GB/T 32918.3-2016Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 3: Key exchange protocol (English PDF)

3.1 Key confirmation from A to B

A guarantee which makes user B be convinced that user A has a specific secret key.

3.2 Key derivation function

The function of one or more shared secret keys generated by acting on the shared key and other parameters known to both parties.

3.3 Initiator

The user who sends the first round of exchange information during the operation of a protocol.

3.4 Responder

The user who does not send the first round of information exchange during the operation of a protocol.

3.5 Distinguishing identifier

Information which can distinguish an entity's identity without ambiguity.

5.2 Elliptic curve's system parameters

Elliptic curve's system parameters include the size q of the finite field F q (When q=2 m , it also includes the identification of element representation notation and the reduced polynomial). Two elements a, b which define the equation of the elliptic curve E(Fq ) shall in Fq . The base point G on E(Fq ) shall = (xG, yG) (G!=O), where xG and y G are two elements in Fq ; the order n of G and other alternatives (such as the cofactor h of n, etc.).

Elliptic curve's system parameters and their verification shall comply with the provisions of Clause 5 of GB/T 32918.1-2016.

5.3 User's key pair

User A's key pair includes its private key d A and public key PA =[dA ]G= (xA , yA).

User B's key pair includes its private key dB and public key PB =[dB ]G= (xB , yB ).

The generation algorithm of user's key pair and the public key verification algorithm shall be in accordance with the provisions of Clause 6 of GB/T 32918.1-2016.

5.4 Auxiliary function

5.4.1 Overview

In the elliptic curve's key exchange protocol specified in this Part, three types of auxiliary functions are involved: cryptographic hash algorithm, key derivation function, and random number generator. The strength of these three types of auxiliary functions directly affects the security of key exchange protocol.

5.4.2 Cryptographic hash algorithm

This Part specifies the use of cryptographic hash algorithms approved by the

State Cryptography Administration, such as the SM3 cryptographic hash algorithm.

5.4.3 Key derivation function

The key derivation function is used to derive key data from a shared secret bit string. In the key negotiation process, the key derivation function acts on the shared secret bit string obtained by key exchange, from which the required session key or the key data required for further encryption is generated.

The key derivation function needs to call the cryptographic hash algorithm.

A.1 Overview

This appendix selects the cryptographic hash algorithm given in GB/T 32905-

2016. The input is a message bit string of length less than 2

64

. The output is a hash value of 256 bits in length, which is recorded as H 256 ().

In this appendix, all numbers expressed in hexadecimal form are high on the left and low on the right.

Assume that user A's identity is: ALICE123@YAHOO.COM. USE the code in

GB/T 1988 to record IDA : 414C 49434531 32334059 41484F4F 2E434F4D.

ENTLA =0090.

Assume that user B's identity is: BILL456@YAHOO.COM. USE the code in

GB/T 1988 to record IDB : 42 494C4C34 35364059 41484F4F 2E434F4D.

ENTLB =0088.

A.2 Elliptic curve's key exchange protocol on Fp

The elliptic curve equation is: y

2

=x

3

+ax+b

Example 1: F p-256

Cofactor h: 1

Base point G= (xG, yG). Its order is recorded as n.

User A's public key P A= (xA, yA):

Prime number p

Factor a

Factor b

Coordinate xG

Coordinate yG

Order n

User A's private key d A […]