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.