Method for establishing secure public-key cryptography against quantum computing attacks

Abstract

The present invention relates to the field of information safety, and discloses a method for establishing public key cryptogram against quantum computing attack. The method comprises the following steps of: (11) a protocol first party selects a braid group Bn with an index n of being not small than 7, and selects a subgroup A generated by employing a1, a2, ..., ak in the Bn and a subgroup B generated by employing b1, b2, ..., bm in the Bn; (12) the protocol first party selects [Theta], wherein Bn maps to {0, 1}k is an Hash function from Bn to plaintext space {0, 1}k collision resistance; (13)the protocol first party selects an element x as a private key, wherein x=x(a1, a2, ..., ak) belonging to A, and selects (Bn, A, B, [Theta], X-1b1x, x-1b2x, ..., x-1bmx) as a public key; (14) a protocol second party selects an element y, wherein y=y(b1, b2, ..., bm) belonging to B, calculates KB=(y< 1>y(x< 1>b1x, x< 1>b2x, ..., x< 1>bmx))< 1>=(y< 1>x< 1>yx)< 1>=x< 1>y< 1>xy, performs encryption calculation of a plaintext p to obtain a ciphertext (img file='DDA0001531187730000011. TIF' wi='286' he='71' / ) and sends t to the protocol first party; and (15) the protocol first party calculates KA=x<1>x(y< 1>a1y,y< 1>a2y, ...,y< 1>aky)=x< 1>y< 1>xy, performs decryption calculation to obtain a plaintext (img file='DDA0001531187730000012. TIF' wi='283' he='70' / )(img file='DDA0001531187730000013. TIF' wi='510' he='63' / ). The method provided by the invention can resist all the known attacks comprising quantum computing attack.

Description

technical field [0001] The invention relates to the field of information security, in particular to a public key encryption technology, a digital signature technology and an identity authentication technology for establishing resistance to various known attacks including quantum computing attacks. Background technique [0002] In the classical public-key cryptography algorithm, as a practical computationally difficult problem for security, its intractability will be greatly reduced with the improvement of computer performance. In particular, the famous Shor quantum algorithm proposed by Shor in 1997 will perform the factorization of large integers and the calculation of discrete logarithms in polynomial time, which means that once the quantum computer is realized, it will be based on RSA, ECC, E1Gamal Algorithms and other established public key cryptographic protocols will no longer be safe. Aiming at the conjugation problem of the elements of the braid group proposed by Ko...

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Problems solved by technology

[0004] In order to solve the problem of hidden dangers based on the security of existing public key cryptography, the purpose of the present invention is to introduce the structure of the Mihailova subgroup of the braided group again, and take elements in these subgroups to generate private keys, and use its unsolvability To establish public key cryptography, digital signature and identity authentication methods that are resistant to various attacks

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