WO2008127428A3 - Efficient non-interactive proof systems for bilinear groups - Google Patents

Efficient non-interactive proof systems for bilinear groups Download PDF

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Publication number
WO2008127428A3
WO2008127428A3 PCT/US2007/085018 US2007085018W WO2008127428A3 WO 2008127428 A3 WO2008127428 A3 WO 2008127428A3 US 2007085018 W US2007085018 W US 2007085018W WO 2008127428 A3 WO2008127428 A3 WO 2008127428A3
Authority
WO
WIPO (PCT)
Prior art keywords
interactive
proofs
groups
efficient non
interactive proof
Prior art date
Application number
PCT/US2007/085018
Other languages
French (fr)
Other versions
WO2008127428A2 (en
Inventor
Jens Groth
Amit Sahai
Original Assignee
Univ California
Jens Groth
Amit Sahai
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Univ California, Jens Groth, Amit Sahai filed Critical Univ California
Publication of WO2008127428A2 publication Critical patent/WO2008127428A2/en
Publication of WO2008127428A3 publication Critical patent/WO2008127428A3/en

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    • 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
    • H04L9/008—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols involving homomorphic encryption
    • 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
    • H04L9/0819—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s)
    • H04L9/083—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s) involving central third party, e.g. key distribution center [KDC] or trusted third party [TTP]
    • H04L9/0833—Key transport or distribution, i.e. key establishment techniques where one party creates or otherwise obtains a secret value, and securely transfers it to the other(s) involving central third party, e.g. key distribution center [KDC] or trusted third party [TTP] involving conference or group key
    • 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
    • H04L9/0844—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 with user authentication or key authentication, e.g. ElGamal, MTI, MQV-Menezes-Qu-Vanstone protocol or Diffie-Hellman protocols using implicitly-certified keys
    • 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
    • H04L9/3218—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 using proof of knowledge, e.g. Fiat-Shamir, GQ, Schnorr, ornon-interactive zero-knowledge proofs
    • 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
    • H04L2209/08—Randomization, e.g. dummy operations or using noise
    • 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
    • H04L2209/16—Obfuscation or hiding, e.g. involving white box
    • 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
    • H04L2209/42—Anonymization, e.g. involving pseudonyms

Abstract

An apparatus and method for constructing efficient non-interactive zero-knowledge proofs and non-interactive witness-indistinguishable proofs that work directly for groups with a bilinear map is described. Groups with bilinear maps have enjoyed tremendous success in the field of cryptography in recent years and have been used to construct a plethora of protocols. This disclosure provides n on -interactive witness-indistinguishable proofs and non-interactive zero-knowledge proofs that can be used in connection with these protocols.
PCT/US2007/085018 2006-11-17 2007-11-16 Efficient non-interactive proof systems for bilinear groups WO2008127428A2 (en)

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US85987506P 2006-11-17 2006-11-17
US60/859,875 2006-11-17

Publications (2)

Publication Number Publication Date
WO2008127428A2 WO2008127428A2 (en) 2008-10-23
WO2008127428A3 true WO2008127428A3 (en) 2008-12-24

Family

ID=39864548

Family Applications (1)

Application Number Title Priority Date Filing Date
PCT/US2007/085018 WO2008127428A2 (en) 2006-11-17 2007-11-16 Efficient non-interactive proof systems for bilinear groups

Country Status (1)

Country Link
WO (1) WO2008127428A2 (en)

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JP5612494B2 (en) * 2011-01-21 2014-10-22 日本電信電話株式会社 Timed cryptographic system, timed cryptographic method, apparatus, and program using function encryption
JP6041864B2 (en) * 2011-04-29 2016-12-14 インターナショナル・ビジネス・マシーンズ・コーポレーションＩｎｔｅｒｎａｔｉｏｎａｌ Ｂｕｓｉｎｅｓｓ Ｍａｃｈｉｎｅｓ Ｃｏｒｐｏｒａｔｉｏｎ Method, computer program, and apparatus for data encryption
JP5863683B2 (en) * 2013-02-04 2016-02-17 日本電信電話株式会社 Commitment system, common reference information generation device, commit generation device, commit reception device, commitment method, and program
US11282139B1 (en) 2013-06-28 2022-03-22 Gemini Ip, Llc Systems, methods, and program products for verifying digital assets held in a custodial digital asset wallet
US10068228B1 (en) 2013-06-28 2018-09-04 Winklevoss Ip, Llc Systems and methods for storing digital math-based assets using a secure portal
US10269009B1 (en) 2013-06-28 2019-04-23 Winklevoss Ip, Llc Systems, methods, and program products for a digital math-based asset exchange
US9892460B1 (en) 2013-06-28 2018-02-13 Winklevoss Ip, Llc Systems, methods, and program products for operating exchange traded products holding digital math-based assets
US10354325B1 (en) 2013-06-28 2019-07-16 Winklevoss Ip, Llc Computer-generated graphical user interface
JP6225097B2 (en) * 2014-11-06 2017-11-01 日本電信電話株式会社 Signature / Verification System, Signature Device, Verification Device, Signature / Verification Method, Program
US9853977B1 (en) 2015-01-26 2017-12-26 Winklevoss Ip, Llc System, method, and program product for processing secure transactions within a cloud computing system
US10915891B1 (en) 2015-03-16 2021-02-09 Winklevoss Ip, Llc Autonomous devices
US10158480B1 (en) 2015-03-16 2018-12-18 Winklevoss Ip, Llc Autonomous devices
EP3278287A4 (en) 2015-03-31 2018-08-22 Nasdaq, Inc. Systems and methods of blockchain transaction recordation
US10097356B2 (en) 2015-07-02 2018-10-09 Nasdaq, Inc. Systems and methods of secure provenance for distributed transaction databases
US10108812B2 (en) 2016-01-28 2018-10-23 Nasdaq, Inc. Systems and methods for securing and disseminating time sensitive information using a blockchain
SG11201806404SA (en) 2016-02-04 2018-08-30 Nasdaq Tech Ab Systems and methods for storing and sharing transactional data using distributed computer systems
US10426424B2 (en) 2017-11-21 2019-10-01 General Electric Company System and method for generating and performing imaging protocol simulations
EP3711255A1 (en) * 2017-11-23 2020-09-23 Huawei Technologies Co., Ltd. Device, system and method for secure data communication
US11475442B1 (en) 2018-02-12 2022-10-18 Gemini Ip, Llc System, method and program product for modifying a supply of stable value digital asset tokens
US11200569B1 (en) 2018-02-12 2021-12-14 Winklevoss Ip, Llc System, method and program product for making payments using fiat-backed digital assets
US11139955B1 (en) 2018-02-12 2021-10-05 Winklevoss Ip, Llc Systems, methods, and program products for loaning digital assets and for depositing, holding and/or distributing collateral as a token in the form of digital assets on an underlying blockchain
US11308487B1 (en) 2018-02-12 2022-04-19 Gemini Ip, Llc System, method and program product for obtaining digital assets
US11909860B1 (en) 2018-02-12 2024-02-20 Gemini Ip, Llc Systems, methods, and program products for loaning digital assets and for depositing, holding and/or distributing collateral as a token in the form of digital assets on an underlying blockchain
US10373129B1 (en) 2018-03-05 2019-08-06 Winklevoss Ip, Llc System, method and program product for generating and utilizing stable value digital assets
US11522700B1 (en) 2018-02-12 2022-12-06 Gemini Ip, Llc Systems, methods, and program products for depositing, holding and/or distributing collateral as a token in the form of digital assets on an underlying blockchain
US10373158B1 (en) 2018-02-12 2019-08-06 Winklevoss Ip, Llc System, method and program product for modifying a supply of stable value digital asset tokens
US10540654B1 (en) 2018-02-12 2020-01-21 Winklevoss Ip, Llc System, method and program product for generating and utilizing stable value digital assets
US10929842B1 (en) 2018-03-05 2021-02-23 Winklevoss Ip, Llc System, method and program product for depositing and withdrawing stable value digital assets in exchange for fiat
US10438290B1 (en) 2018-03-05 2019-10-08 Winklevoss Ip, Llc System, method and program product for generating and utilizing stable value digital assets
US11334883B1 (en) 2018-03-05 2022-05-17 Gemini Ip, Llc Systems, methods, and program products for modifying the supply, depositing, holding and/or distributing collateral as a stable value token in the form of digital assets
US11501370B1 (en) 2019-06-17 2022-11-15 Gemini Ip, Llc Systems, methods, and program products for non-custodial trading of digital assets on a digital asset exchange
DE102021006430B4 (en) 2021-12-31 2023-12-07 Kcrypt Lab UG (haftungsbeschränkt) Method for generating distributed one-way trapdoor permutations via additive sharing without a trusted dealer

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US20060129545A1 (en) * 2004-12-09 2006-06-15 Philippe Golle System and method for performing a conjunctive keyword search over encrypted data

Patent Citations (2)

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Publication number Priority date Publication date Assignee Title
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US20060129545A1 (en) * 2004-12-09 2006-06-15 Philippe Golle System and method for performing a conjunctive keyword search over encrypted data

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