a single call of SVP oracle. However, the relation between the density and the pseudo-density was not clear. Our research's motivation is to investigate the relation between this two notions of density. Our research resulted a new notion of density, which naturally includes the previous two density. By this new notion of density we can show and describe the necessary condition for a knapsack scheme to be secure.

  • Research Products

    (14 results)

All 2007 2006 2005

All Journal Article (14 results)

  • [Journal Article] Deterministic Polynomial Time Equivalence between Factoring and Key-Recovery Attack on Takagi' s RSA.2007

    • Author(s)
      Noboru Kunihiro, Kaoru Kurosawa
    • Journal Title

      Public Key Cryptography-PKC 2007-Lecture Notes in Computer Science 4450

      Pages: 412-425

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] ナップザック暗号における密度の再考.2007

    • Author(s)
      國廣昇, 北原恵介, 太田和夫
    • Journal Title

      電子情報通信学会技術研究報(ISEC-Technical Report) 106-595

      Pages: 93-98

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Deterministic Polynomial Time Equivalence between Factoring and Key-Recovery Attack on Takagi's RSA.2007

    • Author(s)
      Noboru Kunihiro, Kaoru Kurosawa
    • Journal Title

      Public Key CryptographyPKC 2007-Lecture Notes in Computer Science Vol.4450

      Pages: 412-425

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] New Definition of Density on Knapsack Cryptosystems.2007

    • Author(s)
      Noboru Kunihiro, Keisuke Kitahara, Kazuo Ohta
    • Journal Title

      ISEC Technical Report

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Factorization of Square-Free Integers with High Bits Known2006

    • Author(s)
      Bagus Santoso, Noboru Kunihiro, Naoki Kanayama, Kazuo Ohta.
    • Journal Title

      Progress in Cryptology-VIETCRYPT 2006-Lecture Notes in Computer Science 4341

      Pages: 115-130

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Factorization of Square-Free Integers with High Bits Known2006

    • Author(s)
      Bagus Santoso, Noboru Kunihiro, Naoki Kanayama, Kazuo Ohta.
    • Journal Title

      Progress in Cryptology-VIETCRYPT 2006-Lecture Notes in Computer Science Vol.4341

      Pages: 115-130

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] 最小ベクトルの係数の存在範囲に関する考察.2005

    • Author(s)
      金山直樹, 木田雅成, 太田和夫, 國廣昇
    • Journal Title

      暗号と情報セキュリティシンポジウム (SCIS) 2005

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Coppersmithの方法を用いたP^rQ型合成数の素因数分解について(2)2005

    • Author(s)
      宮永望, 金山直樹, 小宮山雄木, 内山成憲
    • Journal Title

      暗号と情報セキュリティシンポジウム (SCIS) 2005

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] p^rq型合成数に対するVanstone-Zuccherato方式についての考察2005

    • Author(s)
      金山直樹, 内山成憲
    • Journal Title

      電子情報通信学会技術研究報(ISEC-Technical Report)

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] Quantum algorithms for solving exact shortest vector problem2005

    • Author(s)
      Naoki Kanayama, Masanari Kida, Noboru Kunihiro, Tetsuro Nishino, Kazuo Ohta, Seiya Okubo.
    • Journal Title

      Proceedings of ERATO Conference on Quantum Information Science (EQIS) 2005

    • Description
      「研究成果報告書概要(和文)」より
  • [Journal Article] A note on the existence region of the coefficients of the shortest vector2005

    • Author(s)
      Naoki Kanayama, Masanari Kida, Kazuo Ohta, Noboru Kunihiro.
    • Journal Title

      The 2005 Symposium on Cryptography and Information Security

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] On factoring integers of the form PrQ using Coppersmith's method.2005

    • Author(s)
      Nozomi Miyanaga, Naoki Kanayama, Yuki Komiyama, Shigenori Uchiyama
    • Journal Title

      The 2005 Symposium on Cryptography and Information Security

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] The Vanstone- Zuccherato schemes for modulus of the form prq.2005

    • Author(s)
      Naoki Kanayama, Shigenori Uchiyama
    • Journal Title

      SEC Technical Report

    • Description
      「研究成果報告書概要(欧文)」より
  • [Journal Article] Quantum algorithms for solving exact shortest vector problem.2005

    • Author(s)
      Naoki Kanayama, Masanari Kida, Noboru Kunihiro, Tetsuro Nishino, Kazuo Ohta, Seiya Okubo
    • Journal Title

      Proceedings of ERATO Conference on Quantum Information Science (EQIS)

    • Description
      「研究成果報告書概要(欧文)」より

URL: 

Published: 2008-05-27  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi