WO2022054130A1 - 暗号システム、方法及びプログラム - Google Patents

暗号システム、方法及びプログラム Download PDF

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Publication number
WO2022054130A1
WO2022054130A1 PCT/JP2020/033946 JP2020033946W WO2022054130A1 WO 2022054130 A1 WO2022054130 A1 WO 2022054130A1 JP 2020033946 W JP2020033946 W JP 2020033946W WO 2022054130 A1 WO2022054130 A1 WO 2022054130A1
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WO
WIPO (PCT)
Prior art keywords
function
secret
inner product
secret key
encryption
Prior art date
Legal status (The legal status 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 status listed.)
Ceased
Application number
PCT/JP2020/033946
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English (en)
French (fr)
Japanese (ja)
Inventor
潤一 富田
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
NTT Inc
Original Assignee
Nippon Telegraph and Telephone Corp
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 Nippon Telegraph and Telephone Corp filed Critical Nippon Telegraph and Telephone Corp
Priority to JP2022548270A priority Critical patent/JP7452676B2/ja
Priority to US18/041,103 priority patent/US20230291553A1/en
Priority to PCT/JP2020/033946 priority patent/WO2022054130A1/ja
Publication of WO2022054130A1 publication Critical patent/WO2022054130A1/ja
Anticipated expiration legal-status Critical
Ceased legal-status Critical Current

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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
    • H04L9/08—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
    • 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
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • 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
    • H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
    • 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)
    • H04L9/0822—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) using key encryption 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
    • H04L9/0819—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)
    • H04L9/0825—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) using asymmetric-key encryption or public key infrastructure [PKI], e.g. key signature or public key certificates
    • 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
    • H04L9/14—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using a plurality of keys or algorithms
    • 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
    • H04L9/3006—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy underlying computational problems or public-key parameters

Definitions

  • the present invention relates to cryptographic systems, methods and programs.
  • Multi-input function encryption is an encryption method that can decrypt only the function values that input those data from the ciphertext of multiple data, and at this time, the contents of the original data other than the function values are not leaked. It is one of the features. More specifically, the ciphertexts of n data x 1 , ..., X n are CT 1 , ..., CT n , the function having n arguments is f, and the secret corresponding to the function f.
  • the key is SK
  • CT 1 , ..., CT n is decrypted with the private key SK, only the function value f (x 1 , ..., x n ) is obtained, and x 1 , ... , X n No other information is leaked.
  • Non-Patent Document 1 a specific function called a function
  • Non-Patent Document 2 a specific function called a function
  • One embodiment of the present invention has been made in view of the above points, and an object thereof is to realize an efficient multi-input functional cryptography using a quadratic function.
  • the cryptographic system is encrypted and decrypted by functional cryptography using a quadratic function having n (where n is a predetermined integer of 2 or more) arguments.
  • a master secret key of a function secret inner product function type cipher composed of pairing operations and a master of a multi-input function secret inner product function type cipher that extends the function secret inner product function type cipher to multiple inputs.
  • the setup unit that generates the master secret key of the functional cipher using the private key, the master secret key of the function secret inner product function cipher, and the master secret key of the multi-input function secret inner product function cipher.
  • An encryption unit that generates n ciphers that encrypt n data using the master secret key of the functional cipher, data that expresses the quadratic function, and concealment of the multi-input function.
  • the key generation unit that generates the secret key for decrypting the n cryptographic statements, and the secret key generated by the key generation unit, the n pieces. It is characterized by having a decryption unit for decrypting the ciphertext of the above and generating the value of the quadratic function for the n data.
  • ⁇ Preparation ⁇ P is a prime number
  • Z is an integer ring
  • the quotient ring Z / pZ is expressed as Z p (however, Z is expressed in white letters to be exact.
  • Z in the text of the specification is similarly expressed. To be exact, it is written in white letters.)
  • the operation of randomly selecting the element from Z p is expressed as z ⁇ Z p . It should be noted that the fact that the output of a certain algorithm Alg is y is expressed as y ⁇ Alg.
  • iFE (iSetup, iEnc, iKeyGen, iDec)
  • miFE (miSetup, miEnc, miKeyGen). , MiDec).
  • the pairing constituting these function concealment inner product function type ciphers the one defined by using the known bilinear type group may be used, or the bilinear type group generated by the setup algorithm Setup described later may be used. You may use the one defined in.
  • multi-input function concealed inner product function type cipher miFE (miSetup, miEnc, miKeyGen, miDec) composed of pairing, for example, Reference 2 “P. Datta, T. Okamoto, and J. Tomida. Full -hiding (unbounded) multi-input inner product functional encryption from the k-linear assumption.
  • the multi-input function concealed inner product function type encryption or the like may be used.
  • the multi-input function type encryption is composed of four algorithms, that is, a setup algorithm Step, an encryption algorithm Enc, a key generation algorithm KeyGen, and a decryption algorithm Dec.
  • iMSK 1 is an iFE master secret key having 2 n + 3 + mn dimensions
  • iMSK 2 is an iFE master secret key having an input number n, which is one dimension
  • miMSK is a master secret key of miFE having an input number of n, which is two-dimensional.
  • x (x 1 , ..., X m ).
  • e i, j ⁇ Z p mn is a vector in which the (i, j) component is 1 and the other components are 0.
  • FIG. 1 is a diagram showing an example of the overall configuration of the encryption system 1 according to the present embodiment.
  • the encryption system 1 includes a setup device 10, an encryption device 20, a key generation device 30, and a decryption device 40. Further, each of these devices is communicably connected via the communication network N.
  • the setup device 10 is a computer or a computer system that executes the setup algorithm Setup.
  • the setup device 10 has a setup processing unit 101 that executes the setup algorithm Setup, and a storage unit 102 that stores various data used for executing the setup algorithm Setup, output results thereof, and the like.
  • the encryption device 20 is a computer or a computer system that executes the encryption algorithm Enc (MSK, i, x).
  • the encryption device 20 includes an encryption processing unit 201 that executes the encryption algorithm Enc (MSK, i, x), various data used for executing the encryption algorithm Enc (MSK, i, x), output results thereof, and the like. It has a storage unit 202 for storing the data.
  • the key generation device 30 is a computer or a computer system that executes the key generation algorithm KeyGen (MSK, c).
  • the key generation device 30 stores a key generation processing unit 301 that executes the key generation algorithm KeyGen (MSK, c), various data used for executing the key generation algorithm KeyGen (MSK, c), and output results thereof. It has a unit 302.
  • the decoding device 40 is a computer or a computer system that executes the decoding algorithm Dec (CT 1 , ..., CT n , SK).
  • the decoding device 40 is used to execute the decoding processing unit 401 that executes the decoding algorithm Dec (CT 1 , ..., CT n , SK) and the decoding algorithm Dec (CT 1 , ..., CT n , SK). It has a storage unit 402 for storing various data and output results thereof.
  • the overall configuration of the encryption system 1 shown in FIG. 1 is an example, and the encryption system 1 may have another configuration.
  • the setup device 10 and the key generation device 30 may be integrally configured.
  • FIG. 2 is a flowchart showing an example of the flow of the setup process according to the present embodiment.
  • the setup processing unit 101 of the setup device 10 executes the setup algorithm Setup to generate and output the master private key MSK (step S101).
  • the setup algorithm Setput for example, the security parameter 1 ⁇ or the like is input.
  • the setup processing unit 101 of the setup device 10 transmits the master private key MSK generated and output in the above step S101 to the encryption device 20 and the key generation device 30 (step S102).
  • the setup device 10 may transmit the master private key MSK to the encryption device 20 and the key generation device 30 by any secure method.
  • FIG. 3 is a flowchart showing an example of the flow of the encryption process according to the present embodiment.
  • the encryption processing unit 201 of the encryption device 20 executes the encryption algorithm Enc (MSK, i, x) to generate and output the ciphertext CT i corresponding to the input i of x ⁇ Z m (step S201). ). It is assumed that the data x to be encrypted and the master secret key MSK are stored in the storage unit 202 of the encryption device 20.
  • the encryption processing unit 201 of the encryption device 20 transmits the ciphertext CT i generated and output in the above step S201 to the decryption device 40 (step S202).
  • FIG. 4 is a flowchart showing an example of the flow of the key generation process according to the present embodiment.
  • the key generation processing unit 301 of the key generation device 30 executes the key generation algorithm KeyGen (MSK, c) to generate and output the private key SK corresponding to c (step S301). It is assumed that the data c representing the quadratic function and the master secret key MSK are stored in the storage unit 302 of the key generation device 30.
  • the key generation processing unit 301 of the key generation device 30 transmits the private key SK generated and output in the above step S301 to the decryption device 40 (step S302).
  • the key generation device 30 may transmit the private key SK to the decryption device 40 by any secure method.
  • FIG. 5 is a flowchart showing an example of the flow of the decoding process according to the present embodiment.
  • the decoding processing unit 401 of the decoding device 40 executes the decoding algorithm Dec (CT 1 , ..., CT n , SK) to generate and output the decoding result d (step S401).
  • the decoding processing unit 401 of the decoding device 40 stores the composite result d generated and output in the above step S401 in the storage unit 402 (step S402).
  • FIG. 6 is a diagram showing an example of the hardware configuration of the computer 500.
  • the computer 500 shown in FIG. 6 has an input device 501, a display device 502, an external I / F 503, a communication I / F 504, a processor 505, and a memory device 506 as hardware. Each of these hardware is communicably connected via bus 507.
  • the input device 501 is, for example, a keyboard, a mouse, a touch panel, or the like.
  • the display device 502 is, for example, a display or the like.
  • the computer 500 may not have, for example, at least one of the input device 501 and the display device 502.
  • the external I / F 503 is an interface with an external device such as a recording medium 503a.
  • Examples of the recording medium 503a include a flexible disk, a CD (Compact Disc), a DVD (Digital Versatile Disk), an SD memory card (Secure Digital memory card), a USB (Universal Serial Bus) memory card, and the like.
  • the communication I / F 504 is an interface for connecting the computer 500 to the communication network N.
  • the processor 505 is, for example, an arithmetic unit such as a CPU (Central Processing Unit).
  • the memory device 506 is, for example, various storage devices such as HDD (Hard Disk Drive), SSD (Solid State Drive), RAM (Random Access Memory), ROM (Read Only Memory), and flash memory.
  • the setup device 10, the encryption device 20, the key generation device 30, and the decryption device 40 according to the present embodiment can realize the above-mentioned various processes by having the hardware configuration of the computer 500 shown in FIG.
  • the hardware configuration shown in FIG. 6 is an example, and the computer 500 may have another hardware configuration.
  • the computer 500 may have a plurality of processors 505 or a plurality of memory devices 506.
  • the cryptosystem 1 is a function concealed internal product cryptographic iFE that can be configured by pairing and a multi-input function (that is, an extension to multiple inputs) of the multi-input function concealed internal product function.
  • Type encryption Encryption and decryption are realized by multi-input function type encryption of a quadratic function using miFE as a component. Since the functional concealment inner product function type cipher itself can be configured by a pairing operation that can be calculated at high speed, as a result, the multi-input function type cipher using these function concealed inner product function type ciphers as a component can also be calculated at high speed. Is. Therefore, the cryptosystem 1 according to the present embodiment can realize efficient multi-input functional cryptography using a quadratic function.
  • the encryption system 1 it is possible to calculate the quadratic function value at an extremely high speed as compared with the conventional technique without leaking the information of other original data from a plurality of ciphertexts.
  • the encryption system 1 according to the present embodiment in a situation where the user does not want to disclose the data, it is possible to calculate only the statistical values at high speed without leaking the information of the original data.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Theoretical Computer Science (AREA)
  • Computing Systems (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • General Engineering & Computer Science (AREA)
  • Algebra (AREA)
  • Computer Hardware Design (AREA)
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  • Mathematical Optimization (AREA)
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PCT/JP2020/033946 2020-09-08 2020-09-08 暗号システム、方法及びプログラム Ceased WO2022054130A1 (ja)

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JP2022548270A JP7452676B2 (ja) 2020-09-08 2020-09-08 暗号システム、方法及びプログラム
US18/041,103 US20230291553A1 (en) 2020-09-08 2020-09-08 Cypher system, method and program
PCT/JP2020/033946 WO2022054130A1 (ja) 2020-09-08 2020-09-08 暗号システム、方法及びプログラム

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JP7786593B2 (ja) 2022-08-01 2025-12-16 Ｎｔｔ株式会社 暗号システム、方法及びプログラム

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