WO2019000231A1 - Procédé d'établissement d'un chiffrement de clé publique anti-attaque - Google Patents

Procédé d'établissement d'un chiffrement de clé publique anti-attaque Download PDF

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Publication number
WO2019000231A1
WO2019000231A1 PCT/CN2017/090362 CN2017090362W WO2019000231A1 WO 2019000231 A1 WO2019000231 A1 WO 2019000231A1 CN 2017090362 W CN2017090362 W CN 2017090362W WO 2019000231 A1 WO2019000231 A1 WO 2019000231A1
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WO
WIPO (PCT)
Prior art keywords
agreement
party
group
subgroup
key
Prior art date
Application number
PCT/CN2017/090362
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English (en)
Chinese (zh)
Inventor
王威鉴
王晓峰
李敏
Original Assignee
王威鉴
王晓峰
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 王威鉴, 王晓峰 filed Critical 王威鉴
Priority to PCT/CN2017/090362 priority Critical patent/WO2019000231A1/fr
Publication of WO2019000231A1 publication Critical patent/WO2019000231A1/fr

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Classifications

    • 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

Definitions

  • the present invention relates to the field of information security, and in particular, to a method for establishing an anti-attack public key cipher.
  • Symmetric cryptography such as AES has proven to be a very efficient and secure method of transmitting secret information.
  • AES symmetric key
  • both parties of the secret information transmission must establish a shared key through the key exchange protocol.
  • the object of the present invention is to establish an inelasticity of the subgroup member problem of the Mihailova subgroup of the group and the conjugate characteristic of the element of the group.
  • the object of the present invention is achieved by a method for establishing an anti-attack public key cipher, including The following steps:
  • the elements of the group B n are represented by words in the set ⁇ 1 , ⁇ 2 , ..., ⁇ n-1 ⁇ representing the unique formal form of the element;
  • B n agreement were selected two sets of elements a 1, a 2, ..., a k and b 1, b 2, ..., b m; a 1, a 2, ..., a k and b 1, b 2 ,...,b m respectively generate two subgroups A and B of B n ;
  • the ⁇ group B n is a Mihailova subgroup having subgroup members that are unsolvable, and the subgroups A and B are both Mihailova subgroups.
  • the group B n is a group defined by the following presentation:
  • the elements of the group B n are represented by words in the set ⁇ 1 , ⁇ 2 , . . . , ⁇ n-1 ⁇ representing a unique formal form of the element;
  • B n contains two subgroups that are isomorphic with F 2 ⁇ F 2 , that is, two subgroups of direct product isomorphisms of free groups with rank 2:
  • the finite representation group of the unsolvable word problem generated by the two elements is rendered, so that the subgroup A of the construction P is a Mihailova subgroup, and the subgroup B of the construction Q is a Mihailova subgroup;
  • the first private key x and the second private key y are selected to satisfy not less than 78 bits.
  • the shared key generated in the present invention is unsolvable to third parties. This can be used as a core element in the creation of a new, highly secure cryptosystem.
  • the equivalence of the security of the algorithm of the present invention with the unsolvable problem proves its immunity to all attacks.
  • the key sharing method established by the present invention is based on an unsolvable decision problem as a security guarantee, the method is strongly guaranteed both in theory and in practical applications. Compared with the prior art, it has the following advantages:
  • B n is an exponential growth, that is, the number of elements whose length is a positive integer n in B n ⁇ ⁇ an exponential function about n;
  • the group B n of the index n ⁇ 7 is selected to have the above properties and is defined by the following group:
  • the elements of the group are represented by words in the set ⁇ 1 , ⁇ 2 , ..., ⁇ n-1 ⁇ representing the unique formal form of the element.
  • B n contains two subgroups that are isomorphic with F 2 ⁇ F 2 , that is, two subgroups of direct product isomorphisms of free groups with rank 2:
  • the two groups generate the finite representation group whose word problem is unsolvable.
  • the subgroup A of construct P is a Mihailova subgroup
  • the subgroup B of Q is also a Mihailova subgroup.
  • the parties to the agreement are Alice and Bob, respectively.
  • the elements of the group are represented by words in the set ⁇ 1 , ⁇ 2 , ..., ⁇ n-1 ⁇ representing the unique formal form of the element;
  • Subgroup membership problem or generalized word problem (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. That is, it is determined whether g is an element in H.
  • GWP generalized word problem
  • CSP Conjugacy search problem
  • Two sets of two Mihailova subgroups A and B of the ⁇ group B n , B n with an index of n ⁇ 7 generate elements a 1 , a 2 , ..., a k ⁇ A and b 1 , b 2 , ..., b m ⁇ B, and the element in B n x -1 b 1 x,x -1 b 2 x,...,x -1 b m x and y -1 a 1 y,y -1 a 2 y,...,y -1 a k y.
  • the index of the group B n is n ⁇ 7, and the selection of the private keys x and y in the protocol is to satisfy not less than 78 bits.

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  • Engineering & Computer Science (AREA)
  • Computer Security & Cryptography (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Data Exchanges In Wide-Area Networks (AREA)

Abstract

La présente invention se rapporte au domaine de la sécurité de l'information. L'invention concerne un procédé d'établissement d'un chiffrement de clé publique anti-attaque, le procédé comprenant les étapes suivantes : (1) deux parties d'un accord sélectionnent un groupe de tresses Bn, dont l'indice est n ≥ 7, le groupe défini Bn étant présenté comme suit ; (2) les deux parties de l'accord sélectionnent respectivement deux sous-groupes A et B dans Bn ; (3) une première partie de l'accord sélectionne un élément x = x(a1, a2, ..., ak) ∈ A et prend celui-ci en tant que première clé privée, et en envoie x-1b1x, x-1b2x, ..., x-1bmx à une seconde partie de l'accord ; (4) la seconde partie de l'accord sélectionne un élément y = y(b1, b2, ..., bm) ∈ B et prend celui-ci en tant que seconde clé privée, et en envoie y-1a1y, y-1a2y, ..., y-1aky à la première partie de l'accord ; (5) la première partie de l'accord obtient KA = x(y-1a1y, y-1a2y, ..., y-1aky) = y-1x-1yx ; (6) la seconde partie de l'accord obtient y(x-1b1x, x-1b2x, ..., x-1bkx) = x-1y-1xy, et effectue un calcul pour obtenir KB=(x-1y-1xy)-1 = y-1x-1yx. Étant donné que KA = KB, une clé partagée, K = KA= KB , est convenue. La sécurité d'un algorithme de partage de clé établi dans la présente invention est théoriquement complètement prouvée, et étant donné que le problème d'insolvabilité d'élément de sous-groupe est introduit de manière innovante en tant qu'assurance de sécurité, la clé partagée établie a l'avantage de résister à toutes les attaques connues, y compris des attaques informatiques quantiques.
PCT/CN2017/090362 2017-06-27 2017-06-27 Procédé d'établissement d'un chiffrement de clé publique anti-attaque WO2019000231A1 (fr)

Priority Applications (1)

Application Number Priority Date Filing Date Title
PCT/CN2017/090362 WO2019000231A1 (fr) 2017-06-27 2017-06-27 Procédé d'établissement d'un chiffrement de clé publique anti-attaque

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
PCT/CN2017/090362 WO2019000231A1 (fr) 2017-06-27 2017-06-27 Procédé d'établissement d'un chiffrement de clé publique anti-attaque

Publications (1)

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WO2019000231A1 true WO2019000231A1 (fr) 2019-01-03

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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2021223090A1 (fr) * 2020-05-06 2021-11-11 深圳大学 Procédé et appareil permettant l'établissement d'une clé partagée

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2009026771A1 (fr) * 2007-08-24 2009-03-05 Guan, Haiying Procédé pour négocier une clé, chiffrer et déchiffrer des informations, signer et authentifier les informations
CN103414569A (zh) * 2013-08-21 2013-11-27 王威鉴 一种建立抗攻击的公钥密码的方法
CN105393488A (zh) * 2013-12-04 2016-03-09 王威鉴 建立抗量子计算攻击的公钥密码的方法
CN106664199A (zh) * 2015-10-12 2017-05-10 王晓峰 建立抗攻击的安全性公钥密码的方法

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2009026771A1 (fr) * 2007-08-24 2009-03-05 Guan, Haiying Procédé pour négocier une clé, chiffrer et déchiffrer des informations, signer et authentifier les informations
CN103414569A (zh) * 2013-08-21 2013-11-27 王威鉴 一种建立抗攻击的公钥密码的方法
CN105393488A (zh) * 2013-12-04 2016-03-09 王威鉴 建立抗量子计算攻击的公钥密码的方法
CN106664199A (zh) * 2015-10-12 2017-05-10 王晓峰 建立抗攻击的安全性公钥密码的方法

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
WO2021223090A1 (fr) * 2020-05-06 2021-11-11 深圳大学 Procédé et appareil permettant l'établissement d'une clé partagée
US11743036B2 (en) 2020-05-06 2023-08-29 Shenzhen University Method and apparatus for establishing shared key

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