Computer Science ›› 2020, Vol. 47 ›› Issue (12): 311-318.doi: 10.11896/jsjkx.190900197

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Formalization of Finite Field GF(2n) Based on COQ

FAN Yong-qian, CHEN Gang, CUI Min   

  1. College of Computer Science and Technology Nanjing University of Aeronautics and Astronauitcs Nanjing 211000,China
    Key Laboratory of Safety-critical Software Ministry of Industry and Information Technology Nanjing 211106,China
  • Received:2019-09-29 Revised:2020-03-09 Published:2020-12-17
  • About author:FAN Yong-qian,born in 1993postgraduateis a student member of China Computer Federation.His main research interests include formal methods and so on.
    CHEN Gang,born in 1958Ph.Dprofessoris a senior member of China Computer Federation.His main research interests include formal methods and so on.

Abstract: The finite field GF(2n) is the basis of many security-critical algorithmsincluding AES encryption algorithmselliptic curve cryptographyinfection function masksand so on.There is data that the operations on the finite field are prone to errors due to their complexitywhich causes problems in the system.Verification methods based on testing and model checking can only be applied on specific finite field with fixed by nand the computation time for the verification often exceeds the capability of the computer.Formal verification using interactive theorem provers provides the possibility for generic verification of finite field pro-pertiesbut working in this direction fairly challenging.The existing researches mainly focused on the formal verification of abstract properties of finite fieldshoweversolving practical problems require the use of constructive definitions of finite fields and the verification of its properties.In response to this requirementthis paper uses the theorem prover COQ to develop a constructive and generic definition of finite field GF(2n)and formally verified a large amount basic properties of finite fieldsincluding verification of the basic properties of finite field additionverification of the basic properties of polynomial multiplication which is the buliding block of finite field multiplicationas well as verification of other related properties.This work lays a foundation for the complete formalization of finite fieldswhich will support formal verfications of various algorithms using finite field.

Key words: Finite field, COQ, Formal verification, Theorem proving, Polynomial operation

CLC Number: 

  • TP311
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