WO2017063114A1 - Procédé d'établissement d'algorithme cryptographique à clé publique sécurisée résistant aux attaques - Google Patents

Procédé d'établissement d'algorithme cryptographique à clé publique sécurisée résistant aux attaques Download PDF

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Publication number
WO2017063114A1
WO2017063114A1 PCT/CN2015/091710 CN2015091710W WO2017063114A1 WO 2017063114 A1 WO2017063114 A1 WO 2017063114A1 CN 2015091710 W CN2015091710 W CN 2015091710W WO 2017063114 A1 WO2017063114 A1 WO 2017063114A1
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WIPO (PCT)
Prior art keywords
party
agreement
protocol
calculates
selects
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PCT/CN2015/091710
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English (en)
Chinese (zh)
Inventor
王晓峰
王威鉴
Original Assignee
王晓峰
王威鉴
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Application filed by 王晓峰, 王威鉴 filed Critical 王晓峰
Priority to CN201580000535.1A priority Critical patent/CN106664199A/zh
Priority to PCT/CN2015/091710 priority patent/WO2017063114A1/fr
Publication of WO2017063114A1 publication Critical patent/WO2017063114A1/fr

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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
    • H04L9/32—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
    • 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
    • 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
    • H04L63/14—Network architectures or network communication protocols for network security for detecting or protecting against malicious traffic
    • H04L63/1441—Countermeasures against malicious traffic
    • 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

Definitions

  • the present invention relates to the field of information security, and in particular to a cryptographic technique for establishing public key cryptography against various known attacks including quantum computing attacks.
  • the object of the present invention is Through the innovative introduction of double-lock technology to establish a public key cipher to resist various attacks.
  • the object of the present invention is achieved by a method for establishing an anti-attack security public key cipher, comprising a method for generating a shared key, and a method for generating a shared key is also referred to as generating a shared key protocol, and the generating is shared.
  • the method of the key includes the following steps:
  • Both parties of the agreement select an element g in G, wherein the first party of the agreement selects four elements b 1 , b 2 , b 3 , b 4 ⁇ A as the private key, and the second party of the agreement selects four elements d 1 . d 2 , d 3 , d 4 ⁇ B as a private key;
  • the first party of the agreement selects four elements a 1 , a 2 , a 3 , a 4 ⁇ A, and calculates
  • the second party of the agreement selects two elements c 3 , c 4 ⁇ B, and calculates
  • a method for encrypting and decrypting information data is further included, and the method for encrypting and decrypting the information data includes the following steps;
  • (21) Define the encoded plaintext information to be encrypted as m ⁇ 0,1 ⁇ k , that is, a 0-1 string of length k; and define ⁇ : G ⁇ 0,1 ⁇ k is a group G to The plaintext space ⁇ 0,1 ⁇ k anti-collision Hash function, the first party of the protocol selects (G, A, B, g, ⁇ ) as its public key;
  • a method for digital signature is further included, and the method for digital signature includes the following steps:
  • G ⁇ 0,1 ⁇ k is an anti-collision Hash function, and the first party of the protocol selects (G, A, B, g, ⁇ ) is its public key;
  • the method further includes the method of identity authentication, where the first party of the protocol is a witness, and the second party of the protocol is a verifier; the method for authenticating the identity includes the following steps:
  • the first party of the agreement selects an anti-collision Hash function ⁇ : G ⁇ 0,1 ⁇ k , and the first party of the protocol selects (G, A, B, g, ⁇ ) as its public key;
  • a method for establishing an anti-attack security public key cryptography includes a method for generating a shared key, and another method for generating a shared key includes the following steps:
  • Both parties of the agreement select an element g in G, where the first party of the agreement selects four elements b 10 , b 30 ⁇ A and d 20 , d 40 ⁇ B as the private key, and the second party of the agreement selects four elements b 20 , b 40 ⁇ A and d 10 , d 30 ⁇ B as private keys;
  • the first party of the agreement selects four elements a 10 , a 30 ⁇ A and c 20 , c 40 ⁇ B, to calculate
  • the second party of the agreement selects two elements a 40 ⁇ A and c 30 ⁇ B, to calculate
  • a method for encrypting and decrypting information data is further included, and the method for encrypting and decrypting the information data includes the following steps;
  • (21.1) Define the encoded plaintext information that needs to be encrypted as m ⁇ 0,1 ⁇ k , that is, a 0-1 string of length k; and define ⁇ : G ⁇ 0,1 ⁇ k is a group G to The plaintext space ⁇ 0,1 ⁇ k anti-collision Hash function, the first party of the protocol selects (G, A, B, g, ⁇ ) as its public key;
  • a method for digital signature is further included, and the method for digital signature includes the following steps:
  • G ⁇ 0,1 ⁇ k is an anti-collision Hash function, and the first party of the protocol selects (G, A, B, g, ⁇ ) is its public key;
  • a method for identity authentication is further included, where the first party of the protocol is a witness, and the second party of the protocol is a certifier; the method for identity authentication includes the following steps;
  • the first party of the agreement selects an anti-collision Hash function ⁇ : G ⁇ 0,1 ⁇ k , and the first party of the protocol selects (G, A, B, g, ⁇ ) as its public key;
  • the infinite non-exchange group G is preferably a unitary group, and a generator element system of the Mihailova subgroup having an unsolvable subgroup member problem of the group B n (n ⁇ 12) is given, and the group B n is given ( n ⁇ 12)
  • the private key of both protocols is generated by the generator of the Mihailova subgroup.
  • the infinite non-exchange group G takes a group B n with an index of n ⁇ 12 and is represented by the group defined as follows:
  • the elements of the group are represented by words in the set ⁇ 1 , ⁇ 2 , ..., ⁇ n-1 ⁇ representing the unique formal form of the element.
  • the group B n contains the following two subgroups:
  • a braid group B n LB n braids left and right respectively braids RB n
  • subgroups generated by ⁇ 1 , ⁇ 2 , . . . , ⁇ m-1 and ⁇ m+1 , ⁇ m+2 , . . . , ⁇ n-1 , respectively, and for any a ⁇ LB n and any b ⁇ RB n , with ab ba, the subgroup A of the G is taken as LB n , and the subgroup B of G is taken as RB n ;
  • LB n and RB n respectively contain a subgroup that is isomorphic to F 2 ⁇ F 2 , that is, a subgroup of two products of two free ranks of rank 2:
  • LA ⁇ m-5 2 , ⁇ m-4 2 , ⁇ m-2 2 , ⁇ m-1 2 > ⁇ LB n
  • RA ⁇ m+1 2 , ⁇ m+2 2 , ⁇ m+4 2 , ⁇ m+5 2 > ⁇ RB n ;
  • the invention performs bilateral double insurance technology by selecting four elements as the respective private keys on both sides of the agreement, and proves that all possible attacks can be uncalculated, that is, the public key cryptography method of the present invention is resistant to quantum computing. All known attacks of the attack. Compared with the prior art, it has the following advantages:
  • G must also meet the following conditions:
  • G is at least exponential growth, that is, the number of elements in which the word length in G is a positive integer n is entangled in an exponential function about n;
  • the elements of the group are represented by words in the set ⁇ 1 , ⁇ 2 , ..., ⁇ n - 1 ⁇ representing the unique formal form of the element.
  • the group B n contains the following two subgroups:
  • a braid group B n LB n braids left and right respectively braids RB n
  • LB n and RB n respectively contain a subgroup with F 2 ⁇ F 2 , that is, a direct product isomorphism of two free groups of rank 2.
  • LA ⁇ m-5 2 , ⁇ m-4 2 , ⁇ m-2 2 , ⁇ m-1 2 > ⁇ LB n
  • RA ⁇ m+1 2 , ⁇ m+2 2 , ⁇ m+4 2 , ⁇ m+5 2 > ⁇ RB n
  • the parties to the agreement are Alice and Bob, respectively.
  • step 4) of the above protocol since d 1 , d 2 ⁇ RB n , a 1 , a 2 , b 3 , b 4 ⁇ LB n , d 1 -1 , d 2 -1 and b 3 , respectively.
  • the a 1 and b 4 , a 2 multiplications are interchangeable, so the last equation in this step is obtained.
  • the last equation in step 5) is obtained.
  • B n ⁇ 0,1 ⁇ k is a group B n to the plaintext space ⁇ 0, 1 ⁇ k anti-collision Hash function.
  • Alice's public key is (B n , LB n , RB n , g, ⁇ ), and a 1 , a 2 , a 3 , a 4 , b 1 , b 2 , b 3 , b 4 ⁇ LB n are selected .
  • the keys are b 1 , b 2 , b 3 , b 4 .
  • Bob selects c 1 , c 2 , c 3 , c 4 , d 1 , d 2 , d 3 , d 4 ⁇ RB n , and uses d 1 , d 2 , d 3 , d 4 as the private key.
  • B n ⁇ 0,1 ⁇ k is an anti-collision hash function.
  • Alice's public key is (B n , LB n , RB n , g, ⁇ ), and a 1 , a 2 , a 3 , a 4 , b 1 , b 2 , b 3 , b 4 ⁇ LB n are selected .
  • the keys are b 1 , b 2 , b 3 , b 4 .
  • Alice's public key is (B n , LB n , RB n , g, x, ⁇ ), and the private key is b 1 , b 2 , b 3 , b 4 .
  • the parties to the agreement are Alice and Bob, respectively.
  • Alice and Bob jointly select an element g in B n , Alice selects four elements b 1 , b 3 ⁇ LB n and d 2 , d 4 ⁇ RB n as a private key, and Bob selects four elements b 2 , b 4 ⁇ LB n and d 1 , d 3 ⁇ RB n as private keys;
  • step 4.1) of the above protocol since c 1 , c 2 , c 3 , c 4 , d 1 , d 2 ⁇ RB n , a 1 , a 2 , a 3 , a 4 , b 1 , b 2 ⁇ LB n , so d 1 -1 , d 2 -1 are interchangeable with a 1 , a 2 , a 3 , a 4 , b 1 , b 2 respectively, and b 1 -1 , b 2 -1 and c 1 respectively , c 2 , c 3 , c 4 , d 1 , d 2 multiplication can be exchanged so that the last equation in this step is obtained. In the same way, the last equation in step 5.1) is obtained.
  • Subgroup membership problem or generalized wordproblem (abbreviated as GWP): a subgroup H of a given group G whose generated metaset is X, and determines whether any element g in G can be represented by a word on X, ie It is determined whether g is an element in H.
  • GWP generalized wordproblem
  • GDSP extended decomposition search problem
  • the non-commutative group G taken infinite index n ⁇ 12 braid group B n, A and B taken subgroup B n LB n and RB n, while the private key b 1, b 2, b 3 , b 4 , and d 1 , d 2 , d 3 , d 4 are selected in the Mihailova subgroup M LA (H) of LB n and the Mihailova subgroup M RA (H) of RB n respectively, in the above Eve
  • she solved h 1 , h 2 , h 3 , h 4 , h 5 , h 6 ⁇ LB n , and g 1 , g 2 , g 3 , g 4 , g 5 , g 6 ⁇ by solving the GDSP problem.
  • the private keys b 1 , b 2 , b 3 , b 4 and d 1 , d 2 , d 3 , d 4 are selected from the Mihailova subgroups M LA (H) and M RA (H) of the ⁇ group B n , respectively.
  • the private key in the protocol is not attackable.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Computing Systems (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • General Engineering & Computer Science (AREA)
  • Storage Device Security (AREA)
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Abstract

La présente invention se rapporte au domaine de la sécurité de l'information. L'invention concerne un procédé permettant d'établir un algorithme cryptographique à clé publique sécurisée résistant aux attaques comprenant un procédé de génération d'une clé partagée. Le procédé de génération d'une clé secrète partagée comprend les étapes suivantes : (11) établir un groupe non abélien infini G; (12) choisir, par chacune de deux entités d'un protocole, quatre éléments dans G en tant que clés privées; (13) calculer y par une seconde entité du protocole, et envoyer y à une première entité du protocole; (14) calculer x et z par la première entité du protocole, et envoyer (x, z) à la seconde entité du protocole; (15) calculer w et v par la seconde entité du protocole, et envoyer (w, v) à la première entité du protocole; (16) calculer u par la première entité du protocole, et envoyer u à la seconde entité du protocole; et (17) calculer K A par la première entité du protocole, et calculer K B par la seconde entité du protocole, de façon à obtenir une clé partagée K = K A = K B . La sécurité du procédé ci-dessus pour établir un algorithme cryptographique à clé publique a été démontrée théoriquement de manière adéquate. L'introduction d'une double technique de verrouillage permet au procédé d'établissement d'algorithme cryptographique à clé publique d'empêcher toutes les attaques connues, y compris une attaque par calcul quantique. De plus, étant donné qu'une sélection d'une clé privée est indéchiffrable, le procédé présente un niveau de sécurité élevé.
PCT/CN2015/091710 2015-10-12 2015-10-12 Procédé d'établissement d'algorithme cryptographique à clé publique sécurisée résistant aux attaques WO2017063114A1 (fr)

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CN201580000535.1A CN106664199A (zh) 2015-10-12 2015-10-12 建立抗攻击的安全性公钥密码的方法
PCT/CN2015/091710 WO2017063114A1 (fr) 2015-10-12 2015-10-12 Procédé d'établissement d'algorithme cryptographique à clé publique sécurisée résistant aux attaques

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WO2019000231A1 (fr) * 2017-06-27 2019-01-03 王威鉴 Procédé d'établissement d'un chiffrement de clé publique anti-attaque
CN108449754A (zh) * 2018-03-16 2018-08-24 丘佳珏 智能设备通过无线路由上网的方法
CN109787752A (zh) * 2018-09-30 2019-05-21 王威鉴 建立抗攻击的共享密钥的方法
CN111400773B (zh) * 2020-03-12 2022-09-09 深圳大学 数字签名方法、数字签名装置、系统和存储介质
CN114221753B (zh) * 2021-11-23 2023-08-04 深圳大学 密钥数据处理方法和电子设备
CN114640463B (zh) * 2022-02-25 2023-05-12 深圳大学 一种数字签名方法、计算机设备及介质

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