WO2010123151A3 - ペアリング演算装置、ペアリング演算方法、及びぺアリング演算プログラムを記録した記録媒体 - Google Patents

ペアリング演算装置、ペアリング演算方法、及びぺアリング演算プログラムを記録した記録媒体 Download PDF

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Publication number
WO2010123151A3
WO2010123151A3 PCT/JP2010/057534 JP2010057534W WO2010123151A3 WO 2010123151 A3 WO2010123151 A3 WO 2010123151A3 JP 2010057534 W JP2010057534 W JP 2010057534W WO 2010123151 A3 WO2010123151 A3 WO 2010123151A3
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Prior art keywords
pairing
pairing arithmetic
calculates
calculating means
rational
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PCT/JP2010/057534
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English (en)
French (fr)
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WO2010123151A2 (ja
Inventor
野上保之
酒見由美
那須弘明
森川良孝
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国立大学法人岡山大学
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Application filed by 国立大学法人岡山大学 filed Critical 国立大学法人岡山大学
Priority to JP2011510399A priority Critical patent/JP5549018B2/ja
Priority to US13/264,897 priority patent/US8477934B2/en
Priority to EP10767199.2A priority patent/EP2423828B1/en
Priority to CN2010800172506A priority patent/CN102405469A/zh
Publication of WO2010123151A2 publication Critical patent/WO2010123151A2/ja
Publication of WO2010123151A3 publication Critical patent/WO2010123151A3/ja

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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
    • G06F17/10—Complex mathematical operations
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F7/00—Methods or arrangements for processing data by operating upon the order or content of the data handled
    • G06F7/60—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers
    • G06F7/72—Methods or arrangements for performing computations using a digital non-denominational number representation, i.e. number representation without radix; Computing devices using combinations of denominational and non-denominational quantity representations, e.g. using difunction pulse trains, STEELE computers, phase computers using residue arithmetic
    • G06F7/724—Finite field arithmetic
    • G06F7/725—Finite field arithmetic over elliptic curves
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09C—CIPHERING OR DECIPHERING APPARATUS FOR CRYPTOGRAPHIC OR OTHER PURPOSES INVOLVING THE NEED FOR SECRECY
    • G09C1/00—Apparatus or methods whereby a given sequence of signs, e.g. an intelligible text, is transformed into an unintelligible sequence of signs by transposing the signs or groups of signs or by replacing them by others according to a predetermined system
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
    • H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
    • H04L9/3073—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves involving pairings, e.g. identity based encryption [IBE], bilinear mappings or bilinear pairings, e.g. Weil or Tate pairing
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/32—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials
    • H04L9/3247—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures
    • H04L9/3252—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols including means for verifying the identity or authority of a user of the system or for message authentication, e.g. authorization, entity authentication, data integrity or data verification, non-repudiation, key authentication or verification of credentials involving digital signatures using DSA or related signature schemes, e.g. elliptic based signatures, ElGamal or Schnorr schemes

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  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Mathematical Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Computer Security & Cryptography (AREA)
  • Mathematical Physics (AREA)
  • Computational Mathematics (AREA)
  • Computing Systems (AREA)
  • Signal Processing (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Data Mining & Analysis (AREA)
  • Software Systems (AREA)
  • Databases & Information Systems (AREA)
  • Management, Administration, Business Operations System, And Electronic Commerce (AREA)
  • Developing Agents For Electrophotography (AREA)
  • Numerical Control (AREA)
  • Pinball Game Machines (AREA)
  • Navigation (AREA)
  • Joining Of Glass To Other Materials (AREA)

Abstract

S∈G1、Q∈G2、所定の整数変数をϰ、マルチペアリングに対するミラーのアルゴリズム(MMA)を用いて計算される有理関数をFとして、ペアリングe(S,Q)を演算するCPUを備えたぺアリング演算装置であって、位数rと、フロベニウス自己準同形写像ϕpのトレースtを、前記埋め込み次数kに応じて前記整数変数ϰを用いて特定しておき、前記CPUは、記整数変数ϰと、前記有理点Sと、前記有理点Qをそれぞれ所定のレジスタに入カする入力手段と、Fを演算する演算手段と、所定の有理点を通る直線の有理点Q(xQ,yQ)における値を演算する演算手段と、前記Fと前記値を用いてf'ϰ,s(Q)を演算する演算手段と、前記f'ϰ,s(Q)を用いて前記ペアリングe(S,Q)を[数83]として演算する演算手段とによって演算を行う。
PCT/JP2010/057534 2009-04-21 2010-04-21 ペアリング演算装置、ペアリング演算方法、及びぺアリング演算プログラムを記録した記録媒体 WO2010123151A2 (ja)

Priority Applications (4)

Application Number Priority Date Filing Date Title
JP2011510399A JP5549018B2 (ja) 2009-04-21 2010-04-21 ペアリング演算装置、ペアリング演算方法、及びペアリング演算プログラムを記録した記録媒体
US13/264,897 US8477934B2 (en) 2009-04-21 2010-04-21 Pairing computation device, pairing computation method and recording medium storing pairing computation program
EP10767199.2A EP2423828B1 (en) 2009-04-21 2010-04-21 Pairing arithmetic device, pairing arithmetic method and recording medium having pairing arithmetic program recorded thereon
CN2010800172506A CN102405469A (zh) 2009-04-21 2010-04-21 配对运算装置、配对运算方法以及记录有配对运算程序的记录介质

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
JP2009121398 2009-04-21
JP2009-121398 2009-04-21

Publications (2)

Publication Number Publication Date
WO2010123151A2 WO2010123151A2 (ja) 2010-10-28
WO2010123151A3 true WO2010123151A3 (ja) 2010-12-23

Family

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PCT/JP2010/057534 WO2010123151A2 (ja) 2009-04-21 2010-04-21 ペアリング演算装置、ペアリング演算方法、及びぺアリング演算プログラムを記録した記録媒体

Country Status (6)

Country Link
US (1) US8477934B2 (ja)
EP (1) EP2423828B1 (ja)
JP (1) JP5549018B2 (ja)
KR (1) KR101633148B1 (ja)
CN (1) CN102405469A (ja)
WO (1) WO2010123151A2 (ja)

Families Citing this family (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2423828B1 (en) 2009-04-21 2017-08-09 National University Corporation Okayama University Pairing arithmetic device, pairing arithmetic method and recording medium having pairing arithmetic program recorded thereon
US10148285B1 (en) 2012-07-25 2018-12-04 Erich Schmitt Abstraction and de-abstraction of a digital data stream
JP6057725B2 (ja) * 2013-01-15 2017-01-11 三菱電機株式会社 情報処理装置
US10795858B1 (en) 2014-02-18 2020-10-06 Erich Schmitt Universal abstraction and de-abstraction of a digital data stream
JP6610277B2 (ja) * 2016-01-15 2019-11-27 富士通株式会社 共有鍵生成プログラム、共有鍵生成方法および情報処理端末
CN113254985B (zh) * 2021-07-15 2021-12-21 北京信安世纪科技股份有限公司 数据加密方法、数据处理方法、数据解密方法及电子设备

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JP2005316267A (ja) 2004-04-30 2005-11-10 Hitachi Ltd 楕円曲線ペアリング演算装置
WO2007003230A1 (en) * 2005-06-30 2007-01-11 Freescale Semiconductor, Inc Encryption apparatus and method therefor
US8111826B2 (en) * 2006-01-11 2012-02-07 Mitsubishi Electric Corporation Apparatus for generating elliptic curve cryptographic parameter, apparatus for processing elliptic curve cryptograph, program for generating elliptic curve cryptographic parameter, and program for processing elliptic cyptograph
JP4649456B2 (ja) * 2007-09-26 2011-03-09 株式会社東芝 べき乗計算装置、べき乗計算方法及びプログラム
JP4189828B1 (ja) * 2007-10-30 2008-12-03 国立大学法人 岡山大学 ペアリング演算装置、ペアリング演算方法、及びペアリング演算プログラム
US8356181B2 (en) * 2007-11-15 2013-01-15 Intel Corporation Apparatus and method for a direct anonymous attestation scheme from short-group signatures
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EP2423828B1 (en) 2009-04-21 2017-08-09 National University Corporation Okayama University Pairing arithmetic device, pairing arithmetic method and recording medium having pairing arithmetic program recorded thereon

Non-Patent Citations (5)

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Title
LEE, E. ET AL.: "Efficient and Generalized Pairing Computation on Abelian Varieties", IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 55, no. 4, 16 March 2009 (2009-03-16), pages 1793 - 1803, XP011253787 *
NOGAMI, Y. ET AL.: "Integer Variable x-Based Ate Pairing", COMPUTER SCIENCE, vol. 5209, 2008, pages 178 - 191, XP019103346 *
SAKEMI, Y. ET AL.: "An Improvement of Twisted Ate Pairing with Barreto-Naehrig Curve by using Frobenius Mapping", THIRD INTERNATIONAL CONFERENCE ON CONVERGENCE AND HYBRID INFORMATION TECHNOLOGY, 18 November 2008 (2008-11-18), pages 406 - 410, XP008156677 *
VERCAUTEREN, F.: "Optimal Pairings", CRYPTOLOGY, 7 March 2008 (2008-03-07), pages 1 - 14, XP011286723 *
YUMI SAKEMI ET AL.: "Multi Pairing o Mochiita Twisted Ate Pairing no Kairyo", 2010 NEN SYMPOSIUM ON CRYPTOGRAPHY AND INFORMATION SECURITY KOEN RONBUNSHU, 19 January 2010 (2010-01-19), pages 1 - 6, XP008156685 *

Also Published As

Publication number Publication date
US20120045051A1 (en) 2012-02-23
CN102405469A (zh) 2012-04-04
JP5549018B2 (ja) 2014-07-16
WO2010123151A2 (ja) 2010-10-28
EP2423828A4 (en) 2015-03-11
EP2423828B1 (en) 2017-08-09
KR20120014254A (ko) 2012-02-16
US8477934B2 (en) 2013-07-02
JPWO2010123151A1 (ja) 2012-10-25
EP2423828A2 (en) 2012-02-29
KR101633148B1 (ko) 2016-06-23

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