## GB/T 32918.1-2016: Translated English of Chinese Standard. (GBT 32918.1-2016, GB/T32918.1-2016, GBT32918.1-2016): Information security technology - Public key cryptographic algorithm SM2 based on elliptic curves - Part 1: GeneralThis part of GB/T 32918 specifies the necessary mathematical basics and related cryptography techniques which are involved in the SM2 elliptic curve public key cryptography algorithm, to help implement the cryptographic mechanisms as specified in other parts. This part is applicable to the design, development and use of elliptic curve public key cryptography algorithms of which the base field is prime field and binary field. |

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### Contents

4 | |

Data types and their conversion | 14 |

Key pair generation and public key verification | 23 |

Appendix B Informative Number theory algorithm | 55 |

Informative Curve example | 68 |

Informative Quasirandom generation and verification | 71 |

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Abstract Syntax Notation affine coordinate representation anti-MOV attack conditions base field base point based on elliptic binary extension binary extension-field bit string SEED coefficient composite number compressed representation cryptographic curve on Fp curve’s discrete logarithm curve’s system parameters cyclic group Digital Signature Algorithm discrete logarithm problem E(Fp Elliptic Curve Cryptography elliptic curve equation elliptic curve’s discrete elliptic curve’s system field element yP finite field Fq following algorithm Gaussian normal-base GB/T infinity point inverse element irreducible trinomial Jacobian weighted projective Lucas sequence mixed representation modulo multiplication unit element normal-base of type odd prime number otherwise output is invalid outputs correct outputs error parameters of elliptic point G polynomial f(x positive integer prime field prime number greater projective coordinate representation projective coordinate system public key cryptography reduced polynomial standard projective coordinates string of length Table A.3 trinomial-base valid Verify weighted projective coordinate xP and yP