JP7221872B2 - 楕円曲線の同種に基づくキー合意プロトコル - Google Patents

楕円曲線の同種に基づくキー合意プロトコル Download PDF

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JP7221872B2
JP7221872B2 JP2019546160A JP2019546160A JP7221872B2 JP 7221872 B2 JP7221872 B2 JP 7221872B2 JP 2019546160 A JP2019546160 A JP 2019546160A JP 2019546160 A JP2019546160 A JP 2019546160A JP 7221872 B2 JP7221872 B2 JP 7221872B2
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elliptic curve
point
public
key
private
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JP2020509695A5 (enExample
JP2020509695A (ja
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モーション オスカー ガルシア
サウヴィク バタチャリア
ルドヴィクス マリヌス ジェラルダス マリア トルフィツェン
ロナルド リートマン
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Koninklijke Philips NV
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Koninklijke Philips NV
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    • G—PHYSICS
    • G06—COMPUTING OR CALCULATING; 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
    • 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
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0643—Hash functions, e.g. MD5, SHA, HMAC or f9 MAC
    • 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
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0816—Key establishment, i.e. cryptographic processes or cryptographic protocols whereby a shared secret becomes available to two or more parties, for subsequent use
    • H04L9/0838—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these
    • H04L9/0841—Key agreement, i.e. key establishment technique in which a shared key is derived by parties as a function of information contributed by, or associated with, each of these involving Diffie-Hellman or related key agreement protocols
    • 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
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0866—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving user or device identifiers, e.g. serial number, physical or biometrical information, DNA, hand-signature or measurable physical characteristics
    • 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
    • H04L9/3257—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 blind signatures
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/60—Digital content management, e.g. content distribution
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L2209/00—Additional information or applications relating to cryptographic mechanisms or cryptographic arrangements for secret or secure communication H04L9/00
    • H04L2209/80—Wireless

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Theoretical Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Mathematical Optimization (AREA)
  • Mathematical Analysis (AREA)
  • Pure & Applied Mathematics (AREA)
  • Mathematical Physics (AREA)
  • Computing Systems (AREA)
  • Computational Mathematics (AREA)
  • Algebra (AREA)
  • Power Engineering (AREA)
  • General Engineering & Computer Science (AREA)
  • Storage Device Security (AREA)
  • Mobile Radio Communication Systems (AREA)
JP2019546160A 2017-02-28 2018-02-12 楕円曲線の同種に基づくキー合意プロトコル Active JP7221872B2 (ja)

Applications Claiming Priority (3)

Application Number Priority Date Filing Date Title
EP17158508.6 2017-02-28
EP17158508.6A EP3367608A1 (en) 2017-02-28 2017-02-28 Elliptic curve isogeny based key agreement protocol
PCT/EP2018/053389 WO2018158065A1 (en) 2017-02-28 2018-02-12 Elliptic curve isogeny based key agreement protocol

Publications (3)

Publication Number Publication Date
JP2020509695A JP2020509695A (ja) 2020-03-26
JP2020509695A5 JP2020509695A5 (enExample) 2021-03-25
JP7221872B2 true JP7221872B2 (ja) 2023-02-14

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JP2019546160A Active JP7221872B2 (ja) 2017-02-28 2018-02-12 楕円曲線の同種に基づくキー合意プロトコル

Country Status (6)

Country Link
US (2) US11728988B2 (enExample)
EP (2) EP3367608A1 (enExample)
JP (1) JP7221872B2 (enExample)
CN (1) CN110383754B (enExample)
RU (1) RU2728519C1 (enExample)
WO (1) WO2018158065A1 (enExample)

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US12056549B1 (en) 2015-06-28 2024-08-06 Lcip Jv Method and apparatus for activating a remote device
US11005656B2 (en) * 2018-12-07 2021-05-11 Arris Enterprises Llc Embedding information in elliptic curve base point
US11032074B2 (en) * 2019-02-11 2021-06-08 Pqsecure Technologies, Llc Cryptosystem and method using isogeny-based computations to reduce a memory footprint
US11438152B2 (en) 2020-01-31 2022-09-06 Visa International Service Association Distributed symmetric encryption
US11431487B2 (en) 2020-04-28 2022-08-30 Visa International Service Association Adaptive attack resistant distributed symmetric encryption
EP4144042B1 (en) * 2020-04-28 2025-01-29 Visa International Service Association Adaptive attack resistant distributed symmetric encryption
CN111935163B (zh) * 2020-08-14 2022-08-09 支付宝(杭州)信息技术有限公司 保护隐私的数据联合处理方法及装置
DE112020007408B4 (de) * 2020-09-23 2024-12-05 Mitsubishi Electric Corporation Kryptographisches system, verschlüsselungseinrichtung, entschlüsselungseinrichtung und schlüsselerzeugungseinrichtung
WO2022146437A1 (en) * 2020-12-30 2022-07-07 Pqsecure Technologies, Llc High-performance systems to validate isogeny-based cryptography keys
US11757630B2 (en) * 2021-04-27 2023-09-12 Cisco Technology, Inc. Set up and distribution of post-quantum secure pre-shared keys using extendible authentication protocol
US20240184699A1 (en) * 2021-05-25 2024-06-06 Pqsecure Technologies, Llc An efficient and scalable architecture and method for isogeny-based cryptosystems
US11683171B2 (en) * 2021-06-03 2023-06-20 International Business Machines Corporation Acceleration of elliptic curve-based isogeny cryptosystems
US11483151B1 (en) 2021-07-16 2022-10-25 Pqsecure Technologies, Llc Method and system for computing large-degree isogenies with an odd degree
US12242847B2 (en) 2021-08-13 2025-03-04 Pqsecure Technologies, Llc Fast multiple core method and system for chaining isogeny computations
CN113992325B (zh) * 2021-10-09 2023-07-11 深圳前海微众银行股份有限公司 一种隐私数据共享方法及装置
EP4195581A1 (en) * 2021-12-08 2023-06-14 Nagravision Sàrl Improvements in and relating to cryptography
CN117834138B (zh) * 2024-03-04 2024-05-24 北卡科技有限公司 一种适用于即时通信的密钥协商方法、系统、设备及介质

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JP2003208096A (ja) 2001-10-25 2003-07-25 Matsushita Electric Ind Co Ltd 楕円曲線変換装置、楕円曲線変換方法、楕円曲線利用装置及び楕円曲線生成装置
JP2005141200A (ja) 2003-11-03 2005-06-02 Microsoft Corp 暗号システムの設計におけるアイソジャニの使用
JP2006221161A (ja) 2005-02-08 2006-08-24 Microsoft Corp Ｃａｒｔｉｅｒ対形成の暗号化適用

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US7639799B2 (en) * 2004-12-14 2009-12-29 Microsoft Corporation Cryptographically processing data based on a Cassels-Tate pairing
US7623655B2 (en) 2005-03-14 2009-11-24 Microsoft Corporation Computing modular polynomials modulo large primes
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US8250367B2 (en) 2008-09-30 2012-08-21 Microsoft Corporation Cryptographic applications of efficiently evaluating large degree isogenies
WO2017103226A1 (en) 2015-12-17 2017-06-22 Koninklijke Philips N.V. Improved system for key sharing
US10637656B2 (en) * 2017-11-28 2020-04-28 Blackberry Limited Method and system for key agreement utilizing semigroups
US10116443B1 (en) * 2018-02-02 2018-10-30 ISARA Corporation Pairing verification in supersingular isogeny-based cryptographic protocols

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JP2003208096A (ja) 2001-10-25 2003-07-25 Matsushita Electric Ind Co Ltd 楕円曲線変換装置、楕円曲線変換方法、楕円曲線利用装置及び楕円曲線生成装置
JP2005141200A (ja) 2003-11-03 2005-06-02 Microsoft Corp 暗号システムの設計におけるアイソジャニの使用
JP2006221161A (ja) 2005-02-08 2006-08-24 Microsoft Corp Ｃａｒｔｉｅｒ対形成の暗号化適用

Non-Patent Citations (1)

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KOSHIBA, Takeshi and TAKASHIMA, Katsuyuki，Pairing Cryptography Meets Isogeny: A New Framework of Isogenous Pairing Groups，Cryptology ePrint Archive，International Association for Cryptologic Research，2016年12月，Report 2016/1138, Ver. 20161214:185829，pp.1-36，［2022年1月27日検索］，インターネット，＜URL: https://eprint.iacr.org/2016/1138＞

Also Published As

Publication number Publication date
CN110383754A (zh) 2019-10-25
US20230336346A1 (en) 2023-10-19
EP3367608A1 (en) 2018-08-29
WO2018158065A1 (en) 2018-09-07
US11728988B2 (en) 2023-08-15
JP2020509695A (ja) 2020-03-26
EP3590224B1 (en) 2020-07-01
US20200014534A1 (en) 2020-01-09
EP3590224A1 (en) 2020-01-08
CN110383754B (zh) 2023-04-04
RU2728519C1 (ru) 2020-07-30

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