GM/T 0080-2020SM9 cryptographic algorithm application specification (English PDF)

3.1 Algorithm identifier

Digitized information that is used to indicate algorithmic mechanisms.

3.2 SM9 algorithm

PPS: Public Parameter Service.

5.1 Generator

The Generator P1 point on G1 is marked as (xp1, yP1); and the ASN.1 of the data format is defined as SM9P1::=BIT STRING; the type is BIT STRING; and its content is:

04||X1||Y1, where X1 and Y1 respectively identify the x component and y component of the point; and each component has a length of 256 bits.

The Generator P2 point on G2 is marked as (xp2, yP2); and the ASN.1 of the data format is defined as SM9P2::=BIT STRING; the type is BIT STRING; and its content is:

04||X1||X2||Y1||Y2, where X1, X2 and Y1, Y2 respectively identify the x component and y component of the public key; and each component has a length of 256 bits, or 03||X1||X2, where X1 and X2 respectively identify each x component of the public key;

and each component has a length of 256 bits. Select the value whose rightmost bit is 1 in the decompressed Y root value (Y1||Y2). After the restoration, the rightmost bit of the Y root value shall be 1; otherwise, Y1=base field q - root Y1, Y2=base field q - root Y2. or 02||X1||X2, where X1 and X2 respectively identify the 2 x components of the public key; and each component has a length of 256 bits. Select the option value whose rightmost bit is 0 in the decompressed Y root value (Y1||Y2). After the restoration, the Y root value takes the option value whose rightmost bit is 0, otherwise Y1=base field q - root Y1, Y2=base field q - root Y2.

5.2 SM9 master private key

It includes the SM9 signature master private key and the encryption master private key;

both are an integer greater than or equal to 1 and less than N-1 (N is the order of the cyclic group G1, G2, and GT, and its value is shown in Appendix A.1 of GB/T 38635.2-

2020), abbreviated as s, with the length of 256 bits.

5.3 SM9 master public key

It includes SM9 signature master public key Ppub2 and encryption master public key Ppub1. They are points on G2 and G1; and the coordinates are expressed as (xSPub, ySPub) and (xEPub, yEPub). Thereof, the x and y coordinates of the signature master public key also contain two components, namely x1 component and x2 component, y1 component and y2 component, and the length of each component is 256 bits. The length of the x and y coordinates of the encryption master public key are both 256 bits.

5.4 SM9 user private key

It includes SM9 user signature private key and user encryption private key, which are points on G1 and G2 respectively; and the coordinates are expressed as (xSPri, ySPri) and (xEPri, yEPri). The length of the x and y coordinates of the user signature key are both 256 bits. The x and y coordinates of the user's encryption private key also contain two components, namely x1 component and x2 component, y1 component and y2 component, and the length of each component is 256 bits.

5.5 SM9 user public key

In IBC technology, the user identification ID can uniquely determine the user's public key, which represents the public key in applications. The representation of ID coordinates based on bilinear pairing can be divided into user signature public key coordinates and user encryption public key coordinates. The user signature public key and the signature master public key are of the same coordinate structure; and there are two respective components on the x and y coordinates, which are marked as QS;

and user encryption public key and the encryption master public key are of the same coordinate structure, which is marked as QE.

NOTE: Here is how to generate the user's public key coordinates.

Input: Algorithm function H, userID, hid, master public key Ppubi, generator Pi i=1,2.

Output: User public key QA.

Calculation method:

, signature public key coordinates are used for signature/verification of signature.

, encryption public key coordinates are used for key encapsulation, encryption/decryption.

6.1 Key data structure

The key is divided into signature/encryption master key, and signature/encryption user key:

a) The ASN.1 of data format of SM9 algorithm signature master private key is defined as: